id	sid	tid	token	lemma	pos
american_scientific_journal-591	1	1	type	type	VERB
american_scientific_journal-591	1	2	the	the	DET
american_scientific_journal-591	1	3	title	title	NOUN
american_scientific_journal-591	1	4	of	of	ADP
american_scientific_journal-591	1	5	your	your	PRON
american_scientific_journal-591	1	6	paper	paper	NOUN
american_scientific_journal-591	1	7	,	,	PUNCT
american_scientific_journal-591	1	8	capitalize	capitalize	VERB
american_scientific_journal-591	1	9	first	first	ADJ
american_scientific_journal-591	1	10	letter	letter	NOUN
american_scientific_journal-591	1	11	from	from	ADP
american_scientific_journal-591	1	12	each	each	DET
american_scientific_journal-591	1	13	word	word	NOUN
american_scientific_journal-591	1	14	(	(	PUNCT
american_scientific_journal-591	1	15	use	use	NOUN
american_scientific_journal-591	1	16	18	18	NUM
american_scientific_journal-591	1	17	times	time	NOUN
american_scientific_journal-591	1	18	new	new	ADJ
american_scientific_journal-591	1	19	roman	roman	NOUN
american_scientific_journal-591	1	20	;	;	PUNCT
american_scientific_journal-591	1	21	bold	bold	ADJ
american_scientific_journal-591	1	22	)	)	PUNCT
american_scientific_journal-591	1	23	american	american	ADJ
american_scientific_journal-591	1	24	scientific	scientific	ADJ
american_scientific_journal-591	1	25	research	research	NOUN
american_scientific_journal-591	1	26	journal	journal	NOUN
american_scientific_journal-591	1	27	for	for	ADP
american_scientific_journal-591	1	28	engineering	engineering	NOUN
american_scientific_journal-591	1	29	,	,	PUNCT
american_scientific_journal-591	1	30	technology	technology	NOUN
american_scientific_journal-591	1	31	,	,	PUNCT
american_scientific_journal-591	1	32	and	and	CCONJ
american_scientific_journal-591	1	33	sciences	science	NOUN
american_scientific_journal-591	1	34	(	(	PUNCT
american_scientific_journal-591	1	35	asrjets	asrjet	NOUN
american_scientific_journal-591	1	36	)	)	PUNCT
american_scientific_journal-591	1	37	issn	issn	PROPN
american_scientific_journal-591	1	38	(	(	PUNCT
american_scientific_journal-591	1	39	print	print	NOUN
american_scientific_journal-591	1	40	)	)	PUNCT
american_scientific_journal-591	1	41	2313	2313	NUM
american_scientific_journal-591	1	42	-	-	SYM
american_scientific_journal-591	1	43	4410	4410	NUM
american_scientific_journal-591	1	44	,	,	PUNCT
american_scientific_journal-591	1	45	issn	issn	PROPN
american_scientific_journal-591	1	46	(	(	PUNCT
american_scientific_journal-591	1	47	online	online	ADJ
american_scientific_journal-591	1	48	)	)	PUNCT
american_scientific_journal-591	1	49	2313	2313	NUM
american_scientific_journal-591	1	50	-	-	SYM
american_scientific_journal-591	1	51	4402	4402	NUM
american_scientific_journal-591	1	52	©	©	PROPN
american_scientific_journal-591	1	53	global	global	ADJ
american_scientific_journal-591	1	54	society	society	NOUN
american_scientific_journal-591	1	55	of	of	ADP
american_scientific_journal-591	1	56	scientific	scientific	ADJ
american_scientific_journal-591	1	57	research	research	NOUN
american_scientific_journal-591	1	58	and	and	CCONJ
american_scientific_journal-591	1	59	researchers	researcher	NOUN
american_scientific_journal-591	1	60	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-591	1	61	on	on	ADP
american_scientific_journal-591	1	62	minimum	minimum	ADJ
american_scientific_journal-591	1	63	distance	distance	NOUN
american_scientific_journal-591	1	64	problem	problem	NOUN
american_scientific_journal-591	1	65	romer	romer	PROPN
american_scientific_journal-591	1	66	c.	c.	PROPN
american_scientific_journal-591	1	67	castilloa	castilloa	PROPN
american_scientific_journal-591	1	68	,	,	PUNCT
american_scientific_journal-591	1	69	eugene	eugene	PROPN
american_scientific_journal-591	1	70	e.	e.	PROPN
american_scientific_journal-591	1	71	mendozab	mendozab	PROPN
american_scientific_journal-591	1	72	,	,	PUNCT
american_scientific_journal-591	1	73	jenny	jenny	PROPN
american_scientific_journal-591	1	74	b.	b.	PROPN
american_scientific_journal-591	1	75	comiac	comiac	PROPN
american_scientific_journal-591	1	76	acollege	acollege	PROPN
american_scientific_journal-591	1	77	of	of	ADP
american_scientific_journal-591	1	78	accountancy	accountancy	NOUN
american_scientific_journal-591	1	79	,	,	PUNCT
american_scientific_journal-591	1	80	business	business	NOUN
american_scientific_journal-591	1	81	,	,	PUNCT
american_scientific_journal-591	1	82	economics	economic	NOUN
american_scientific_journal-591	1	83	and	and	CCONJ
american_scientific_journal-591	1	84	international	international	ADJ
american_scientific_journal-591	1	85	hospitality	hospitality	NOUN
american_scientific_journal-591	1	86	management	management	NOUN
american_scientific_journal-591	1	87	,	,	PUNCT
american_scientific_journal-591	1	88	batangas	batangas	PROPN
american_scientific_journal-591	1	89	state	state	PROPN
american_scientific_journal-591	1	90	university	university	PROPN
american_scientific_journal-591	1	91	,	,	PUNCT
american_scientific_journal-591	1	92	rizal	rizal	PROPN
american_scientific_journal-591	1	93	ave	ave	PROPN
american_scientific_journal-591	1	94	.	.	PROPN
american_scientific_journal-591	1	95	,	,	PUNCT
american_scientific_journal-591	1	96	batangas	batangas	PROPN
american_scientific_journal-591	1	97	city	city	PROPN
american_scientific_journal-591	1	98	4200	4200	NUM
american_scientific_journal-591	1	99	,	,	PUNCT
american_scientific_journal-591	1	100	philippines	philippine	NOUN
american_scientific_journal-591	1	101	bcollege	bcollege	PROPN
american_scientific_journal-591	1	102	of	of	ADP
american_scientific_journal-591	1	103	arts	art	NOUN
american_scientific_journal-591	1	104	and	and	CCONJ
american_scientific_journal-591	1	105	sciences	sciences	PROPN
american_scientific_journal-591	1	106	,	,	PUNCT
american_scientific_journal-591	1	107	batangas	batangas	PROPN
american_scientific_journal-591	1	108	state	state	PROPN
american_scientific_journal-591	1	109	university	university	PROPN
american_scientific_journal-591	1	110	,	,	PUNCT
american_scientific_journal-591	1	111	rizal	rizal	PROPN
american_scientific_journal-591	1	112	ave	ave	PROPN
american_scientific_journal-591	1	113	.	.	PROPN
american_scientific_journal-591	1	114	,	,	PUNCT
american_scientific_journal-591	1	115	batangas	batangas	PROPN
american_scientific_journal-591	1	116	city	city	PROPN
american_scientific_journal-591	1	117	4200	4200	NUM
american_scientific_journal-591	1	118	,	,	PUNCT
american_scientific_journal-591	1	119	philippines	philippine	NOUN
american_scientific_journal-591	1	120	ccollege	ccollege	NOUN
american_scientific_journal-591	1	121	of	of	ADP
american_scientific_journal-591	1	122	arts	art	NOUN
american_scientific_journal-591	1	123	and	and	CCONJ
american_scientific_journal-591	1	124	sciences	sciences	PROPN
american_scientific_journal-591	1	125	,	,	PUNCT
american_scientific_journal-591	1	126	batangas	batangas	PROPN
american_scientific_journal-591	1	127	state	state	PROPN
american_scientific_journal-591	1	128	university	university	PROPN
american_scientific_journal-591	1	129	,	,	PUNCT
american_scientific_journal-591	1	130	rizal	rizal	PROPN
american_scientific_journal-591	1	131	ave	ave	PROPN
american_scientific_journal-591	1	132	.	.	PROPN
american_scientific_journal-591	1	133	,	,	PUNCT
american_scientific_journal-591	1	134	batangas	batangas	PROPN
american_scientific_journal-591	1	135	city	city	PROPN
american_scientific_journal-591	1	136	4200	4200	NUM
american_scientific_journal-591	1	137	,	,	PUNCT
american_scientific_journal-591	1	138	philippines	philippine	NOUN
american_scientific_journal-591	1	139	aemail	aemail	NOUN
american_scientific_journal-591	1	140	:	:	PUNCT
american_scientific_journal-591	2	1	romercastillo@rocketmail.com	romercastillo@rocketmail.com	X
american_scientific_journal-591	3	1	bemail	bemail	PROPN
american_scientific_journal-591	3	2	:	:	PUNCT
american_scientific_journal-591	3	3	azodnem1994@yahoo.com	azodnem1994@yahoo.com	X
american_scientific_journal-591	4	1	cemail	cemail	NOUN
american_scientific_journal-591	4	2	:	:	PUNCT
american_scientific_journal-591	4	3	comiajenny@gmail.com	comiajenny@gmail.com	X
american_scientific_journal-591	5	1	abstract	abstract	ADJ
american_scientific_journal-591	5	2	this	this	DET
american_scientific_journal-591	5	3	study	study	NOUN
american_scientific_journal-591	5	4	provides	provide	VERB
american_scientific_journal-591	5	5	a	a	DET
american_scientific_journal-591	5	6	clear	clear	ADV
american_scientific_journal-591	5	7	-	-	PUNCT
american_scientific_journal-591	5	8	cut	cut	VERB
american_scientific_journal-591	5	9	solution	solution	NOUN
american_scientific_journal-591	5	10	to	to	ADP
american_scientific_journal-591	5	11	a	a	DET
american_scientific_journal-591	5	12	minimum	minimum	ADJ
american_scientific_journal-591	5	13	distance	distance	NOUN
american_scientific_journal-591	5	14	problem	problem	NOUN
american_scientific_journal-591	5	15	,	,	PUNCT
american_scientific_journal-591	5	16	in	in	ADP
american_scientific_journal-591	5	17	particular	particular	ADJ
american_scientific_journal-591	5	18	,	,	PUNCT
american_scientific_journal-591	5	19	the	the	DET
american_scientific_journal-591	5	20	problem	problem	NOUN
american_scientific_journal-591	5	21	of	of	ADP
american_scientific_journal-591	5	22	finding	find	VERB
american_scientific_journal-591	5	23	the	the	DET
american_scientific_journal-591	5	24	minimum	minimum	ADJ
american_scientific_journal-591	5	25	distance	distance	NOUN
american_scientific_journal-591	5	26	from	from	ADP
american_scientific_journal-591	5	27	a	a	DET
american_scientific_journal-591	5	28	point	point	NOUN
american_scientific_journal-591	5	29	to	to	ADP
american_scientific_journal-591	5	30	a	a	DET
american_scientific_journal-591	5	31	line	line	NOUN
american_scientific_journal-591	5	32	to	to	ADP
american_scientific_journal-591	5	33	another	another	DET
american_scientific_journal-591	5	34	point	point	NOUN
american_scientific_journal-591	5	35	on	on	ADP
american_scientific_journal-591	5	36	the	the	DET
american_scientific_journal-591	5	37	same	same	ADJ
american_scientific_journal-591	5	38	side	side	NOUN
american_scientific_journal-591	5	39	of	of	ADP
american_scientific_journal-591	5	40	the	the	DET
american_scientific_journal-591	5	41	line	line	NOUN
american_scientific_journal-591	5	42	.	.	PUNCT
american_scientific_journal-591	6	1	the	the	DET
american_scientific_journal-591	6	2	straightforward	straightforward	ADJ
american_scientific_journal-591	6	3	solution	solution	NOUN
american_scientific_journal-591	6	4	is	be	AUX
american_scientific_journal-591	6	5	a	a	DET
american_scientific_journal-591	6	6	pythagorean	pythagorean	ADJ
american_scientific_journal-591	6	7	relation	relation	NOUN
american_scientific_journal-591	6	8	or	or	CCONJ
american_scientific_journal-591	6	9	formula	formula	NOUN
american_scientific_journal-591	6	10	which	which	PRON
american_scientific_journal-591	6	11	can	can	AUX
american_scientific_journal-591	6	12	be	be	AUX
american_scientific_journal-591	6	13	derived	derive	VERB
american_scientific_journal-591	6	14	through	through	ADP
american_scientific_journal-591	6	15	geometrical	geometrical	ADJ
american_scientific_journal-591	6	16	construction	construction	NOUN
american_scientific_journal-591	6	17	and	and	CCONJ
american_scientific_journal-591	6	18	reasoning	reasoning	NOUN
american_scientific_journal-591	6	19	,	,	PUNCT
american_scientific_journal-591	6	20	and	and	CCONJ
american_scientific_journal-591	6	21	analytical	analytical	ADJ
american_scientific_journal-591	6	22	approach	approach	NOUN
american_scientific_journal-591	6	23	using	use	VERB
american_scientific_journal-591	6	24	differentiation	differentiation	NOUN
american_scientific_journal-591	6	25	,	,	PUNCT
american_scientific_journal-591	6	26	particularly	particularly	ADV
american_scientific_journal-591	6	27	,	,	PUNCT
american_scientific_journal-591	6	28	the	the	DET
american_scientific_journal-591	6	29	application	application	NOUN
american_scientific_journal-591	6	30	of	of	ADP
american_scientific_journal-591	6	31	extreme	extreme	ADJ
american_scientific_journal-591	6	32	-	-	PUNCT
american_scientific_journal-591	6	33	value	value	NOUN
american_scientific_journal-591	6	34	theorem	theorem	NOUN
american_scientific_journal-591	6	35	.	.	PUNCT
american_scientific_journal-591	7	1	such	such	ADJ
american_scientific_journal-591	7	2	formula	formula	NOUN
american_scientific_journal-591	7	3	is	be	AUX
american_scientific_journal-591	7	4	vital	vital	ADJ
american_scientific_journal-591	7	5	in	in	ADP
american_scientific_journal-591	7	6	solving	solve	VERB
american_scientific_journal-591	7	7	minimum	minimum	ADJ
american_scientific_journal-591	7	8	distance	distance	NOUN
american_scientific_journal-591	7	9	problems	problem	NOUN
american_scientific_journal-591	7	10	with	with	ADP
american_scientific_journal-591	7	11	greater	great	ADJ
american_scientific_journal-591	7	12	ease	ease	NOUN
american_scientific_journal-591	7	13	,	,	PUNCT
american_scientific_journal-591	7	14	accuracy	accuracy	NOUN
american_scientific_journal-591	7	15	and	and	CCONJ
american_scientific_journal-591	7	16	speed	speed	NOUN
american_scientific_journal-591	7	17	.	.	PUNCT
american_scientific_journal-591	8	1	this	this	PRON
american_scientific_journal-591	8	2	will	will	AUX
american_scientific_journal-591	8	3	lessen	lessen	VERB
american_scientific_journal-591	8	4	the	the	DET
american_scientific_journal-591	8	5	cost	cost	NOUN
american_scientific_journal-591	8	6	and	and	CCONJ
american_scientific_journal-591	8	7	waste	waste	NOUN
american_scientific_journal-591	8	8	of	of	ADP
american_scientific_journal-591	8	9	materials	material	NOUN
american_scientific_journal-591	8	10	in	in	ADP
american_scientific_journal-591	8	11	practical	practical	ADJ
american_scientific_journal-591	8	12	engineering	engineering	NOUN
american_scientific_journal-591	8	13	and	and	CCONJ
american_scientific_journal-591	8	14	business	business	NOUN
american_scientific_journal-591	8	15	applications	application	NOUN
american_scientific_journal-591	8	16	.	.	PUNCT
american_scientific_journal-591	9	1	keywords	keyword	NOUN
american_scientific_journal-591	9	2	:	:	PUNCT
american_scientific_journal-591	9	3	minimum	minimum	ADJ
american_scientific_journal-591	9	4	distance	distance	NOUN
american_scientific_journal-591	9	5	formula	formula	NOUN
american_scientific_journal-591	9	6	;	;	PUNCT
american_scientific_journal-591	9	7	geometrical	geometrical	ADJ
american_scientific_journal-591	9	8	construction	construction	NOUN
american_scientific_journal-591	9	9	;	;	PUNCT
american_scientific_journal-591	9	10	extreme	extreme	ADJ
american_scientific_journal-591	9	11	-	-	PUNCT
american_scientific_journal-591	9	12	value	value	NOUN
american_scientific_journal-591	9	13	theorem	theorem	NOUN
american_scientific_journal-591	9	14	;	;	PUNCT
american_scientific_journal-591	9	15	optimization	optimization	NOUN
american_scientific_journal-591	9	16	1	1	NUM
american_scientific_journal-591	9	17	.	.	PUNCT
american_scientific_journal-591	10	1	introduction	introduction	NOUN
american_scientific_journal-591	10	2	mathematicians	mathematician	NOUN
american_scientific_journal-591	10	3	,	,	PUNCT
american_scientific_journal-591	10	4	engineers	engineer	NOUN
american_scientific_journal-591	10	5	,	,	PUNCT
american_scientific_journal-591	10	6	economists	economist	NOUN
american_scientific_journal-591	10	7	and	and	CCONJ
american_scientific_journal-591	10	8	business	business	NOUN
american_scientific_journal-591	10	9	professionals	professional	NOUN
american_scientific_journal-591	10	10	have	have	VERB
american_scientific_journal-591	10	11	the	the	DET
american_scientific_journal-591	10	12	same	same	ADJ
american_scientific_journal-591	10	13	opinion	opinion	NOUN
american_scientific_journal-591	10	14	that	that	PRON
american_scientific_journal-591	10	15	to	to	PART
american_scientific_journal-591	10	16	remain	remain	VERB
american_scientific_journal-591	10	17	competitive	competitive	ADJ
american_scientific_journal-591	10	18	in	in	ADP
american_scientific_journal-591	10	19	today	today	NOUN
american_scientific_journal-591	10	20	’s	’s	PART
american_scientific_journal-591	10	21	global	global	ADJ
american_scientific_journal-591	10	22	economy	economy	NOUN
american_scientific_journal-591	10	23	,	,	PUNCT
american_scientific_journal-591	10	24	businesses	business	NOUN
american_scientific_journal-591	10	25	need	need	VERB
american_scientific_journal-591	10	26	to	to	PART
american_scientific_journal-591	10	27	minimize	minimize	VERB
american_scientific_journal-591	10	28	cost	cost	NOUN
american_scientific_journal-591	10	29	,	,	PUNCT
american_scientific_journal-591	10	30	waste	waste	NOUN
american_scientific_journal-591	10	31	and	and	CCONJ
american_scientific_journal-591	10	32	production	production	NOUN
american_scientific_journal-591	10	33	time	time	NOUN
american_scientific_journal-591	10	34	while	while	SCONJ
american_scientific_journal-591	10	35	maximizing	maximize	VERB
american_scientific_journal-591	10	36	productivity	productivity	NOUN
american_scientific_journal-591	10	37	,	,	PUNCT
american_scientific_journal-591	10	38	profit	profit	NOUN
american_scientific_journal-591	10	39	and	and	CCONJ
american_scientific_journal-591	10	40	return	return	NOUN
american_scientific_journal-591	10	41	of	of	ADP
american_scientific_journal-591	10	42	investment	investment	NOUN
american_scientific_journal-591	10	43	.	.	PUNCT
american_scientific_journal-591	11	1	with	with	ADP
american_scientific_journal-591	11	2	this	this	DET
american_scientific_journal-591	11	3	backdrop	backdrop	NOUN
american_scientific_journal-591	11	4	,	,	PUNCT
american_scientific_journal-591	11	5	the	the	DET
american_scientific_journal-591	11	6	researchers	researcher	NOUN
american_scientific_journal-591	11	7	agree	agree	VERB
american_scientific_journal-591	11	8	to	to	ADP
american_scientific_journal-591	11	9	the	the	DET
american_scientific_journal-591	11	10	statement	statement	NOUN
american_scientific_journal-591	11	11	of	of	ADP
american_scientific_journal-591	11	12	smith	smith	PROPN
american_scientific_journal-591	11	13	and	and	CCONJ
american_scientific_journal-591	11	14	minton	minton	PROPN
american_scientific_journal-591	12	1	[	[	X
american_scientific_journal-591	12	2	1	1	NUM
american_scientific_journal-591	12	3	]	]	PUNCT
american_scientific_journal-591	12	4	that	that	SCONJ
american_scientific_journal-591	12	5	it	it	PRON
american_scientific_journal-591	12	6	is	be	AUX
american_scientific_journal-591	12	7	increasingly	increasingly	ADV
american_scientific_journal-591	12	8	important	important	ADJ
american_scientific_journal-591	12	9	to	to	PART
american_scientific_journal-591	12	10	use	use	VERB
american_scientific_journal-591	12	11	mathematical	mathematical	ADJ
american_scientific_journal-591	12	12	methods	method	NOUN
american_scientific_journal-591	12	13	to	to	PART
american_scientific_journal-591	12	14	maximize	maximize	VERB
american_scientific_journal-591	12	15	and	and	CCONJ
american_scientific_journal-591	12	16	minimize	minimize	VERB
american_scientific_journal-591	12	17	various	various	ADJ
american_scientific_journal-591	12	18	quantities	quantity	NOUN
american_scientific_journal-591	12	19	of	of	ADP
american_scientific_journal-591	12	20	interest	interest	NOUN
american_scientific_journal-591	12	21	.	.	PUNCT
american_scientific_journal-591	13	1	mathematics	mathematic	NOUN
american_scientific_journal-591	13	2	is	be	AUX
american_scientific_journal-591	13	3	the	the	DET
american_scientific_journal-591	13	4	study	study	NOUN
american_scientific_journal-591	13	5	of	of	ADP
american_scientific_journal-591	13	6	relationships	relationship	NOUN
american_scientific_journal-591	13	7	among	among	ADP
american_scientific_journal-591	13	8	quantities	quantity	NOUN
american_scientific_journal-591	13	9	,	,	PUNCT
american_scientific_journal-591	13	10	magnitudes	magnitude	NOUN
american_scientific_journal-591	13	11	,	,	PUNCT
american_scientific_journal-591	13	12	and	and	CCONJ
american_scientific_journal-591	13	13	properties	property	NOUN
american_scientific_journal-591	13	14	and	and	CCONJ
american_scientific_journal-591	13	15	of	of	ADP
american_scientific_journal-591	13	16	logical	logical	ADJ
american_scientific_journal-591	13	17	operations	operation	NOUN
american_scientific_journal-591	13	18	by	by	ADP
american_scientific_journal-591	13	19	which	which	PRON
american_scientific_journal-591	13	20	unknown	unknown	ADJ
american_scientific_journal-591	13	21	quantities	quantity	NOUN
american_scientific_journal-591	13	22	,	,	PUNCT
american_scientific_journal-591	13	23	magnitudes	magnitude	NOUN
american_scientific_journal-591	13	24	,	,	PUNCT
american_scientific_journal-591	13	25	and	and	CCONJ
american_scientific_journal-591	13	26	properties	property	NOUN
american_scientific_journal-591	13	27	may	may	AUX
american_scientific_journal-591	13	28	be	be	AUX
american_scientific_journal-591	13	29	deduced	deduce	VERB
american_scientific_journal-591	13	30	.	.	PUNCT
american_scientific_journal-591	14	1	berggren	berggren	PROPN
american_scientific_journal-591	15	1	[	[	X
american_scientific_journal-591	15	2	2	2	X
american_scientific_journal-591	15	3	]	]	PUNCT
american_scientific_journal-591	15	4	emphasized	emphasize	VERB
american_scientific_journal-591	15	5	that	that	SCONJ
american_scientific_journal-591	15	6	mathematics	mathematic	NOUN
american_scientific_journal-591	15	7	,	,	PUNCT
american_scientific_journal-591	15	8	in	in	ADP
american_scientific_journal-591	15	9	the	the	DET
american_scientific_journal-591	15	10	past	past	NOUN
american_scientific_journal-591	15	11	,	,	PUNCT
american_scientific_journal-591	15	12	was	be	AUX
american_scientific_journal-591	15	13	regarded	regard	VERB
american_scientific_journal-591	15	14	as	as	ADP
american_scientific_journal-591	15	15	the	the	DET
american_scientific_journal-591	15	16	science	science	NOUN
american_scientific_journal-591	15	17	of	of	ADP
american_scientific_journal-591	15	18	quantity	quantity	NOUN
american_scientific_journal-591	15	19	,	,	PUNCT
american_scientific_journal-591	15	20	whether	whether	SCONJ
american_scientific_journal-591	15	21	of	of	ADP
american_scientific_journal-591	15	22	magnitudes	magnitude	NOUN
american_scientific_journal-591	15	23	as	as	ADP
american_scientific_journal-591	15	24	in	in	ADP
american_scientific_journal-591	15	25	geometry	geometry	NOUN
american_scientific_journal-591	15	26	,	,	PUNCT
american_scientific_journal-591	15	27	or	or	CCONJ
american_scientific_journal-591	15	28	of	of	ADP
american_scientific_journal-591	15	29	numbers	number	NOUN
american_scientific_journal-591	15	30	as	as	ADP
american_scientific_journal-591	15	31	in	in	ADP
american_scientific_journal-591	15	32	arithmetic	arithmetic	ADJ
american_scientific_journal-591	15	33	,	,	PUNCT
american_scientific_journal-591	15	34	or	or	CCONJ
american_scientific_journal-591	15	35	the	the	DET
american_scientific_journal-591	15	36	generalization	generalization	NOUN
american_scientific_journal-591	15	37	of	of	ADP
american_scientific_journal-591	15	38	these	these	DET
american_scientific_journal-591	15	39	two	two	NUM
american_scientific_journal-591	15	40	fields	field	NOUN
american_scientific_journal-591	15	41	as	as	ADP
american_scientific_journal-591	15	42	in	in	ADP
american_scientific_journal-591	15	43	algebra	algebra	NOUN
american_scientific_journal-591	15	44	.	.	PUNCT
american_scientific_journal-591	16	1	a	a	DET
american_scientific_journal-591	16	2	well	well	ADV
american_scientific_journal-591	16	3	-	-	PUNCT
american_scientific_journal-591	16	4	known	know	VERB
american_scientific_journal-591	16	5	and	and	CCONJ
american_scientific_journal-591	16	6	a	a	DET
american_scientific_journal-591	16	7	very	very	ADV
american_scientific_journal-591	16	8	important	important	ADJ
american_scientific_journal-591	16	9	branch	branch	NOUN
american_scientific_journal-591	16	10	of	of	ADP
american_scientific_journal-591	16	11	mathematics	mathematic	NOUN
american_scientific_journal-591	16	12	is	be	AUX
american_scientific_journal-591	16	13	the	the	DET
american_scientific_journal-591	16	14	calculus	calculus	NOUN
american_scientific_journal-591	16	15	.	.	PUNCT
american_scientific_journal-591	17	1	for	for	ADP
american_scientific_journal-591	17	2	seeley	seeley	NOUN
american_scientific_journal-591	17	3	[	[	X
american_scientific_journal-591	17	4	3	3	NUM
american_scientific_journal-591	17	5	]	]	PUNCT
american_scientific_journal-591	17	6	,	,	PUNCT
american_scientific_journal-591	17	7	calculus	calculus	NOUN
american_scientific_journal-591	17	8	has	have	AUX
american_scientific_journal-591	17	9	been	be	AUX
american_scientific_journal-591	17	10	the	the	DET
american_scientific_journal-591	17	11	84	84	NUM
american_scientific_journal-591	17	12	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-591	17	13	mailto:romercastillo@rocketmail.com	mailto:romercastillo@rocketmail.com	NOUN
american_scientific_journal-591	17	14	mailto:azodnem1994@yahoo.com	mailto:azodnem1994@yahoo.com	PROPN
american_scientific_journal-591	17	15	mailto:comiajenny@gmail.com	mailto:comiajenny@gmail.com	PROPN
american_scientific_journal-591	17	16	american	american	PROPN
american_scientific_journal-591	17	17	scientific	scientific	PROPN
american_scientific_journal-591	17	18	research	research	PROPN
american_scientific_journal-591	17	19	journal	journal	NOUN
american_scientific_journal-591	17	20	for	for	ADP
american_scientific_journal-591	17	21	engineering	engineering	NOUN
american_scientific_journal-591	17	22	,	,	PUNCT
american_scientific_journal-591	17	23	technology	technology	NOUN
american_scientific_journal-591	17	24	,	,	PUNCT
american_scientific_journal-591	17	25	and	and	CCONJ
american_scientific_journal-591	17	26	sciences	science	NOUN
american_scientific_journal-591	17	27	(	(	PUNCT
american_scientific_journal-591	17	28	asrjets	asrjet	NOUN
american_scientific_journal-591	17	29	)	)	PUNCT
american_scientific_journal-591	17	30	(	(	PUNCT
american_scientific_journal-591	17	31	2015	2015	NUM
american_scientific_journal-591	17	32	)	)	PUNCT
american_scientific_journal-591	17	33	volume	volume	NOUN
american_scientific_journal-591	17	34	11	11	NUM
american_scientific_journal-591	17	35	,	,	PUNCT
american_scientific_journal-591	17	36	no	no	DET
american_scientific_journal-591	17	37	1	1	NUM
american_scientific_journal-591	17	38	,	,	PUNCT
american_scientific_journal-591	17	39	pp	pp	ADV
american_scientific_journal-591	17	40	84	84	NUM
american_scientific_journal-591	17	41	-	-	SYM
american_scientific_journal-591	17	42	95	95	NUM
american_scientific_journal-591	17	43	principal	principal	ADJ
american_scientific_journal-591	17	44	language	language	NOUN
american_scientific_journal-591	17	45	of	of	ADP
american_scientific_journal-591	17	46	science	science	NOUN
american_scientific_journal-591	17	47	ever	ever	ADV
american_scientific_journal-591	17	48	since	since	SCONJ
american_scientific_journal-591	17	49	the	the	DET
american_scientific_journal-591	17	50	seventeenth	seventeenth	ADJ
american_scientific_journal-591	17	51	century	century	NOUN
american_scientific_journal-591	17	52	,	,	PUNCT
american_scientific_journal-591	17	53	when	when	SCONJ
american_scientific_journal-591	17	54	it	it	PRON
american_scientific_journal-591	17	55	was	be	AUX
american_scientific_journal-591	17	56	invented	invent	VERB
american_scientific_journal-591	17	57	,	,	PUNCT
american_scientific_journal-591	17	58	and	and	CCONJ
american_scientific_journal-591	17	59	it	it	PRON
american_scientific_journal-591	17	60	is	be	AUX
american_scientific_journal-591	17	61	likely	likely	ADJ
american_scientific_journal-591	17	62	to	to	PART
american_scientific_journal-591	17	63	continue	continue	VERB
american_scientific_journal-591	17	64	in	in	ADP
american_scientific_journal-591	17	65	this	this	DET
american_scientific_journal-591	17	66	central	central	ADJ
american_scientific_journal-591	17	67	role	role	NOUN
american_scientific_journal-591	17	68	for	for	ADP
american_scientific_journal-591	17	69	some	some	DET
american_scientific_journal-591	17	70	time	time	NOUN
american_scientific_journal-591	17	71	to	to	PART
american_scientific_journal-591	17	72	come	come	VERB
american_scientific_journal-591	17	73	.	.	PUNCT
american_scientific_journal-591	18	1	kalmanson	kalmanson	PROPN
american_scientific_journal-591	18	2	and	and	CCONJ
american_scientific_journal-591	18	3	kenschaft	kenschaft	VERB
american_scientific_journal-591	18	4	[	[	X
american_scientific_journal-591	18	5	4	4	X
american_scientific_journal-591	18	6	]	]	PUNCT
american_scientific_journal-591	18	7	said	say	VERB
american_scientific_journal-591	18	8	that	that	SCONJ
american_scientific_journal-591	18	9	calculus	calculus	NOUN
american_scientific_journal-591	18	10	is	be	AUX
american_scientific_journal-591	18	11	one	one	NUM
american_scientific_journal-591	18	12	of	of	ADP
american_scientific_journal-591	18	13	the	the	DET
american_scientific_journal-591	18	14	most	most	ADV
american_scientific_journal-591	18	15	beautiful	beautiful	ADJ
american_scientific_journal-591	18	16	subjects	subject	NOUN
american_scientific_journal-591	18	17	ever	ever	ADV
american_scientific_journal-591	18	18	created	create	VERB
american_scientific_journal-591	18	19	by	by	ADP
american_scientific_journal-591	18	20	the	the	DET
american_scientific_journal-591	18	21	human	human	ADJ
american_scientific_journal-591	18	22	mind	mind	NOUN
american_scientific_journal-591	18	23	.	.	PUNCT
american_scientific_journal-591	19	1	they	they	PRON
american_scientific_journal-591	19	2	defined	define	VERB
american_scientific_journal-591	19	3	calculus	calculus	NOUN
american_scientific_journal-591	19	4	as	as	ADP
american_scientific_journal-591	19	5	the	the	DET
american_scientific_journal-591	19	6	study	study	NOUN
american_scientific_journal-591	19	7	of	of	ADP
american_scientific_journal-591	19	8	change	change	NOUN
american_scientific_journal-591	19	9	,	,	PUNCT
american_scientific_journal-591	19	10	both	both	DET
american_scientific_journal-591	19	11	instantaneous	instantaneous	ADJ
american_scientific_journal-591	19	12	change	change	NOUN
american_scientific_journal-591	19	13	as	as	ADP
american_scientific_journal-591	19	14	in	in	ADP
american_scientific_journal-591	19	15	differential	differential	ADJ
american_scientific_journal-591	19	16	calculus	calculus	NOUN
american_scientific_journal-591	19	17	and	and	CCONJ
american_scientific_journal-591	19	18	total	total	ADJ
american_scientific_journal-591	19	19	change	change	NOUN
american_scientific_journal-591	19	20	as	as	ADP
american_scientific_journal-591	19	21	in	in	ADP
american_scientific_journal-591	19	22	integral	integral	ADJ
american_scientific_journal-591	19	23	calculus	calculus	NOUN
american_scientific_journal-591	19	24	;	;	PUNCT
american_scientific_journal-591	19	25	and	and	CCONJ
american_scientific_journal-591	19	26	change	change	NOUN
american_scientific_journal-591	19	27	is	be	AUX
american_scientific_journal-591	19	28	such	such	DET
american_scientific_journal-591	19	29	a	a	DET
american_scientific_journal-591	19	30	pervasive	pervasive	ADJ
american_scientific_journal-591	19	31	part	part	NOUN
american_scientific_journal-591	19	32	of	of	ADP
american_scientific_journal-591	19	33	modern	modern	ADJ
american_scientific_journal-591	19	34	life	life	NOUN
american_scientific_journal-591	19	35	that	that	PRON
american_scientific_journal-591	19	36	the	the	DET
american_scientific_journal-591	19	37	subject	subject	NOUN
american_scientific_journal-591	19	38	became	become	VERB
american_scientific_journal-591	19	39	useful	useful	ADJ
american_scientific_journal-591	19	40	and	and	CCONJ
american_scientific_journal-591	19	41	essential	essential	ADJ
american_scientific_journal-591	19	42	in	in	ADP
american_scientific_journal-591	19	43	the	the	DET
american_scientific_journal-591	19	44	study	study	NOUN
american_scientific_journal-591	19	45	of	of	ADP
american_scientific_journal-591	19	46	many	many	ADJ
american_scientific_journal-591	19	47	diverse	diverse	ADJ
american_scientific_journal-591	19	48	fields	field	NOUN
american_scientific_journal-591	19	49	.	.	PUNCT
american_scientific_journal-591	20	1	optimization	optimization	NOUN
american_scientific_journal-591	20	2	problems	problem	NOUN
american_scientific_journal-591	20	3	usually	usually	ADV
american_scientific_journal-591	20	4	arise	arise	VERB
american_scientific_journal-591	20	5	in	in	ADP
american_scientific_journal-591	20	6	business	business	NOUN
american_scientific_journal-591	20	7	and	and	CCONJ
american_scientific_journal-591	20	8	industry	industry	NOUN
american_scientific_journal-591	20	9	today	today	NOUN
american_scientific_journal-591	20	10	.	.	PUNCT
american_scientific_journal-591	21	1	it	it	PRON
american_scientific_journal-591	21	2	is	be	AUX
american_scientific_journal-591	21	3	in	in	ADP
american_scientific_journal-591	21	4	this	this	DET
american_scientific_journal-591	21	5	position	position	NOUN
american_scientific_journal-591	21	6	that	that	SCONJ
american_scientific_journal-591	21	7	the	the	DET
american_scientific_journal-591	21	8	power	power	NOUN
american_scientific_journal-591	21	9	of	of	ADP
american_scientific_journal-591	21	10	calculus	calculus	NOUN
american_scientific_journal-591	21	11	can	can	AUX
american_scientific_journal-591	21	12	be	be	AUX
american_scientific_journal-591	21	13	brought	bring	VERB
american_scientific_journal-591	21	14	into	into	ADP
american_scientific_journal-591	21	15	,	,	PUNCT
american_scientific_journal-591	21	16	i.e.	i.e.	X
american_scientific_journal-591	21	17	solving	solving	NOUN
american_scientific_journal-591	21	18	problems	problem	NOUN
american_scientific_journal-591	21	19	involving	involve	VERB
american_scientific_journal-591	21	20	finding	find	VERB
american_scientific_journal-591	21	21	a	a	DET
american_scientific_journal-591	21	22	maximum	maximum	NOUN
american_scientific_journal-591	21	23	or	or	CCONJ
american_scientific_journal-591	21	24	a	a	DET
american_scientific_journal-591	21	25	minimum	minimum	NOUN
american_scientific_journal-591	21	26	.	.	PUNCT
american_scientific_journal-591	22	1	according	accord	VERB
american_scientific_journal-591	22	2	to	to	ADP
american_scientific_journal-591	22	3	dick	dick	PROPN
american_scientific_journal-591	22	4	and	and	CCONJ
american_scientific_journal-591	22	5	patron	patron	NOUN
american_scientific_journal-591	22	6	[	[	X
american_scientific_journal-591	22	7	5	5	NUM
american_scientific_journal-591	22	8	]	]	PUNCT
american_scientific_journal-591	22	9	,	,	PUNCT
american_scientific_journal-591	22	10	the	the	DET
american_scientific_journal-591	22	11	full	full	ADJ
american_scientific_journal-591	22	12	power	power	NOUN
american_scientific_journal-591	22	13	of	of	ADP
american_scientific_journal-591	22	14	calculus	calculus	NOUN
american_scientific_journal-591	22	15	can	can	AUX
american_scientific_journal-591	22	16	be	be	AUX
american_scientific_journal-591	22	17	unleashed	unleashed	ADJ
american_scientific_journal-591	22	18	if	if	SCONJ
american_scientific_journal-591	22	19	one	one	PRON
american_scientific_journal-591	22	20	can	can	AUX
american_scientific_journal-591	22	21	model	model	VERB
american_scientific_journal-591	22	22	a	a	DET
american_scientific_journal-591	22	23	problem	problem	NOUN
american_scientific_journal-591	22	24	situation	situation	NOUN
american_scientific_journal-591	22	25	and	and	CCONJ
american_scientific_journal-591	22	26	its	its	PRON
american_scientific_journal-591	22	27	constraints	constraint	NOUN
american_scientific_journal-591	22	28	as	as	ADP
american_scientific_journal-591	22	29	functional	functional	ADJ
american_scientific_journal-591	22	30	expressions	expression	NOUN
american_scientific_journal-591	22	31	or	or	CCONJ
american_scientific_journal-591	22	32	as	as	ADP
american_scientific_journal-591	22	33	equations	equation	NOUN
american_scientific_journal-591	22	34	or	or	CCONJ
american_scientific_journal-591	22	35	inequalities	inequality	NOUN
american_scientific_journal-591	22	36	.	.	PUNCT
american_scientific_journal-591	23	1	then	then	ADV
american_scientific_journal-591	23	2	,	,	PUNCT
american_scientific_journal-591	23	3	a	a	DET
american_scientific_journal-591	23	4	problem	problem	NOUN
american_scientific_journal-591	23	5	solving	solving	NOUN
american_scientific_journal-591	23	6	process	process	NOUN
american_scientific_journal-591	23	7	can	can	AUX
american_scientific_journal-591	23	8	be	be	AUX
american_scientific_journal-591	23	9	applied	apply	VERB
american_scientific_journal-591	23	10	,	,	PUNCT
american_scientific_journal-591	23	11	for	for	ADP
american_scientific_journal-591	23	12	instance	instance	NOUN
american_scientific_journal-591	23	13	,	,	PUNCT
american_scientific_journal-591	23	14	the	the	DET
american_scientific_journal-591	23	15	four	four	NUM
american_scientific_journal-591	23	16	basic	basic	ADJ
american_scientific_journal-591	23	17	steps	step	NOUN
american_scientific_journal-591	23	18	in	in	ADP
american_scientific_journal-591	23	19	mathematical	mathematical	ADJ
american_scientific_journal-591	23	20	problem	problem	NOUN
american_scientific_journal-591	23	21	solving	solving	NOUN
american_scientific_journal-591	23	22	provided	provide	VERB
american_scientific_journal-591	23	23	by	by	ADP
american_scientific_journal-591	23	24	polya	polya	NOUN
american_scientific_journal-591	23	25	(	(	PUNCT
american_scientific_journal-591	23	26	1887	1887	NUM
american_scientific_journal-591	23	27	-	-	SYM
american_scientific_journal-591	23	28	1985	1985	NUM
american_scientific_journal-591	23	29	)	)	PUNCT
american_scientific_journal-591	23	30	as	as	SCONJ
american_scientific_journal-591	23	31	follows	follow	VERB
american_scientific_journal-591	23	32	:	:	PUNCT
american_scientific_journal-591	23	33	understand	understand	VERB
american_scientific_journal-591	23	34	the	the	DET
american_scientific_journal-591	23	35	problem	problem	NOUN
american_scientific_journal-591	23	36	,	,	PUNCT
american_scientific_journal-591	23	37	devise	devise	VERB
american_scientific_journal-591	23	38	a	a	DET
american_scientific_journal-591	23	39	plan	plan	NOUN
american_scientific_journal-591	23	40	,	,	PUNCT
american_scientific_journal-591	23	41	carry	carry	VERB
american_scientific_journal-591	23	42	out	out	ADP
american_scientific_journal-591	23	43	the	the	DET
american_scientific_journal-591	23	44	plan	plan	NOUN
american_scientific_journal-591	23	45	,	,	PUNCT
american_scientific_journal-591	23	46	and	and	CCONJ
american_scientific_journal-591	23	47	look	look	VERB
american_scientific_journal-591	23	48	back	back	ADV
american_scientific_journal-591	23	49	.	.	PUNCT
american_scientific_journal-591	24	1	several	several	ADJ
american_scientific_journal-591	24	2	methods	method	NOUN
american_scientific_journal-591	24	3	can	can	AUX
american_scientific_journal-591	24	4	be	be	AUX
american_scientific_journal-591	24	5	applied	apply	VERB
american_scientific_journal-591	24	6	in	in	ADP
american_scientific_journal-591	24	7	problem	problem	NOUN
american_scientific_journal-591	24	8	solving	solving	NOUN
american_scientific_journal-591	24	9	;	;	PUNCT
american_scientific_journal-591	24	10	some	some	PRON
american_scientific_journal-591	24	11	are	be	AUX
american_scientific_journal-591	24	12	long	long	ADJ
american_scientific_journal-591	24	13	and	and	CCONJ
american_scientific_journal-591	24	14	cumbersome	cumbersome	ADJ
american_scientific_journal-591	24	15	while	while	SCONJ
american_scientific_journal-591	24	16	others	other	NOUN
american_scientific_journal-591	24	17	are	be	AUX
american_scientific_journal-591	24	18	short	short	ADJ
american_scientific_journal-591	24	19	and	and	CCONJ
american_scientific_journal-591	24	20	easy	easy	ADJ
american_scientific_journal-591	24	21	.	.	PUNCT
american_scientific_journal-591	25	1	smith	smith	PROPN
american_scientific_journal-591	25	2	and	and	CCONJ
american_scientific_journal-591	25	3	minton	minton	PROPN
american_scientific_journal-591	26	1	[	[	X
american_scientific_journal-591	26	2	1	1	NUM
american_scientific_journal-591	26	3	]	]	PUNCT
american_scientific_journal-591	26	4	suggested	suggest	VERB
american_scientific_journal-591	26	5	that	that	SCONJ
american_scientific_journal-591	26	6	mathematicians	mathematician	NOUN
american_scientific_journal-591	26	7	should	should	AUX
american_scientific_journal-591	26	8	always	always	ADV
american_scientific_journal-591	26	9	seek	seek	VERB
american_scientific_journal-591	26	10	the	the	DET
american_scientific_journal-591	26	11	shortest	short	ADJ
american_scientific_journal-591	26	12	and	and	CCONJ
american_scientific_journal-591	26	13	most	most	ADV
american_scientific_journal-591	26	14	efficient	efficient	ADJ
american_scientific_journal-591	26	15	computations	computation	NOUN
american_scientific_journal-591	26	16	in	in	ADP
american_scientific_journal-591	26	17	problem	problem	NOUN
american_scientific_journal-591	26	18	solving	solving	NOUN
american_scientific_journal-591	26	19	but	but	CCONJ
american_scientific_journal-591	26	20	should	should	AUX
american_scientific_journal-591	26	21	also	also	ADV
american_scientific_journal-591	26	22	remember	remember	VERB
american_scientific_journal-591	26	23	that	that	SCONJ
american_scientific_journal-591	26	24	shortcuts	shortcut	NOUN
american_scientific_journal-591	26	25	must	must	AUX
american_scientific_journal-591	26	26	always	always	ADV
american_scientific_journal-591	26	27	be	be	AUX
american_scientific_journal-591	26	28	carefully	carefully	ADV
american_scientific_journal-591	26	29	proved	prove	VERB
american_scientific_journal-591	26	30	.	.	PUNCT
american_scientific_journal-591	27	1	mame	mame	PROPN
american_scientific_journal-591	28	1	[	[	X
american_scientific_journal-591	28	2	6	6	NUM
american_scientific_journal-591	28	3	]	]	PUNCT
american_scientific_journal-591	28	4	,	,	PUNCT
american_scientific_journal-591	28	5	referring	refer	VERB
american_scientific_journal-591	28	6	to	to	ADP
american_scientific_journal-591	28	7	the	the	DET
american_scientific_journal-591	28	8	computation	computation	NOUN
american_scientific_journal-591	28	9	of	of	ADP
american_scientific_journal-591	28	10	the	the	DET
american_scientific_journal-591	28	11	derivative	derivative	NOUN
american_scientific_journal-591	28	12	of	of	ADP
american_scientific_journal-591	28	13	algebraic	algebraic	ADJ
american_scientific_journal-591	28	14	function	function	NOUN
american_scientific_journal-591	28	15	,	,	PUNCT
american_scientific_journal-591	28	16	also	also	ADV
american_scientific_journal-591	28	17	said	say	VERB
american_scientific_journal-591	28	18	that	that	SCONJ
american_scientific_journal-591	28	19	lengthy	lengthy	ADJ
american_scientific_journal-591	28	20	and	and	CCONJ
american_scientific_journal-591	28	21	laborious	laborious	ADJ
american_scientific_journal-591	28	22	computations	computation	NOUN
american_scientific_journal-591	28	23	could	could	AUX
american_scientific_journal-591	28	24	possibly	possibly	ADV
american_scientific_journal-591	28	25	lead	lead	VERB
american_scientific_journal-591	28	26	to	to	ADP
american_scientific_journal-591	28	27	errors	error	NOUN
american_scientific_journal-591	28	28	in	in	ADP
american_scientific_journal-591	28	29	simplifying	simplify	VERB
american_scientific_journal-591	28	30	solutions	solution	NOUN
american_scientific_journal-591	28	31	.	.	PUNCT
american_scientific_journal-591	29	1	in	in	ADP
american_scientific_journal-591	29	2	his	his	PRON
american_scientific_journal-591	29	3	masters	master	NOUN
american_scientific_journal-591	29	4	thesis	thesis	NOUN
american_scientific_journal-591	29	5	,	,	PUNCT
american_scientific_journal-591	29	6	he	he	PRON
american_scientific_journal-591	29	7	developed	develop	VERB
american_scientific_journal-591	29	8	corollaries	corollary	NOUN
american_scientific_journal-591	29	9	of	of	ADP
american_scientific_journal-591	29	10	some	some	DET
american_scientific_journal-591	29	11	basic	basic	ADJ
american_scientific_journal-591	29	12	theorems	theorem	NOUN
american_scientific_journal-591	29	13	in	in	ADP
american_scientific_journal-591	29	14	differential	differential	ADJ
american_scientific_journal-591	29	15	calculus	calculus	NOUN
american_scientific_journal-591	29	16	for	for	ADP
american_scientific_journal-591	29	17	the	the	DET
american_scientific_journal-591	29	18	purpose	purpose	NOUN
american_scientific_journal-591	29	19	of	of	ADP
american_scientific_journal-591	29	20	simplifying	simplify	VERB
american_scientific_journal-591	29	21	the	the	DET
american_scientific_journal-591	29	22	application	application	NOUN
american_scientific_journal-591	29	23	of	of	ADP
american_scientific_journal-591	29	24	the	the	DET
american_scientific_journal-591	29	25	theorems	theorem	NOUN
american_scientific_journal-591	29	26	and	and	CCONJ
american_scientific_journal-591	29	27	minimizing	minimize	VERB
american_scientific_journal-591	29	28	steps	step	NOUN
american_scientific_journal-591	29	29	in	in	ADP
american_scientific_journal-591	29	30	computations	computation	NOUN
american_scientific_journal-591	29	31	,	,	PUNCT
american_scientific_journal-591	29	32	thereby	thereby	ADV
american_scientific_journal-591	29	33	saving	save	VERB
american_scientific_journal-591	29	34	time	time	NOUN
american_scientific_journal-591	29	35	used	use	VERB
american_scientific_journal-591	29	36	in	in	ADP
american_scientific_journal-591	29	37	computing	compute	VERB
american_scientific_journal-591	29	38	.	.	PUNCT
american_scientific_journal-591	30	1	one	one	NUM
american_scientific_journal-591	30	2	problem	problem	NOUN
american_scientific_journal-591	30	3	that	that	PRON
american_scientific_journal-591	30	4	mathematicians	mathematician	NOUN
american_scientific_journal-591	30	5	need	need	VERB
american_scientific_journal-591	30	6	to	to	PART
american_scientific_journal-591	30	7	solve	solve	VERB
american_scientific_journal-591	30	8	in	in	ADP
american_scientific_journal-591	30	9	the	the	DET
american_scientific_journal-591	30	10	shortest	short	ADJ
american_scientific_journal-591	30	11	and	and	CCONJ
american_scientific_journal-591	30	12	fastest	fast	ADJ
american_scientific_journal-591	30	13	possible	possible	ADJ
american_scientific_journal-591	30	14	way	way	NOUN
american_scientific_journal-591	30	15	is	be	AUX
american_scientific_journal-591	30	16	the	the	DET
american_scientific_journal-591	30	17	minimum	minimum	ADJ
american_scientific_journal-591	30	18	distance	distance	NOUN
american_scientific_journal-591	30	19	problem	problem	NOUN
american_scientific_journal-591	30	20	.	.	PUNCT
american_scientific_journal-591	31	1	this	this	DET
american_scientific_journal-591	31	2	problem	problem	NOUN
american_scientific_journal-591	31	3	can	can	AUX
american_scientific_journal-591	31	4	be	be	AUX
american_scientific_journal-591	31	5	found	find	VERB
american_scientific_journal-591	31	6	in	in	ADP
american_scientific_journal-591	31	7	both	both	CCONJ
american_scientific_journal-591	31	8	geometry	geometry	NOUN
american_scientific_journal-591	31	9	and	and	CCONJ
american_scientific_journal-591	31	10	calculus	calculus	NOUN
american_scientific_journal-591	31	11	books	book	NOUN
american_scientific_journal-591	31	12	.	.	PUNCT
american_scientific_journal-591	32	1	for	for	ADP
american_scientific_journal-591	32	2	instance	instance	NOUN
american_scientific_journal-591	32	3	,	,	PUNCT
american_scientific_journal-591	32	4	on	on	ADP
american_scientific_journal-591	32	5	page	page	NOUN
american_scientific_journal-591	32	6	231	231	NUM
american_scientific_journal-591	32	7	of	of	ADP
american_scientific_journal-591	32	8	their	their	PRON
american_scientific_journal-591	32	9	geometry	geometry	NOUN
american_scientific_journal-591	32	10	book	book	NOUN
american_scientific_journal-591	32	11	[	[	X
american_scientific_journal-591	32	12	7	7	NUM
american_scientific_journal-591	32	13	]	]	PUNCT
american_scientific_journal-591	32	14	,	,	PUNCT
american_scientific_journal-591	32	15	moise	moise	PROPN
american_scientific_journal-591	32	16	and	and	CCONJ
american_scientific_journal-591	32	17	dawas	dawas	PROPN
american_scientific_journal-591	32	18	jr	jr	PROPN
american_scientific_journal-591	32	19	.	.	PROPN
american_scientific_journal-591	32	20	have	have	VERB
american_scientific_journal-591	32	21	this	this	DET
american_scientific_journal-591	32	22	problem	problem	NOUN
american_scientific_journal-591	32	23	:	:	PUNCT
american_scientific_journal-591	32	24	given	give	VERB
american_scientific_journal-591	32	25	a	a	DET
american_scientific_journal-591	32	26	line	line	NOUN
american_scientific_journal-591	32	27	l	l	NOUN
american_scientific_journal-591	32	28	and	and	CCONJ
american_scientific_journal-591	32	29	two	two	NUM
american_scientific_journal-591	32	30	points	point	NOUN
american_scientific_journal-591	32	31	,	,	PUNCT
american_scientific_journal-591	32	32	p	p	NOUN
american_scientific_journal-591	32	33	and	and	CCONJ
american_scientific_journal-591	32	34	q	q	NOUN
american_scientific_journal-591	32	35	,	,	PUNCT
american_scientific_journal-591	32	36	on	on	ADP
american_scientific_journal-591	32	37	the	the	DET
american_scientific_journal-591	32	38	same	same	ADJ
american_scientific_journal-591	32	39	side	side	NOUN
american_scientific_journal-591	32	40	of	of	ADP
american_scientific_journal-591	32	41	l.	l.	PROPN
american_scientific_journal-591	32	42	find	find	VERB
american_scientific_journal-591	32	43	the	the	DET
american_scientific_journal-591	32	44	point	point	NOUN
american_scientific_journal-591	32	45	r	r	NOUN
american_scientific_journal-591	32	46	on	on	ADP
american_scientific_journal-591	32	47	l	l	NOUN
american_scientific_journal-591	32	48	for	for	ADP
american_scientific_journal-591	32	49	which	which	PRON
american_scientific_journal-591	32	50	pr	pr	X
american_scientific_journal-591	32	51	+	+	CCONJ
american_scientific_journal-591	32	52	rq	rq	NOUN
american_scientific_journal-591	32	53	is	be	AUX
american_scientific_journal-591	32	54	as	as	ADV
american_scientific_journal-591	32	55	small	small	ADJ
american_scientific_journal-591	32	56	as	as	ADP
american_scientific_journal-591	32	57	possible	possible	ADJ
american_scientific_journal-591	32	58	.	.	PUNCT
american_scientific_journal-591	33	1	this	this	PRON
american_scientific_journal-591	33	2	is	be	AUX
american_scientific_journal-591	33	3	shown	show	VERB
american_scientific_journal-591	33	4	in	in	ADP
american_scientific_journal-591	33	5	figure	figure	NOUN
american_scientific_journal-591	33	6	1	1	NUM
american_scientific_journal-591	33	7	.	.	PUNCT
american_scientific_journal-591	33	8	figure	figure	NOUN
american_scientific_journal-591	33	9	1	1	NUM
american_scientific_journal-591	33	10	:	:	PUNCT
american_scientific_journal-591	33	11	the	the	DET
american_scientific_journal-591	33	12	minimum	minimum	ADJ
american_scientific_journal-591	33	13	distance	distance	NOUN
american_scientific_journal-591	33	14	problem	problem	NOUN
american_scientific_journal-591	33	15	schwartz	schwartz	PROPN
american_scientific_journal-591	33	16	had	have	VERB
american_scientific_journal-591	33	17	an	an	DET
american_scientific_journal-591	33	18	analogous	analogous	ADJ
american_scientific_journal-591	33	19	problem	problem	NOUN
american_scientific_journal-591	33	20	on	on	ADP
american_scientific_journal-591	33	21	page	page	NOUN
american_scientific_journal-591	33	22	427	427	NUM
american_scientific_journal-591	33	23	of	of	ADP
american_scientific_journal-591	33	24	his	his	PRON
american_scientific_journal-591	33	25	calculus	calculus	NOUN
american_scientific_journal-591	33	26	book	book	NOUN
american_scientific_journal-591	34	1	[	[	X
american_scientific_journal-591	34	2	8	8	NUM
american_scientific_journal-591	34	3	]	]	PUNCT
american_scientific_journal-591	34	4	as	as	SCONJ
american_scientific_journal-591	34	5	follows	follow	VERB
american_scientific_journal-591	34	6	:	:	PUNCT
american_scientific_journal-591	34	7	towns	town	NOUN
american_scientific_journal-591	34	8	a	a	PRON
american_scientific_journal-591	34	9	and	and	CCONJ
american_scientific_journal-591	34	10	b	b	NOUN
american_scientific_journal-591	34	11	,	,	PUNCT
american_scientific_journal-591	34	12	situated	situate	VERB
american_scientific_journal-591	34	13	inland	inland	ADV
american_scientific_journal-591	34	14	on	on	ADP
american_scientific_journal-591	34	15	the	the	DET
american_scientific_journal-591	34	16	same	same	ADJ
american_scientific_journal-591	34	17	side	side	NOUN
american_scientific_journal-591	34	18	of	of	ADP
american_scientific_journal-591	34	19	a	a	DET
american_scientific_journal-591	34	20	straight	straight	ADJ
american_scientific_journal-591	34	21	river	river	NOUN
american_scientific_journal-591	34	22	,	,	PUNCT
american_scientific_journal-591	34	23	want	want	VERB
american_scientific_journal-591	34	24	to	to	PART
american_scientific_journal-591	34	25	erect	erect	VERB
american_scientific_journal-591	34	26	a	a	DET
american_scientific_journal-591	34	27	jointly	jointly	ADV
american_scientific_journal-591	34	28	owned	own	VERB
american_scientific_journal-591	34	29	pumping	pumping	NOUN
american_scientific_journal-591	34	30	station	station	NOUN
american_scientific_journal-591	34	31	p	p	NOUN
american_scientific_journal-591	34	32	on	on	ADP
american_scientific_journal-591	34	33	the	the	DET
american_scientific_journal-591	34	34	river	river	NOUN
american_scientific_journal-591	34	35	.	.	PUNCT
american_scientific_journal-591	35	1	where	where	SCONJ
american_scientific_journal-591	35	2	should	should	AUX
american_scientific_journal-591	35	3	p	p	NOUN
american_scientific_journal-591	35	4	be	be	AUX
american_scientific_journal-591	35	5	located	locate	VERB
american_scientific_journal-591	35	6	if	if	SCONJ
american_scientific_journal-591	35	7	the	the	DET
american_scientific_journal-591	35	8	length	length	NOUN
american_scientific_journal-591	35	9	of	of	ADP
american_scientific_journal-591	35	10	pipe	pipe	NOUN
american_scientific_journal-591	35	11	to	to	PART
american_scientific_journal-591	35	12	be	be	AUX
american_scientific_journal-591	35	13	used	use	VERB
american_scientific_journal-591	35	14	from	from	ADP
american_scientific_journal-591	35	15	p	p	NOUN
american_scientific_journal-591	35	16	to	to	ADP
american_scientific_journal-591	35	17	a	a	PRON
american_scientific_journal-591	35	18	and	and	CCONJ
american_scientific_journal-591	35	19	from	from	ADP
american_scientific_journal-591	35	20	p	p	NOUN
american_scientific_journal-591	35	21	to	to	ADP
american_scientific_journal-591	35	22	b	b	NOUN
american_scientific_journal-591	35	23	is	be	AUX
american_scientific_journal-591	35	24	to	to	PART
american_scientific_journal-591	35	25	be	be	AUX
american_scientific_journal-591	35	26	minimum	minimum	ADJ
american_scientific_journal-591	35	27	?	?	PUNCT
american_scientific_journal-591	36	1	leithold	leithold	NOUN
american_scientific_journal-591	36	2	,	,	PUNCT
american_scientific_journal-591	36	3	on	on	ADP
american_scientific_journal-591	36	4	page	page	NOUN
american_scientific_journal-591	36	5	310	310	NUM
american_scientific_journal-591	36	6	of	of	ADP
american_scientific_journal-591	36	7	his	his	PRON
american_scientific_journal-591	36	8	book	book	NOUN
american_scientific_journal-591	37	1	[	[	X
american_scientific_journal-591	37	2	9	9	NUM
american_scientific_journal-591	37	3	]	]	PUNCT
american_scientific_journal-591	37	4	,	,	PUNCT
american_scientific_journal-591	37	5	gave	give	VERB
american_scientific_journal-591	37	6	specific	specific	ADJ
american_scientific_journal-591	37	7	distances	distance	NOUN
american_scientific_journal-591	37	8	between	between	ADP
american_scientific_journal-591	37	9	the	the	DET
american_scientific_journal-591	37	10	towns	town	NOUN
american_scientific_journal-591	37	11	and	and	CCONJ
american_scientific_journal-591	37	12	from	from	ADP
american_scientific_journal-591	37	13	the	the	DET
american_scientific_journal-591	37	14	river	river	NOUN
american_scientific_journal-591	37	15	to	to	ADP
american_scientific_journal-591	37	16	each	each	DET
american_scientific_journal-591	37	17	town	town	NOUN
american_scientific_journal-591	37	18	in	in	ADP
american_scientific_journal-591	37	19	a	a	DET
american_scientific_journal-591	37	20	similar	similar	ADJ
american_scientific_journal-591	37	21	problem	problem	NOUN
american_scientific_journal-591	37	22	of	of	ADP
american_scientific_journal-591	37	23	finding	find	VERB
american_scientific_journal-591	37	24	where	where	SCONJ
american_scientific_journal-591	37	25	the	the	DET
american_scientific_journal-591	37	26	pumping	pumping	NOUN
american_scientific_journal-591	37	27	station	station	NOUN
american_scientific_journal-591	37	28	should	should	AUX
american_scientific_journal-591	37	29	be	be	AUX
american_scientific_journal-591	37	30	located	locate	VERB
american_scientific_journal-591	37	31	so	so	SCONJ
american_scientific_journal-591	37	32	that	that	SCONJ
american_scientific_journal-591	37	33	the	the	DET
american_scientific_journal-591	37	34	least	least	ADJ
american_scientific_journal-591	37	35	amount	amount	NOUN
american_scientific_journal-591	37	36	of	of	ADP
american_scientific_journal-591	37	37	piping	piping	NOUN
american_scientific_journal-591	37	38	is	be	AUX
american_scientific_journal-591	37	39	required	require	VERB
american_scientific_journal-591	37	40	:	:	PUNCT
american_scientific_journal-591	37	41	two	two	NUM
american_scientific_journal-591	37	42	towns	town	NOUN
american_scientific_journal-591	37	43	a	a	PRON
american_scientific_journal-591	37	44	and	and	CCONJ
american_scientific_journal-591	37	45	b	b	NOUN
american_scientific_journal-591	37	46	are	be	AUX
american_scientific_journal-591	37	47	to	to	PART
american_scientific_journal-591	37	48	get	get	VERB
american_scientific_journal-591	37	49	their	their	PRON
american_scientific_journal-591	37	50	water	water	NOUN
american_scientific_journal-591	37	51	supply	supply	NOUN
american_scientific_journal-591	37	52	from	from	ADP
american_scientific_journal-591	37	53	the	the	DET
american_scientific_journal-591	37	54	same	same	ADJ
american_scientific_journal-591	37	55	pumping	pumping	NOUN
american_scientific_journal-591	37	56	station	station	NOUN
american_scientific_journal-591	37	57	to	to	PART
american_scientific_journal-591	37	58	be	be	AUX
american_scientific_journal-591	37	59	located	locate	VERB
american_scientific_journal-591	37	60	on	on	ADP
american_scientific_journal-591	37	61	the	the	DET
american_scientific_journal-591	37	62	bank	bank	NOUN
american_scientific_journal-591	37	63	of	of	ADP
american_scientific_journal-591	37	64	a	a	DET
american_scientific_journal-591	37	65	85	85	NUM
american_scientific_journal-591	37	66	american	american	ADJ
american_scientific_journal-591	37	67	scientific	scientific	ADJ
american_scientific_journal-591	37	68	research	research	NOUN
american_scientific_journal-591	37	69	journal	journal	NOUN
american_scientific_journal-591	37	70	for	for	ADP
american_scientific_journal-591	37	71	engineering	engineering	NOUN
american_scientific_journal-591	37	72	,	,	PUNCT
american_scientific_journal-591	37	73	technology	technology	NOUN
american_scientific_journal-591	37	74	,	,	PUNCT
american_scientific_journal-591	37	75	and	and	CCONJ
american_scientific_journal-591	37	76	sciences	science	NOUN
american_scientific_journal-591	37	77	(	(	PUNCT
american_scientific_journal-591	37	78	asrjets	asrjet	NOUN
american_scientific_journal-591	37	79	)	)	PUNCT
american_scientific_journal-591	37	80	(	(	PUNCT
american_scientific_journal-591	37	81	2015	2015	NUM
american_scientific_journal-591	37	82	)	)	PUNCT
american_scientific_journal-591	37	83	volume	volume	NOUN
american_scientific_journal-591	37	84	11	11	NUM
american_scientific_journal-591	37	85	,	,	PUNCT
american_scientific_journal-591	37	86	no	no	DET
american_scientific_journal-591	37	87	1	1	NUM
american_scientific_journal-591	37	88	,	,	PUNCT
american_scientific_journal-591	37	89	pp	pp	ADV
american_scientific_journal-591	37	90	84	84	NUM
american_scientific_journal-591	37	91	-	-	SYM
american_scientific_journal-591	37	92	95	95	NUM
american_scientific_journal-591	37	93	straight	straight	ADJ
american_scientific_journal-591	37	94	river	river	NOUN
american_scientific_journal-591	37	95	that	that	PRON
american_scientific_journal-591	37	96	is	be	AUX
american_scientific_journal-591	37	97	15	15	NUM
american_scientific_journal-591	37	98	km	km	NOUN
american_scientific_journal-591	37	99	from	from	ADP
american_scientific_journal-591	37	100	town	town	NOUN
american_scientific_journal-591	37	101	a	a	PRON
american_scientific_journal-591	37	102	and	and	CCONJ
american_scientific_journal-591	37	103	10	10	NUM
american_scientific_journal-591	37	104	km	km	NOUN
american_scientific_journal-591	37	105	from	from	ADP
american_scientific_journal-591	37	106	town	town	NOUN
american_scientific_journal-591	37	107	b.	b.	PROPN
american_scientific_journal-591	38	1	the	the	DET
american_scientific_journal-591	38	2	points	point	NOUN
american_scientific_journal-591	38	3	on	on	ADP
american_scientific_journal-591	38	4	the	the	DET
american_scientific_journal-591	38	5	river	river	NOUN
american_scientific_journal-591	38	6	nearest	near	ADJ
american_scientific_journal-591	38	7	to	to	ADP
american_scientific_journal-591	38	8	a	a	PRON
american_scientific_journal-591	38	9	and	and	CCONJ
american_scientific_journal-591	38	10	b	b	NOUN
american_scientific_journal-591	38	11	are	be	AUX
american_scientific_journal-591	38	12	20	20	NUM
american_scientific_journal-591	38	13	km	km	NOUN
american_scientific_journal-591	38	14	apart	apart	ADV
american_scientific_journal-591	38	15	and	and	CCONJ
american_scientific_journal-591	38	16	a	a	PRON
american_scientific_journal-591	38	17	and	and	CCONJ
american_scientific_journal-591	38	18	b	b	NOUN
american_scientific_journal-591	38	19	are	be	AUX
american_scientific_journal-591	38	20	on	on	ADP
american_scientific_journal-591	38	21	the	the	DET
american_scientific_journal-591	38	22	same	same	ADJ
american_scientific_journal-591	38	23	side	side	NOUN
american_scientific_journal-591	38	24	of	of	ADP
american_scientific_journal-591	38	25	the	the	DET
american_scientific_journal-591	38	26	river	river	NOUN
american_scientific_journal-591	38	27	.	.	PUNCT
american_scientific_journal-591	39	1	on	on	ADP
american_scientific_journal-591	39	2	the	the	DET
american_scientific_journal-591	39	3	same	same	ADJ
american_scientific_journal-591	39	4	book	book	NOUN
american_scientific_journal-591	39	5	,	,	PUNCT
american_scientific_journal-591	39	6	leithold	leithold	PROPN
american_scientific_journal-591	39	7	discussed	discuss	VERB
american_scientific_journal-591	39	8	that	that	SCONJ
american_scientific_journal-591	39	9	such	such	ADJ
american_scientific_journal-591	39	10	problems	problem	NOUN
american_scientific_journal-591	39	11	can	can	AUX
american_scientific_journal-591	39	12	be	be	AUX
american_scientific_journal-591	39	13	solved	solve	VERB
american_scientific_journal-591	39	14	by	by	ADP
american_scientific_journal-591	39	15	the	the	DET
american_scientific_journal-591	39	16	application	application	NOUN
american_scientific_journal-591	39	17	of	of	ADP
american_scientific_journal-591	39	18	the	the	DET
american_scientific_journal-591	39	19	extreme	extreme	ADJ
american_scientific_journal-591	39	20	-	-	PUNCT
american_scientific_journal-591	39	21	value	value	NOUN
american_scientific_journal-591	39	22	theorem	theorem	NOUN
american_scientific_journal-591	39	23	,	,	PUNCT
american_scientific_journal-591	39	24	the	the	DET
american_scientific_journal-591	39	25	proof	proof	NOUN
american_scientific_journal-591	39	26	of	of	ADP
american_scientific_journal-591	39	27	which	which	PRON
american_scientific_journal-591	39	28	,	,	PUNCT
american_scientific_journal-591	39	29	he	he	PRON
american_scientific_journal-591	39	30	said	say	VERB
american_scientific_journal-591	39	31	can	can	AUX
american_scientific_journal-591	39	32	be	be	AUX
american_scientific_journal-591	39	33	found	find	VERB
american_scientific_journal-591	39	34	in	in	ADP
american_scientific_journal-591	39	35	advanced	advanced	ADJ
american_scientific_journal-591	39	36	calculus	calculus	NOUN
american_scientific_journal-591	39	37	text	text	NOUN
american_scientific_journal-591	39	38	.	.	PUNCT
american_scientific_journal-591	40	1	the	the	DET
american_scientific_journal-591	40	2	theorem	theorem	NOUN
american_scientific_journal-591	40	3	is	be	AUX
american_scientific_journal-591	40	4	stated	state	VERB
american_scientific_journal-591	40	5	as	as	SCONJ
american_scientific_journal-591	40	6	follows	follow	VERB
american_scientific_journal-591	40	7	:	:	PUNCT
american_scientific_journal-591	40	8	if	if	SCONJ
american_scientific_journal-591	40	9	the	the	DET
american_scientific_journal-591	40	10	function	function	NOUN
american_scientific_journal-591	40	11	f	f	PROPN
american_scientific_journal-591	40	12	is	be	AUX
american_scientific_journal-591	40	13	continuous	continuous	ADJ
american_scientific_journal-591	40	14	on	on	ADP
american_scientific_journal-591	40	15	the	the	DET
american_scientific_journal-591	40	16	closed	closed	ADJ
american_scientific_journal-591	40	17	interval	interval	NOUN
american_scientific_journal-591	40	18	[	[	X
american_scientific_journal-591	40	19	a	a	X
american_scientific_journal-591	40	20	,	,	PUNCT
american_scientific_journal-591	40	21	b	b	NOUN
american_scientific_journal-591	40	22	]	]	X
american_scientific_journal-591	40	23	,	,	PUNCT
american_scientific_journal-591	40	24	then	then	ADV
american_scientific_journal-591	40	25	f	f	PROPN
american_scientific_journal-591	40	26	has	have	VERB
american_scientific_journal-591	40	27	an	an	DET
american_scientific_journal-591	40	28	absolute	absolute	ADJ
american_scientific_journal-591	40	29	maximum	maximum	ADJ
american_scientific_journal-591	40	30	value	value	NOUN
american_scientific_journal-591	40	31	and	and	CCONJ
american_scientific_journal-591	40	32	an	an	DET
american_scientific_journal-591	40	33	absolute	absolute	ADJ
american_scientific_journal-591	40	34	minimum	minimum	ADJ
american_scientific_journal-591	40	35	value	value	NOUN
american_scientific_journal-591	40	36	on	on	ADP
american_scientific_journal-591	40	37	[	[	X
american_scientific_journal-591	40	38	a	a	X
american_scientific_journal-591	40	39	,	,	PUNCT
american_scientific_journal-591	40	40	b	b	NOUN
american_scientific_journal-591	40	41	]	]	X
american_scientific_journal-591	40	42	.	.	PUNCT
american_scientific_journal-591	41	1	he	he	PRON
american_scientific_journal-591	41	2	further	far	ADV
american_scientific_journal-591	41	3	explained	explain	VERB
american_scientific_journal-591	41	4	that	that	SCONJ
american_scientific_journal-591	41	5	an	an	DET
american_scientific_journal-591	41	6	absolute	absolute	ADJ
american_scientific_journal-591	41	7	extremum	extremum	NOUN
american_scientific_journal-591	41	8	of	of	ADP
american_scientific_journal-591	41	9	a	a	DET
american_scientific_journal-591	41	10	function	function	NOUN
american_scientific_journal-591	41	11	continuous	continuous	ADJ
american_scientific_journal-591	41	12	on	on	ADP
american_scientific_journal-591	41	13	a	a	DET
american_scientific_journal-591	41	14	closed	closed	ADJ
american_scientific_journal-591	41	15	interval	interval	NOUN
american_scientific_journal-591	41	16	must	must	AUX
american_scientific_journal-591	41	17	be	be	AUX
american_scientific_journal-591	41	18	either	either	CCONJ
american_scientific_journal-591	41	19	a	a	DET
american_scientific_journal-591	41	20	relative	relative	ADJ
american_scientific_journal-591	41	21	extremum	extremum	NOUN
american_scientific_journal-591	41	22	or	or	CCONJ
american_scientific_journal-591	41	23	a	a	DET
american_scientific_journal-591	41	24	function	function	NOUN
american_scientific_journal-591	41	25	value	value	NOUN
american_scientific_journal-591	41	26	at	at	ADP
american_scientific_journal-591	41	27	an	an	DET
american_scientific_journal-591	41	28	endpoint	endpoint	NOUN
american_scientific_journal-591	41	29	of	of	ADP
american_scientific_journal-591	41	30	the	the	DET
american_scientific_journal-591	41	31	interval	interval	NOUN
american_scientific_journal-591	41	32	.	.	PUNCT
american_scientific_journal-591	42	1	such	such	ADJ
american_scientific_journal-591	42	2	solution	solution	NOUN
american_scientific_journal-591	42	3	provided	provide	VERB
american_scientific_journal-591	42	4	by	by	ADP
american_scientific_journal-591	42	5	leithold	leithold	NOUN
american_scientific_journal-591	42	6	and	and	CCONJ
american_scientific_journal-591	42	7	other	other	ADJ
american_scientific_journal-591	42	8	calculus	calculus	NOUN
american_scientific_journal-591	42	9	textbook	textbook	NOUN
american_scientific_journal-591	42	10	authors	author	NOUN
american_scientific_journal-591	42	11	entails	entail	VERB
american_scientific_journal-591	42	12	finding	find	VERB
american_scientific_journal-591	42	13	the	the	DET
american_scientific_journal-591	42	14	derivative	derivative	NOUN
american_scientific_journal-591	42	15	of	of	ADP
american_scientific_journal-591	42	16	a	a	DET
american_scientific_journal-591	42	17	function	function	NOUN
american_scientific_journal-591	42	18	and	and	CCONJ
american_scientific_journal-591	42	19	employs	employ	VERB
american_scientific_journal-591	42	20	somewhat	somewhat	ADV
american_scientific_journal-591	42	21	lengthy	lengthy	ADJ
american_scientific_journal-591	42	22	computations	computation	NOUN
american_scientific_journal-591	42	23	.	.	PUNCT
american_scientific_journal-591	43	1	hence	hence	ADV
american_scientific_journal-591	43	2	,	,	PUNCT
american_scientific_journal-591	43	3	in	in	ADP
american_scientific_journal-591	43	4	order	order	NOUN
american_scientific_journal-591	43	5	to	to	PART
american_scientific_journal-591	43	6	provide	provide	VERB
american_scientific_journal-591	43	7	a	a	DET
american_scientific_journal-591	43	8	straightforward	straightforward	ADJ
american_scientific_journal-591	43	9	solution	solution	NOUN
american_scientific_journal-591	43	10	,	,	PUNCT
american_scientific_journal-591	43	11	this	this	DET
american_scientific_journal-591	43	12	study	study	NOUN
american_scientific_journal-591	43	13	was	be	AUX
american_scientific_journal-591	43	14	conducted	conduct	VERB
american_scientific_journal-591	43	15	.	.	PUNCT
american_scientific_journal-591	44	1	the	the	DET
american_scientific_journal-591	44	2	aims	aim	NOUN
american_scientific_journal-591	44	3	of	of	ADP
american_scientific_journal-591	44	4	the	the	DET
american_scientific_journal-591	44	5	present	present	ADJ
american_scientific_journal-591	44	6	study	study	NOUN
american_scientific_journal-591	44	7	are	be	AUX
american_scientific_journal-591	44	8	two	two	NUM
american_scientific_journal-591	44	9	-	-	PUNCT
american_scientific_journal-591	44	10	fold	fold	ADJ
american_scientific_journal-591	44	11	:	:	PUNCT
american_scientific_journal-591	44	12	(	(	PUNCT
american_scientific_journal-591	44	13	1	1	X
american_scientific_journal-591	44	14	)	)	PUNCT
american_scientific_journal-591	44	15	derive	derive	VERB
american_scientific_journal-591	44	16	the	the	DET
american_scientific_journal-591	44	17	formula	formula	NOUN
american_scientific_journal-591	44	18	for	for	ADP
american_scientific_journal-591	44	19	solving	solve	VERB
american_scientific_journal-591	44	20	the	the	DET
american_scientific_journal-591	44	21	minimum	minimum	ADJ
american_scientific_journal-591	44	22	distance	distance	NOUN
american_scientific_journal-591	44	23	problem	problem	NOUN
american_scientific_journal-591	44	24	(	(	PUNCT
american_scientific_journal-591	44	25	a	a	X
american_scientific_journal-591	44	26	)	)	PUNCT
american_scientific_journal-591	44	27	geometrically	geometrically	ADV
american_scientific_journal-591	44	28	and	and	CCONJ
american_scientific_journal-591	44	29	(	(	PUNCT
american_scientific_journal-591	44	30	b	b	NOUN
american_scientific_journal-591	44	31	)	)	PUNCT
american_scientific_journal-591	44	32	analytically	analytically	ADV
american_scientific_journal-591	44	33	;	;	PUNCT
american_scientific_journal-591	44	34	and	and	CCONJ
american_scientific_journal-591	44	35	(	(	PUNCT
american_scientific_journal-591	44	36	2	2	X
american_scientific_journal-591	44	37	)	)	PUNCT
american_scientific_journal-591	44	38	present	present	ADJ
american_scientific_journal-591	44	39	problems	problem	NOUN
american_scientific_journal-591	44	40	and	and	CCONJ
american_scientific_journal-591	44	41	solutions	solution	NOUN
american_scientific_journal-591	44	42	to	to	PART
american_scientific_journal-591	44	43	illustrate	illustrate	VERB
american_scientific_journal-591	44	44	the	the	DET
american_scientific_journal-591	44	45	use	use	NOUN
american_scientific_journal-591	44	46	of	of	ADP
american_scientific_journal-591	44	47	the	the	DET
american_scientific_journal-591	44	48	derived	derive	VERB
american_scientific_journal-591	44	49	formula	formula	NOUN
american_scientific_journal-591	44	50	.	.	PUNCT
american_scientific_journal-591	45	1	the	the	DET
american_scientific_journal-591	45	2	whole	whole	ADJ
american_scientific_journal-591	45	3	point	point	NOUN
american_scientific_journal-591	45	4	of	of	ADP
american_scientific_journal-591	45	5	deriving	derive	VERB
american_scientific_journal-591	45	6	a	a	DET
american_scientific_journal-591	45	7	formula	formula	NOUN
american_scientific_journal-591	45	8	is	be	AUX
american_scientific_journal-591	45	9	that	that	SCONJ
american_scientific_journal-591	45	10	the	the	DET
american_scientific_journal-591	45	11	problem	problem	NOUN
american_scientific_journal-591	45	12	solver	solver	NOUN
american_scientific_journal-591	45	13	can	can	AUX
american_scientific_journal-591	45	14	go	go	VERB
american_scientific_journal-591	45	15	through	through	ADP
american_scientific_journal-591	45	16	a	a	DET
american_scientific_journal-591	45	17	line	line	NOUN
american_scientific_journal-591	45	18	of	of	ADP
american_scientific_journal-591	45	19	reasoning	reasoning	NOUN
american_scientific_journal-591	45	20	only	only	ADV
american_scientific_journal-591	45	21	once	once	ADV
american_scientific_journal-591	45	22	,	,	PUNCT
american_scientific_journal-591	45	23	and	and	CCONJ
american_scientific_journal-591	45	24	then	then	ADV
american_scientific_journal-591	45	25	apply	apply	VERB
american_scientific_journal-591	45	26	the	the	DET
american_scientific_journal-591	45	27	results	result	NOUN
american_scientific_journal-591	45	28	whenever	whenever	SCONJ
american_scientific_journal-591	45	29	there	there	PRON
american_scientific_journal-591	45	30	is	be	VERB
american_scientific_journal-591	45	31	a	a	DET
american_scientific_journal-591	45	32	need	need	NOUN
american_scientific_journal-591	45	33	for	for	ADP
american_scientific_journal-591	45	34	them	they	PRON
american_scientific_journal-591	45	35	,	,	PUNCT
american_scientific_journal-591	45	36	instead	instead	ADV
american_scientific_journal-591	45	37	of	of	ADP
american_scientific_journal-591	45	38	repeating	repeat	VERB
american_scientific_journal-591	45	39	the	the	DET
american_scientific_journal-591	45	40	same	same	ADJ
american_scientific_journal-591	45	41	reasoning	reasoning	NOUN
american_scientific_journal-591	45	42	process	process	NOUN
american_scientific_journal-591	45	43	over	over	ADV
american_scientific_journal-591	45	44	and	and	CCONJ
american_scientific_journal-591	45	45	over	over	ADV
american_scientific_journal-591	45	46	again	again	ADV
american_scientific_journal-591	45	47	.	.	PUNCT
american_scientific_journal-591	46	1	it	it	PRON
american_scientific_journal-591	46	2	is	be	AUX
american_scientific_journal-591	46	3	considered	consider	VERB
american_scientific_journal-591	46	4	by	by	ADP
american_scientific_journal-591	46	5	many	many	ADJ
american_scientific_journal-591	46	6	that	that	SCONJ
american_scientific_journal-591	46	7	the	the	DET
american_scientific_journal-591	46	8	most	most	ADV
american_scientific_journal-591	46	9	vital	vital	ADJ
american_scientific_journal-591	46	10	tool	tool	NOUN
american_scientific_journal-591	46	11	in	in	ADP
american_scientific_journal-591	46	12	solving	solve	VERB
american_scientific_journal-591	46	13	a	a	DET
american_scientific_journal-591	46	14	mathematical	mathematical	ADJ
american_scientific_journal-591	46	15	problem	problem	NOUN
american_scientific_journal-591	46	16	is	be	AUX
american_scientific_journal-591	46	17	a	a	DET
american_scientific_journal-591	46	18	formula	formula	NOUN
american_scientific_journal-591	46	19	.	.	PUNCT
american_scientific_journal-591	47	1	2	2	X
american_scientific_journal-591	47	2	.	.	X
american_scientific_journal-591	47	3	methodology	methodology	NOUN
american_scientific_journal-591	47	4	this	this	DET
american_scientific_journal-591	47	5	study	study	NOUN
american_scientific_journal-591	47	6	is	be	AUX
american_scientific_journal-591	47	7	a	a	DET
american_scientific_journal-591	47	8	basic	basic	ADJ
american_scientific_journal-591	47	9	research	research	NOUN
american_scientific_journal-591	47	10	that	that	PRON
american_scientific_journal-591	47	11	employs	employ	VERB
american_scientific_journal-591	47	12	mathematical	mathematical	ADJ
american_scientific_journal-591	47	13	exploration	exploration	NOUN
american_scientific_journal-591	47	14	and	and	CCONJ
american_scientific_journal-591	47	15	experimentation	experimentation	NOUN
american_scientific_journal-591	47	16	.	.	PUNCT
american_scientific_journal-591	48	1	the	the	DET
american_scientific_journal-591	48	2	researchers	researcher	NOUN
american_scientific_journal-591	48	3	explored	explore	VERB
american_scientific_journal-591	48	4	the	the	DET
american_scientific_journal-591	48	5	varied	varied	ADJ
american_scientific_journal-591	48	6	concepts	concept	NOUN
american_scientific_journal-591	48	7	regarding	regard	VERB
american_scientific_journal-591	48	8	the	the	DET
american_scientific_journal-591	48	9	subject	subject	NOUN
american_scientific_journal-591	48	10	of	of	ADP
american_scientific_journal-591	48	11	study	study	NOUN
american_scientific_journal-591	48	12	presented	present	VERB
american_scientific_journal-591	48	13	in	in	ADP
american_scientific_journal-591	48	14	different	different	ADJ
american_scientific_journal-591	48	15	areas	area	NOUN
american_scientific_journal-591	48	16	of	of	ADP
american_scientific_journal-591	48	17	mathematics	mathematic	NOUN
american_scientific_journal-591	48	18	namely	namely	ADV
american_scientific_journal-591	48	19	,	,	PUNCT
american_scientific_journal-591	48	20	plane	plane	NOUN
american_scientific_journal-591	48	21	geometry	geometry	NOUN
american_scientific_journal-591	48	22	,	,	PUNCT
american_scientific_journal-591	48	23	analytic	analytic	ADJ
american_scientific_journal-591	48	24	geometry	geometry	NOUN
american_scientific_journal-591	48	25	and	and	CCONJ
american_scientific_journal-591	48	26	differential	differential	ADJ
american_scientific_journal-591	48	27	calculus	calculus	NOUN
american_scientific_journal-591	48	28	.	.	PUNCT
american_scientific_journal-591	49	1	in	in	ADP
american_scientific_journal-591	49	2	this	this	DET
american_scientific_journal-591	49	3	study	study	NOUN
american_scientific_journal-591	49	4	,	,	PUNCT
american_scientific_journal-591	49	5	the	the	DET
american_scientific_journal-591	49	6	derivations	derivation	NOUN
american_scientific_journal-591	49	7	of	of	ADP
american_scientific_journal-591	49	8	the	the	DET
american_scientific_journal-591	49	9	formula	formula	NOUN
american_scientific_journal-591	49	10	for	for	ADP
american_scientific_journal-591	49	11	calculating	calculate	VERB
american_scientific_journal-591	49	12	the	the	DET
american_scientific_journal-591	49	13	minimum	minimum	ADJ
american_scientific_journal-591	49	14	distance	distance	NOUN
american_scientific_journal-591	49	15	were	be	AUX
american_scientific_journal-591	49	16	done	do	VERB
american_scientific_journal-591	49	17	in	in	ADP
american_scientific_journal-591	49	18	two	two	NUM
american_scientific_journal-591	49	19	ways	way	NOUN
american_scientific_journal-591	49	20	:	:	PUNCT
american_scientific_journal-591	49	21	the	the	DET
american_scientific_journal-591	49	22	geometrical	geometrical	ADJ
american_scientific_journal-591	49	23	approach	approach	NOUN
american_scientific_journal-591	49	24	and	and	CCONJ
american_scientific_journal-591	49	25	the	the	DET
american_scientific_journal-591	49	26	analytical	analytical	ADJ
american_scientific_journal-591	49	27	approach	approach	NOUN
american_scientific_journal-591	49	28	.	.	PUNCT
american_scientific_journal-591	50	1	a	a	DET
american_scientific_journal-591	50	2	series	series	NOUN
american_scientific_journal-591	50	3	of	of	ADP
american_scientific_journal-591	50	4	mathematical	mathematical	ADJ
american_scientific_journal-591	50	5	experimentations	experimentation	NOUN
american_scientific_journal-591	50	6	and	and	CCONJ
american_scientific_journal-591	50	7	computations	computation	NOUN
american_scientific_journal-591	50	8	was	be	AUX
american_scientific_journal-591	50	9	also	also	ADV
american_scientific_journal-591	50	10	done	do	VERB
american_scientific_journal-591	50	11	in	in	ADP
american_scientific_journal-591	50	12	order	order	NOUN
american_scientific_journal-591	50	13	to	to	PART
american_scientific_journal-591	50	14	establish	establish	VERB
american_scientific_journal-591	50	15	the	the	DET
american_scientific_journal-591	50	16	proofs	proof	NOUN
american_scientific_journal-591	50	17	of	of	ADP
american_scientific_journal-591	50	18	arguments	argument	NOUN
american_scientific_journal-591	50	19	and	and	CCONJ
american_scientific_journal-591	50	20	the	the	DET
american_scientific_journal-591	50	21	use	use	NOUN
american_scientific_journal-591	50	22	of	of	ADP
american_scientific_journal-591	50	23	the	the	DET
american_scientific_journal-591	50	24	derived	derive	VERB
american_scientific_journal-591	50	25	formula	formula	NOUN
american_scientific_journal-591	50	26	for	for	ADP
american_scientific_journal-591	50	27	different	different	ADJ
american_scientific_journal-591	50	28	cases	case	NOUN
american_scientific_journal-591	50	29	.	.	PUNCT
american_scientific_journal-591	51	1	results	result	NOUN
american_scientific_journal-591	51	2	of	of	ADP
american_scientific_journal-591	51	3	the	the	DET
american_scientific_journal-591	51	4	study	study	NOUN
american_scientific_journal-591	51	5	were	be	AUX
american_scientific_journal-591	51	6	also	also	ADV
american_scientific_journal-591	51	7	compared	compare	VERB
american_scientific_journal-591	51	8	with	with	ADP
american_scientific_journal-591	51	9	previously	previously	ADV
american_scientific_journal-591	51	10	established	establish	VERB
american_scientific_journal-591	51	11	principles	principle	NOUN
american_scientific_journal-591	51	12	.	.	PUNCT
american_scientific_journal-591	52	1	aside	aside	ADV
american_scientific_journal-591	52	2	from	from	ADP
american_scientific_journal-591	52	3	the	the	DET
american_scientific_journal-591	52	4	pythagorean	pythagorean	PROPN
american_scientific_journal-591	52	5	relation	relation	NOUN
american_scientific_journal-591	52	6	and	and	CCONJ
american_scientific_journal-591	52	7	the	the	DET
american_scientific_journal-591	52	8	concepts	concept	NOUN
american_scientific_journal-591	52	9	of	of	ADP
american_scientific_journal-591	52	10	minimum	minimum	ADJ
american_scientific_journal-591	52	11	distance	distance	NOUN
american_scientific_journal-591	52	12	in	in	ADP
american_scientific_journal-591	52	13	geometry	geometry	NOUN
american_scientific_journal-591	52	14	and	and	CCONJ
american_scientific_journal-591	52	15	calculus	calculus	NOUN
american_scientific_journal-591	52	16	,	,	PUNCT
american_scientific_journal-591	52	17	one	one	NUM
american_scientific_journal-591	52	18	principle	principle	NOUN
american_scientific_journal-591	52	19	that	that	PRON
american_scientific_journal-591	52	20	is	be	AUX
american_scientific_journal-591	52	21	found	find	VERB
american_scientific_journal-591	52	22	to	to	PART
american_scientific_journal-591	52	23	be	be	AUX
american_scientific_journal-591	52	24	very	very	ADV
american_scientific_journal-591	52	25	much	much	ADV
american_scientific_journal-591	52	26	related	related	ADJ
american_scientific_journal-591	52	27	is	be	AUX
american_scientific_journal-591	52	28	the	the	DET
american_scientific_journal-591	52	29	fermat	fermat	PROPN
american_scientific_journal-591	52	30	’s	’s	PART
american_scientific_journal-591	52	31	principle	principle	NOUN
american_scientific_journal-591	52	32	of	of	ADP
american_scientific_journal-591	52	33	optics	optic	NOUN
american_scientific_journal-591	52	34	,	,	PUNCT
american_scientific_journal-591	52	35	which	which	PRON
american_scientific_journal-591	52	36	states	state	VERB
american_scientific_journal-591	52	37	that	that	SCONJ
american_scientific_journal-591	52	38	the	the	DET
american_scientific_journal-591	52	39	light	light	NOUN
american_scientific_journal-591	52	40	traveling	travel	VERB
american_scientific_journal-591	52	41	from	from	ADP
american_scientific_journal-591	52	42	one	one	NUM
american_scientific_journal-591	52	43	point	point	NOUN
american_scientific_journal-591	52	44	to	to	ADP
american_scientific_journal-591	52	45	another	another	PRON
american_scientific_journal-591	52	46	follows	follow	VERB
american_scientific_journal-591	52	47	the	the	DET
american_scientific_journal-591	52	48	path	path	NOUN
american_scientific_journal-591	52	49	for	for	ADP
american_scientific_journal-591	52	50	which	which	PRON
american_scientific_journal-591	52	51	the	the	DET
american_scientific_journal-591	52	52	total	total	ADJ
american_scientific_journal-591	52	53	travel	travel	NOUN
american_scientific_journal-591	52	54	time	time	NOUN
american_scientific_journal-591	52	55	is	be	AUX
american_scientific_journal-591	52	56	minimum	minimum	ADJ
american_scientific_journal-591	52	57	.	.	PUNCT
american_scientific_journal-591	53	1	in	in	ADP
american_scientific_journal-591	53	2	a	a	DET
american_scientific_journal-591	53	3	uniform	uniform	ADJ
american_scientific_journal-591	53	4	medium	medium	NOUN
american_scientific_journal-591	53	5	,	,	PUNCT
american_scientific_journal-591	53	6	the	the	DET
american_scientific_journal-591	53	7	paths	path	NOUN
american_scientific_journal-591	53	8	of	of	ADP
american_scientific_journal-591	53	9	minimum	minimum	ADJ
american_scientific_journal-591	53	10	time	time	NOUN
american_scientific_journal-591	53	11	and	and	CCONJ
american_scientific_journal-591	53	12	shortest	short	ADJ
american_scientific_journal-591	53	13	distance	distance	NOUN
american_scientific_journal-591	53	14	turn	turn	VERB
american_scientific_journal-591	53	15	out	out	ADP
american_scientific_journal-591	53	16	to	to	PART
american_scientific_journal-591	53	17	be	be	AUX
american_scientific_journal-591	53	18	the	the	DET
american_scientific_journal-591	53	19	same	same	ADJ
american_scientific_journal-591	53	20	,	,	PUNCT
american_scientific_journal-591	53	21	so	so	SCONJ
american_scientific_journal-591	53	22	that	that	SCONJ
american_scientific_journal-591	53	23	the	the	DET
american_scientific_journal-591	53	24	light	light	NOUN
american_scientific_journal-591	53	25	,	,	PUNCT
american_scientific_journal-591	53	26	if	if	SCONJ
american_scientific_journal-591	53	27	unobstructed	unobstructed	ADJ
american_scientific_journal-591	53	28	,	,	PUNCT
american_scientific_journal-591	53	29	travels	travel	VERB
american_scientific_journal-591	53	30	along	along	ADP
american_scientific_journal-591	53	31	a	a	DET
american_scientific_journal-591	53	32	straight	straight	ADJ
american_scientific_journal-591	53	33	line	line	NOUN
american_scientific_journal-591	53	34	,	,	PUNCT
american_scientific_journal-591	53	35	as	as	SCONJ
american_scientific_journal-591	53	36	mentioned	mention	VERB
american_scientific_journal-591	53	37	in	in	ADP
american_scientific_journal-591	53	38	[	[	X
american_scientific_journal-591	53	39	10	10	NUM
american_scientific_journal-591	53	40	]	]	PUNCT
american_scientific_journal-591	53	41	.	.	PUNCT
american_scientific_journal-591	54	1	3	3	X
american_scientific_journal-591	54	2	.	.	NOUN
american_scientific_journal-591	54	3	results	result	NOUN
american_scientific_journal-591	54	4	and	and	CCONJ
american_scientific_journal-591	54	5	discussion	discussion	VERB
american_scientific_journal-591	54	6	the	the	DET
american_scientific_journal-591	54	7	formula	formula	NOUN
american_scientific_journal-591	54	8	for	for	ADP
american_scientific_journal-591	54	9	finding	find	VERB
american_scientific_journal-591	54	10	the	the	DET
american_scientific_journal-591	54	11	minimum	minimum	ADJ
american_scientific_journal-591	54	12	distance	distance	NOUN
american_scientific_journal-591	54	13	from	from	ADP
american_scientific_journal-591	54	14	a	a	DET
american_scientific_journal-591	54	15	point	point	NOUN
american_scientific_journal-591	54	16	to	to	ADP
american_scientific_journal-591	54	17	a	a	DET
american_scientific_journal-591	54	18	line	line	NOUN
american_scientific_journal-591	54	19	to	to	ADP
american_scientific_journal-591	54	20	another	another	DET
american_scientific_journal-591	54	21	point	point	NOUN
american_scientific_journal-591	54	22	on	on	ADP
american_scientific_journal-591	54	23	the	the	DET
american_scientific_journal-591	54	24	same	same	ADJ
american_scientific_journal-591	54	25	side	side	NOUN
american_scientific_journal-591	54	26	of	of	ADP
american_scientific_journal-591	54	27	the	the	DET
american_scientific_journal-591	54	28	line	line	NOUN
american_scientific_journal-591	54	29	is	be	AUX
american_scientific_journal-591	54	30	given	give	VERB
american_scientific_journal-591	54	31	by	by	ADP
american_scientific_journal-591	54	32	2	2	NUM
american_scientific_journal-591	54	33	2	2	NUM
american_scientific_journal-591	54	34	(	(	PUNCT
american_scientific_journal-591	54	35	)	)	PUNCT
american_scientific_journal-591	54	36	d	d	NOUN
american_scientific_journal-591	54	37	a	a	DET
american_scientific_journal-591	54	38	b	b	NOUN
american_scientific_journal-591	54	39	c=	c=	NOUN
american_scientific_journal-591	54	40	+	+	X
american_scientific_journal-591	55	1	+	+	CCONJ
american_scientific_journal-591	55	2	,	,	PUNCT
american_scientific_journal-591	55	3	86	86	NUM
american_scientific_journal-591	55	4	american	american	ADJ
american_scientific_journal-591	55	5	scientific	scientific	ADJ
american_scientific_journal-591	55	6	research	research	NOUN
american_scientific_journal-591	55	7	journal	journal	NOUN
american_scientific_journal-591	55	8	for	for	ADP
american_scientific_journal-591	55	9	engineering	engineering	NOUN
american_scientific_journal-591	55	10	,	,	PUNCT
american_scientific_journal-591	55	11	technology	technology	NOUN
american_scientific_journal-591	55	12	,	,	PUNCT
american_scientific_journal-591	55	13	and	and	CCONJ
american_scientific_journal-591	55	14	sciences	science	NOUN
american_scientific_journal-591	55	15	(	(	PUNCT
american_scientific_journal-591	55	16	asrjets	asrjet	NOUN
american_scientific_journal-591	55	17	)	)	PUNCT
american_scientific_journal-591	55	18	(	(	PUNCT
american_scientific_journal-591	55	19	2015	2015	NUM
american_scientific_journal-591	55	20	)	)	PUNCT
american_scientific_journal-591	55	21	volume	volume	NOUN
american_scientific_journal-591	55	22	11	11	NUM
american_scientific_journal-591	55	23	,	,	PUNCT
american_scientific_journal-591	55	24	no	no	DET
american_scientific_journal-591	55	25	1	1	NUM
american_scientific_journal-591	55	26	,	,	PUNCT
american_scientific_journal-591	55	27	pp	pp	ADV
american_scientific_journal-591	55	28	84	84	NUM
american_scientific_journal-591	55	29	-	-	SYM
american_scientific_journal-591	55	30	95	95	NUM
american_scientific_journal-591	55	31	where	where	SCONJ
american_scientific_journal-591	55	32	d	d	NOUN
american_scientific_journal-591	55	33	is	be	AUX
american_scientific_journal-591	55	34	the	the	DET
american_scientific_journal-591	55	35	minimum	minimum	ADJ
american_scientific_journal-591	55	36	distance	distance	NOUN
american_scientific_journal-591	55	37	,	,	PUNCT
american_scientific_journal-591	55	38	a	a	PRON
american_scientific_journal-591	55	39	is	be	AUX
american_scientific_journal-591	55	40	the	the	DET
american_scientific_journal-591	55	41	distance	distance	NOUN
american_scientific_journal-591	55	42	from	from	ADP
american_scientific_journal-591	55	43	the	the	DET
american_scientific_journal-591	55	44	first	first	ADJ
american_scientific_journal-591	55	45	point	point	NOUN
american_scientific_journal-591	55	46	to	to	ADP
american_scientific_journal-591	55	47	the	the	DET
american_scientific_journal-591	55	48	line	line	NOUN
american_scientific_journal-591	55	49	,	,	PUNCT
american_scientific_journal-591	55	50	b	b	NOUN
american_scientific_journal-591	55	51	is	be	AUX
american_scientific_journal-591	55	52	the	the	DET
american_scientific_journal-591	55	53	distance	distance	NOUN
american_scientific_journal-591	55	54	from	from	ADP
american_scientific_journal-591	55	55	the	the	DET
american_scientific_journal-591	55	56	second	second	ADJ
american_scientific_journal-591	55	57	point	point	NOUN
american_scientific_journal-591	55	58	to	to	ADP
american_scientific_journal-591	55	59	the	the	DET
american_scientific_journal-591	55	60	line	line	NOUN
american_scientific_journal-591	55	61	and	and	CCONJ
american_scientific_journal-591	55	62	c	c	NOUN
american_scientific_journal-591	55	63	is	be	AUX
american_scientific_journal-591	55	64	the	the	DET
american_scientific_journal-591	55	65	distance	distance	NOUN
american_scientific_journal-591	55	66	between	between	ADP
american_scientific_journal-591	55	67	the	the	DET
american_scientific_journal-591	55	68	two	two	NUM
american_scientific_journal-591	55	69	points	point	NOUN
american_scientific_journal-591	55	70	in	in	ADP
american_scientific_journal-591	55	71	the	the	DET
american_scientific_journal-591	55	72	line	line	NOUN
american_scientific_journal-591	55	73	nearest	nearest	ADP
american_scientific_journal-591	55	74	the	the	DET
american_scientific_journal-591	55	75	two	two	NUM
american_scientific_journal-591	55	76	given	give	VERB
american_scientific_journal-591	55	77	points	point	NOUN
american_scientific_journal-591	55	78	(	(	PUNCT
american_scientific_journal-591	55	79	see	see	VERB
american_scientific_journal-591	55	80	figure	figure	NOUN
american_scientific_journal-591	55	81	2	2	NUM
american_scientific_journal-591	55	82	)	)	PUNCT
american_scientific_journal-591	55	83	.	.	PUNCT
american_scientific_journal-591	56	1	figure	figure	VERB
american_scientific_journal-591	56	2	2	2	NUM
american_scientific_journal-591	56	3	:	:	PUNCT
american_scientific_journal-591	56	4	distances	distance	NOUN
american_scientific_journal-591	56	5	a	a	DET
american_scientific_journal-591	56	6	,	,	PUNCT
american_scientific_journal-591	56	7	b	b	PROPN
american_scientific_journal-591	56	8	and	and	CCONJ
american_scientific_journal-591	56	9	c	c	PROPN
american_scientific_journal-591	56	10	of	of	ADP
american_scientific_journal-591	56	11	the	the	DET
american_scientific_journal-591	56	12	minimum	minimum	ADJ
american_scientific_journal-591	56	13	distance	distance	NOUN
american_scientific_journal-591	56	14	formula	formula	NOUN
american_scientific_journal-591	56	15	in	in	ADP
american_scientific_journal-591	56	16	addition	addition	NOUN
american_scientific_journal-591	56	17	,	,	PUNCT
american_scientific_journal-591	56	18	the	the	DET
american_scientific_journal-591	56	19	formula	formula	NOUN
american_scientific_journal-591	56	20	for	for	ADP
american_scientific_journal-591	56	21	locating	locate	VERB
american_scientific_journal-591	56	22	the	the	DET
american_scientific_journal-591	56	23	point	point	NOUN
american_scientific_journal-591	56	24	in	in	ADP
american_scientific_journal-591	56	25	the	the	DET
american_scientific_journal-591	56	26	line	line	NOUN
american_scientific_journal-591	56	27	that	that	PRON
american_scientific_journal-591	56	28	will	will	AUX
american_scientific_journal-591	56	29	lead	lead	VERB
american_scientific_journal-591	56	30	to	to	ADP
american_scientific_journal-591	56	31	having	have	VERB
american_scientific_journal-591	56	32	the	the	DET
american_scientific_journal-591	56	33	minimum	minimum	ADJ
american_scientific_journal-591	56	34	distance	distance	NOUN
american_scientific_journal-591	56	35	is	be	AUX
american_scientific_journal-591	56	36	given	give	VERB
american_scientific_journal-591	56	37	acx	acx	PROPN
american_scientific_journal-591	56	38	a	a	DET
american_scientific_journal-591	56	39	b	b	NOUN
american_scientific_journal-591	56	40	=	=	SYM
american_scientific_journal-591	57	1	+	+	CCONJ
american_scientific_journal-591	57	2	,	,	PUNCT
american_scientific_journal-591	57	3	where	where	SCONJ
american_scientific_journal-591	57	4	x	x	PRON
american_scientific_journal-591	57	5	is	be	AUX
american_scientific_journal-591	57	6	the	the	DET
american_scientific_journal-591	57	7	distance	distance	NOUN
american_scientific_journal-591	57	8	from	from	ADP
american_scientific_journal-591	57	9	the	the	DET
american_scientific_journal-591	57	10	point	point	NOUN
american_scientific_journal-591	57	11	in	in	ADP
american_scientific_journal-591	57	12	the	the	DET
american_scientific_journal-591	57	13	line	line	NOUN
american_scientific_journal-591	57	14	nearest	nearest	ADP
american_scientific_journal-591	57	15	the	the	DET
american_scientific_journal-591	57	16	first	first	ADJ
american_scientific_journal-591	57	17	point	point	NOUN
american_scientific_journal-591	57	18	to	to	ADP
american_scientific_journal-591	57	19	the	the	DET
american_scientific_journal-591	57	20	point	point	NOUN
american_scientific_journal-591	57	21	in	in	ADP
american_scientific_journal-591	57	22	the	the	DET
american_scientific_journal-591	57	23	line	line	NOUN
american_scientific_journal-591	57	24	where	where	SCONJ
american_scientific_journal-591	57	25	the	the	DET
american_scientific_journal-591	57	26	two	two	NUM
american_scientific_journal-591	57	27	given	give	VERB
american_scientific_journal-591	57	28	points	point	NOUN
american_scientific_journal-591	57	29	are	be	AUX
american_scientific_journal-591	57	30	to	to	PART
american_scientific_journal-591	57	31	be	be	AUX
american_scientific_journal-591	57	32	connected	connect	VERB
american_scientific_journal-591	57	33	to	to	PART
american_scientific_journal-591	57	34	give	give	VERB
american_scientific_journal-591	57	35	the	the	DET
american_scientific_journal-591	57	36	minimum	minimum	ADJ
american_scientific_journal-591	57	37	distance	distance	NOUN
american_scientific_journal-591	57	38	and	and	CCONJ
american_scientific_journal-591	57	39	a	a	DET
american_scientific_journal-591	57	40	,	,	PUNCT
american_scientific_journal-591	57	41	b	b	NOUN
american_scientific_journal-591	57	42	and	and	CCONJ
american_scientific_journal-591	57	43	c	c	PROPN
american_scientific_journal-591	57	44	are	be	AUX
american_scientific_journal-591	57	45	the	the	DET
american_scientific_journal-591	57	46	distances	distance	NOUN
american_scientific_journal-591	57	47	described	describe	VERB
american_scientific_journal-591	57	48	above	above	ADV
american_scientific_journal-591	57	49	.	.	PUNCT
american_scientific_journal-591	58	1	3.1	3.1	NUM
american_scientific_journal-591	58	2	.	.	PUNCT
american_scientific_journal-591	58	3	derivation	derivation	NOUN
american_scientific_journal-591	58	4	of	of	ADP
american_scientific_journal-591	58	5	the	the	DET
american_scientific_journal-591	58	6	formula	formula	NOUN
american_scientific_journal-591	58	7	by	by	ADP
american_scientific_journal-591	58	8	geometrical	geometrical	ADJ
american_scientific_journal-591	58	9	approach	approach	NOUN
american_scientific_journal-591	58	10	the	the	DET
american_scientific_journal-591	58	11	minimum	minimum	ADJ
american_scientific_journal-591	58	12	distance	distance	NOUN
american_scientific_journal-591	58	13	formula	formula	NOUN
american_scientific_journal-591	58	14	given	give	VERB
american_scientific_journal-591	58	15	above	above	ADV
american_scientific_journal-591	58	16	can	can	AUX
american_scientific_journal-591	58	17	be	be	AUX
american_scientific_journal-591	58	18	derived	derive	VERB
american_scientific_journal-591	58	19	using	use	VERB
american_scientific_journal-591	58	20	geometrical	geometrical	ADJ
american_scientific_journal-591	58	21	reasoning	reasoning	NOUN
american_scientific_journal-591	58	22	as	as	SCONJ
american_scientific_journal-591	58	23	follows	follow	VERB
american_scientific_journal-591	58	24	:	:	PUNCT
american_scientific_journal-591	58	25	given	give	VERB
american_scientific_journal-591	58	26	a	a	DET
american_scientific_journal-591	58	27	plane	plane	NOUN
american_scientific_journal-591	58	28	,	,	PUNCT
american_scientific_journal-591	58	29	a	a	DET
american_scientific_journal-591	58	30	line	line	NOUN
american_scientific_journal-591	58	31	l	l	NOUN
american_scientific_journal-591	58	32	and	and	CCONJ
american_scientific_journal-591	58	33	two	two	NUM
american_scientific_journal-591	58	34	points	point	NOUN
american_scientific_journal-591	58	35	a	a	PRON
american_scientific_journal-591	58	36	and	and	CCONJ
american_scientific_journal-591	58	37	b	b	NOUN
american_scientific_journal-591	58	38	on	on	ADP
american_scientific_journal-591	58	39	the	the	DET
american_scientific_journal-591	58	40	plane	plane	NOUN
american_scientific_journal-591	58	41	lying	lie	VERB
american_scientific_journal-591	58	42	on	on	ADP
american_scientific_journal-591	58	43	the	the	DET
american_scientific_journal-591	58	44	same	same	ADJ
american_scientific_journal-591	58	45	side	side	NOUN
american_scientific_journal-591	58	46	of	of	ADP
american_scientific_journal-591	58	47	l	l	NOUN
american_scientific_journal-591	58	48	,	,	PUNCT
american_scientific_journal-591	58	49	let	let	VERB
american_scientific_journal-591	58	50	a	a	PRON
american_scientific_journal-591	58	51	be	be	AUX
american_scientific_journal-591	58	52	the	the	DET
american_scientific_journal-591	58	53	distance	distance	NOUN
american_scientific_journal-591	58	54	from	from	ADP
american_scientific_journal-591	58	55	a	a	PRON
american_scientific_journal-591	58	56	to	to	ADP
american_scientific_journal-591	58	57	l	l	NOUN
american_scientific_journal-591	58	58	,	,	PUNCT
american_scientific_journal-591	58	59	b	b	X
american_scientific_journal-591	58	60	be	be	AUX
american_scientific_journal-591	58	61	the	the	DET
american_scientific_journal-591	58	62	distance	distance	NOUN
american_scientific_journal-591	58	63	from	from	ADP
american_scientific_journal-591	58	64	b	b	PROPN
american_scientific_journal-591	58	65	to	to	ADP
american_scientific_journal-591	58	66	l	l	NOUN
american_scientific_journal-591	58	67	,	,	PUNCT
american_scientific_journal-591	58	68	aʹʹ	aʹʹ	VERB
american_scientific_journal-591	58	69	be	be	AUX
american_scientific_journal-591	58	70	the	the	DET
american_scientific_journal-591	58	71	point	point	NOUN
american_scientific_journal-591	58	72	in	in	ADP
american_scientific_journal-591	58	73	l	l	NOUN
american_scientific_journal-591	59	1	such	such	ADJ
american_scientific_journal-591	59	2	that	that	PRON
american_scientific_journal-591	59	3	aaad	aaad	NOUN
american_scientific_journal-591	59	4	=	=	SYM
american_scientific_journal-591	59	5	′′	′′	PROPN
american_scientific_journal-591	59	6	)	)	PUNCT
american_scientific_journal-591	59	7	,	,	PUNCT
american_scientific_journal-591	59	8	(	(	PUNCT
american_scientific_journal-591	59	9	,	,	PUNCT
american_scientific_journal-591	59	10	bʹʹ	bʹʹ	NOUN
american_scientific_journal-591	59	11	be	be	AUX
american_scientific_journal-591	59	12	the	the	DET
american_scientific_journal-591	59	13	point	point	NOUN
american_scientific_journal-591	59	14	in	in	ADP
american_scientific_journal-591	59	15	l	l	NOUN
american_scientific_journal-591	59	16	such	such	ADJ
american_scientific_journal-591	59	17	that	that	PRON
american_scientific_journal-591	59	18	bbbd	bbbd	NOUN
american_scientific_journal-591	59	19	=	=	SYM
american_scientific_journal-591	59	20	′′	′′	PROPN
american_scientific_journal-591	59	21	)	)	PUNCT
american_scientific_journal-591	59	22	,	,	PUNCT
american_scientific_journal-591	59	23	(	(	PUNCT
american_scientific_journal-591	59	24	,	,	PUNCT
american_scientific_journal-591	59	25	and	and	CCONJ
american_scientific_journal-591	59	26	c	c	PROPN
american_scientific_journal-591	59	27	be	be	AUX
american_scientific_journal-591	59	28	the	the	DET
american_scientific_journal-591	59	29	distance	distance	NOUN
american_scientific_journal-591	59	30	from	from	ADP
american_scientific_journal-591	59	31	aʹʹ	aʹʹ	NOUN
american_scientific_journal-591	59	32	to	to	PART
american_scientific_journal-591	59	33	bʹʹ	bʹʹ	VERB
american_scientific_journal-591	59	34	or	or	CCONJ
american_scientific_journal-591	59	35	symbolically	symbolically	ADV
american_scientific_journal-591	59	36	,	,	PUNCT
american_scientific_journal-591	59	37	cbad	cbad	NOUN
american_scientific_journal-591	59	38	=	=	PROPN
american_scientific_journal-591	59	39	′′′′	′′′′	PROPN
american_scientific_journal-591	59	40	)	)	PUNCT
american_scientific_journal-591	59	41	,	,	PUNCT
american_scientific_journal-591	59	42	(	(	PUNCT
american_scientific_journal-591	59	43	(	(	PUNCT
american_scientific_journal-591	59	44	see	see	VERB
american_scientific_journal-591	59	45	figure	figure	NOUN
american_scientific_journal-591	59	46	3	3	NUM
american_scientific_journal-591	59	47	)	)	PUNCT
american_scientific_journal-591	59	48	.	.	PUNCT
american_scientific_journal-591	60	1	figure	figure	VERB
american_scientific_journal-591	60	2	3	3	NUM
american_scientific_journal-591	60	3	:	:	PUNCT
american_scientific_journal-591	60	4	minimum	minimum	ADJ
american_scientific_journal-591	60	5	distance	distance	NOUN
american_scientific_journal-591	60	6	problem	problem	NOUN
american_scientific_journal-591	60	7	in	in	ADP
american_scientific_journal-591	60	8	geometry	geometry	NOUN
american_scientific_journal-591	60	9	87	87	NUM
american_scientific_journal-591	60	10	american	american	PROPN
american_scientific_journal-591	60	11	scientific	scientific	ADJ
american_scientific_journal-591	60	12	research	research	NOUN
american_scientific_journal-591	60	13	journal	journal	NOUN
american_scientific_journal-591	60	14	for	for	ADP
american_scientific_journal-591	60	15	engineering	engineering	NOUN
american_scientific_journal-591	60	16	,	,	PUNCT
american_scientific_journal-591	60	17	technology	technology	NOUN
american_scientific_journal-591	60	18	,	,	PUNCT
american_scientific_journal-591	60	19	and	and	CCONJ
american_scientific_journal-591	60	20	sciences	science	NOUN
american_scientific_journal-591	60	21	(	(	PUNCT
american_scientific_journal-591	60	22	asrjets	asrjet	NOUN
american_scientific_journal-591	60	23	)	)	PUNCT
american_scientific_journal-591	60	24	(	(	PUNCT
american_scientific_journal-591	60	25	2015	2015	NUM
american_scientific_journal-591	60	26	)	)	PUNCT
american_scientific_journal-591	60	27	volume	volume	NOUN
american_scientific_journal-591	60	28	11	11	NUM
american_scientific_journal-591	60	29	,	,	PUNCT
american_scientific_journal-591	60	30	no	no	DET
american_scientific_journal-591	60	31	1	1	NUM
american_scientific_journal-591	60	32	,	,	PUNCT
american_scientific_journal-591	60	33	pp	pp	ADV
american_scientific_journal-591	60	34	84	84	NUM
american_scientific_journal-591	60	35	-	-	SYM
american_scientific_journal-591	60	36	95	95	NUM
american_scientific_journal-591	60	37	then	then	ADV
american_scientific_journal-591	60	38	,	,	PUNCT
american_scientific_journal-591	60	39	let	let	VERB
american_scientific_journal-591	60	40	p	p	PRON
american_scientific_journal-591	60	41	be	be	AUX
american_scientific_journal-591	60	42	a	a	DET
american_scientific_journal-591	60	43	point	point	NOUN
american_scientific_journal-591	60	44	in	in	ADP
american_scientific_journal-591	60	45	l	l	NOUN
american_scientific_journal-591	60	46	such	such	ADJ
american_scientific_journal-591	60	47	that	that	SCONJ
american_scientific_journal-591	60	48	the	the	DET
american_scientific_journal-591	60	49	distance	distance	NOUN
american_scientific_journal-591	60	50	from	from	ADP
american_scientific_journal-591	60	51	a	a	PRON
american_scientific_journal-591	60	52	to	to	ADP
american_scientific_journal-591	60	53	p	p	NOUN
american_scientific_journal-591	60	54	to	to	ADP
american_scientific_journal-591	60	55	b	b	NOUN
american_scientific_journal-591	60	56	is	be	AUX
american_scientific_journal-591	60	57	to	to	PART
american_scientific_journal-591	60	58	be	be	AUX
american_scientific_journal-591	60	59	the	the	DET
american_scientific_journal-591	60	60	minimum	minimum	ADJ
american_scientific_journal-591	60	61	distance	distance	NOUN
american_scientific_journal-591	60	62	possible	possible	ADJ
american_scientific_journal-591	60	63	denoted	denote	VERB
american_scientific_journal-591	60	64	by	by	ADP
american_scientific_journal-591	60	65	d.	d.	PROPN
american_scientific_journal-591	60	66	symbolically	symbolically	ADV
american_scientific_journal-591	60	67	,	,	PUNCT
american_scientific_journal-591	61	1	d	d	PROPN
american_scientific_journal-591	61	2	=	=	SYM
american_scientific_journal-591	61	3	d(a	d(a	PROPN
american_scientific_journal-591	61	4	,	,	PUNCT
american_scientific_journal-591	61	5	p	p	NOUN
american_scientific_journal-591	61	6	)	)	PUNCT
american_scientific_journal-591	62	1	+	+	CCONJ
american_scientific_journal-591	62	2	d(p	d(p	PROPN
american_scientific_journal-591	62	3	,	,	PUNCT
american_scientific_journal-591	62	4	b	b	NOUN
american_scientific_journal-591	62	5	)	)	PUNCT
american_scientific_journal-591	62	6	.	.	PUNCT
american_scientific_journal-591	63	1	next	next	ADV
american_scientific_journal-591	63	2	,	,	PUNCT
american_scientific_journal-591	63	3	constructing	construct	VERB
american_scientific_journal-591	63	4	a	a	DET
american_scientific_journal-591	63	5	point	point	NOUN
american_scientific_journal-591	63	6	b	b	NOUN
american_scientific_journal-591	63	7	’	'	PUNCT
american_scientific_journal-591	63	8	to	to	PART
american_scientific_journal-591	63	9	be	be	AUX
american_scientific_journal-591	63	10	the	the	DET
american_scientific_journal-591	63	11	reflection	reflection	NOUN
american_scientific_journal-591	63	12	of	of	ADP
american_scientific_journal-591	63	13	b	b	NOUN
american_scientific_journal-591	63	14	with	with	ADP
american_scientific_journal-591	63	15	respect	respect	NOUN
american_scientific_journal-591	63	16	to	to	ADP
american_scientific_journal-591	63	17	l	l	NOUN
american_scientific_journal-591	63	18	produces	produce	NOUN
american_scientific_journal-591	63	19	d(b	d(b	PROPN
american_scientific_journal-591	63	20	,	,	PUNCT
american_scientific_journal-591	63	21	b”)=	b”)=	VERB
american_scientific_journal-591	63	22	d(b”,b	d(b”,b	NOUN
american_scientific_journal-591	63	23	’	'	PUNCT
american_scientific_journal-591	63	24	)	)	PUNCT
american_scientific_journal-591	64	1	=	=	SYM
american_scientific_journal-591	64	2	b.	b.	PROPN
american_scientific_journal-591	64	3	then	then	ADV
american_scientific_journal-591	64	4	,	,	PUNCT
american_scientific_journal-591	64	5	connecting	connect	VERB
american_scientific_journal-591	64	6	a	a	PRON
american_scientific_journal-591	64	7	and	and	CCONJ
american_scientific_journal-591	64	8	b	b	NOUN
american_scientific_journal-591	64	9	’	'	PUNCT
american_scientific_journal-591	64	10	shows	show	VERB
american_scientific_journal-591	64	11	a	a	DET
american_scientific_journal-591	64	12	line	line	NOUN
american_scientific_journal-591	64	13	segment	segment	NOUN
american_scientific_journal-591	64	14	intersecting	intersect	VERB
american_scientific_journal-591	64	15	l	l	NOUN
american_scientific_journal-591	64	16	at	at	ADP
american_scientific_journal-591	64	17	a	a	DET
american_scientific_journal-591	64	18	point	point	NOUN
american_scientific_journal-591	64	19	.	.	PUNCT
american_scientific_journal-591	65	1	it	it	PRON
american_scientific_journal-591	65	2	is	be	AUX
american_scientific_journal-591	65	3	very	very	ADV
american_scientific_journal-591	65	4	clear	clear	ADJ
american_scientific_journal-591	65	5	that	that	SCONJ
american_scientific_journal-591	65	6	the	the	DET
american_scientific_journal-591	65	7	minimum	minimum	ADJ
american_scientific_journal-591	65	8	distance	distance	NOUN
american_scientific_journal-591	65	9	between	between	ADP
american_scientific_journal-591	65	10	a	a	PRON
american_scientific_journal-591	65	11	and	and	CCONJ
american_scientific_journal-591	65	12	b	b	NOUN
american_scientific_journal-591	65	13	’	'	PUNCT
american_scientific_journal-591	65	14	is	be	AUX
american_scientific_journal-591	65	15	equal	equal	ADJ
american_scientific_journal-591	65	16	to	to	ADP
american_scientific_journal-591	65	17	the	the	DET
american_scientific_journal-591	65	18	length	length	NOUN
american_scientific_journal-591	65	19	of	of	ADP
american_scientific_journal-591	65	20	the	the	DET
american_scientific_journal-591	65	21	segment	segment	NOUN
american_scientific_journal-591	65	22	connecting	connect	VERB
american_scientific_journal-591	65	23	the	the	DET
american_scientific_journal-591	65	24	two	two	NUM
american_scientific_journal-591	65	25	points	point	NOUN
american_scientific_journal-591	65	26	such	such	ADJ
american_scientific_journal-591	65	27	that	that	SCONJ
american_scientific_journal-591	65	28	these	these	DET
american_scientific_journal-591	65	29	points	point	NOUN
american_scientific_journal-591	65	30	are	be	AUX
american_scientific_journal-591	65	31	the	the	DET
american_scientific_journal-591	65	32	endpoints	endpoint	NOUN
american_scientific_journal-591	65	33	of	of	ADP
american_scientific_journal-591	65	34	the	the	DET
american_scientific_journal-591	65	35	segment	segment	NOUN
american_scientific_journal-591	65	36	since	since	SCONJ
american_scientific_journal-591	65	37	the	the	DET
american_scientific_journal-591	65	38	shortest	short	ADJ
american_scientific_journal-591	65	39	distance	distance	NOUN
american_scientific_journal-591	65	40	between	between	ADP
american_scientific_journal-591	65	41	two	two	NUM
american_scientific_journal-591	65	42	points	point	NOUN
american_scientific_journal-591	65	43	is	be	AUX
american_scientific_journal-591	65	44	through	through	ADP
american_scientific_journal-591	65	45	the	the	DET
american_scientific_journal-591	65	46	straight	straight	ADJ
american_scientific_journal-591	65	47	line	line	NOUN
american_scientific_journal-591	65	48	connecting	connect	VERB
american_scientific_journal-591	65	49	them	they	PRON
american_scientific_journal-591	65	50	(	(	PUNCT
american_scientific_journal-591	65	51	see	see	VERB
american_scientific_journal-591	65	52	figure	figure	NOUN
american_scientific_journal-591	65	53	4	4	NUM
american_scientific_journal-591	65	54	)	)	PUNCT
american_scientific_journal-591	65	55	.	.	PUNCT
american_scientific_journal-591	66	1	figure	figure	VERB
american_scientific_journal-591	66	2	4	4	NUM
american_scientific_journal-591	66	3	:	:	PUNCT
american_scientific_journal-591	66	4	distance	distance	NOUN
american_scientific_journal-591	66	5	between	between	ADP
american_scientific_journal-591	66	6	a	a	PRON
american_scientific_journal-591	66	7	and	and	CCONJ
american_scientific_journal-591	66	8	bʹ	bʹ	NOUN
american_scientific_journal-591	66	9	now	now	ADV
american_scientific_journal-591	66	10	,	,	PUNCT
american_scientific_journal-591	66	11	let	let	VERB
american_scientific_journal-591	66	12	r	r	PRON
american_scientific_journal-591	66	13	be	be	AUX
american_scientific_journal-591	66	14	the	the	DET
american_scientific_journal-591	66	15	point	point	NOUN
american_scientific_journal-591	66	16	of	of	ADP
american_scientific_journal-591	66	17	intersection	intersection	NOUN
american_scientific_journal-591	66	18	of	of	ADP
american_scientific_journal-591	66	19	l	l	NOUN
american_scientific_journal-591	66	20	and	and	CCONJ
american_scientific_journal-591	66	21	segment	segment	NOUN
american_scientific_journal-591	66	22	ab	ab	NOUN
american_scientific_journal-591	66	23	’	'	PUNCT
american_scientific_journal-591	66	24	.	.	PUNCT
american_scientific_journal-591	67	1	since	since	SCONJ
american_scientific_journal-591	67	2	distance	distance	NOUN
american_scientific_journal-591	67	3	is	be	AUX
american_scientific_journal-591	67	4	preserved	preserve	VERB
american_scientific_journal-591	67	5	under	under	ADP
american_scientific_journal-591	67	6	reflection	reflection	NOUN
american_scientific_journal-591	67	7	across	across	ADP
american_scientific_journal-591	67	8	the	the	DET
american_scientific_journal-591	67	9	line	line	NOUN
american_scientific_journal-591	67	10	,	,	PUNCT
american_scientific_journal-591	67	11	d(r	d(r	PROPN
american_scientific_journal-591	67	12	,	,	PUNCT
american_scientific_journal-591	67	13	b	b	NOUN
american_scientific_journal-591	67	14	’	'	PUNCT
american_scientific_journal-591	67	15	)	)	PUNCT
american_scientific_journal-591	68	1	=	=	SYM
american_scientific_journal-591	68	2	d(r	d(r	PROPN
american_scientific_journal-591	68	3	,	,	PUNCT
american_scientific_journal-591	68	4	b	b	NOUN
american_scientific_journal-591	68	5	)	)	PUNCT
american_scientific_journal-591	68	6	and	and	CCONJ
american_scientific_journal-591	68	7	hence	hence	ADV
american_scientific_journal-591	68	8	,	,	PUNCT
american_scientific_journal-591	68	9	d(a	d(a	PROPN
american_scientific_journal-591	68	10	,	,	PUNCT
american_scientific_journal-591	68	11	r)+d(r	r)+d(r	PROPN
american_scientific_journal-591	68	12	,	,	PUNCT
american_scientific_journal-591	68	13	b	b	NOUN
american_scientific_journal-591	68	14	’	'	PUNCT
american_scientific_journal-591	68	15	)	)	PUNCT
american_scientific_journal-591	69	1	=	=	SYM
american_scientific_journal-591	69	2	d(a	d(a	PROPN
american_scientific_journal-591	69	3	,	,	PUNCT
american_scientific_journal-591	69	4	r)+d(r	r)+d(r	PROPN
american_scientific_journal-591	69	5	,	,	PUNCT
american_scientific_journal-591	69	6	b	b	NOUN
american_scientific_journal-591	69	7	)	)	PUNCT
american_scientific_journal-591	69	8	.	.	PUNCT
american_scientific_journal-591	70	1	thus	thus	ADV
american_scientific_journal-591	70	2	,	,	PUNCT
american_scientific_journal-591	70	3	the	the	DET
american_scientific_journal-591	70	4	point	point	NOUN
american_scientific_journal-591	70	5	p	p	NOUN
american_scientific_journal-591	70	6	in	in	ADP
american_scientific_journal-591	70	7	l	l	NOUN
american_scientific_journal-591	70	8	such	such	ADJ
american_scientific_journal-591	70	9	that	that	SCONJ
american_scientific_journal-591	70	10	the	the	DET
american_scientific_journal-591	70	11	distance	distance	NOUN
american_scientific_journal-591	70	12	from	from	ADP
american_scientific_journal-591	70	13	a	a	PRON
american_scientific_journal-591	70	14	to	to	ADP
american_scientific_journal-591	70	15	p	p	NOUN
american_scientific_journal-591	70	16	to	to	ADP
american_scientific_journal-591	70	17	b	b	NOUN
american_scientific_journal-591	70	18	is	be	AUX
american_scientific_journal-591	70	19	to	to	PART
american_scientific_journal-591	70	20	be	be	AUX
american_scientific_journal-591	70	21	the	the	DET
american_scientific_journal-591	70	22	minimum	minimum	ADJ
american_scientific_journal-591	70	23	distance	distance	NOUN
american_scientific_journal-591	70	24	possible	possible	ADJ
american_scientific_journal-591	70	25	is	be	AUX
american_scientific_journal-591	70	26	that	that	DET
american_scientific_journal-591	70	27	same	same	ADJ
american_scientific_journal-591	70	28	point	point	NOUN
american_scientific_journal-591	70	29	r	r	NOUN
american_scientific_journal-591	70	30	(	(	PUNCT
american_scientific_journal-591	70	31	see	see	VERB
american_scientific_journal-591	70	32	figure	figure	NOUN
american_scientific_journal-591	70	33	5	5	NUM
american_scientific_journal-591	70	34	)	)	PUNCT
american_scientific_journal-591	70	35	.	.	PUNCT
american_scientific_journal-591	71	1	figure	figure	VERB
american_scientific_journal-591	71	2	5	5	NUM
american_scientific_journal-591	71	3	:	:	PUNCT
american_scientific_journal-591	71	4	distance	distance	NOUN
american_scientific_journal-591	71	5	from	from	ADP
american_scientific_journal-591	71	6	a	a	PRON
american_scientific_journal-591	71	7	to	to	ADP
american_scientific_journal-591	71	8	l	l	NOUN
american_scientific_journal-591	71	9	to	to	ADP
american_scientific_journal-591	71	10	b	b	PROPN
american_scientific_journal-591	71	11	is	be	AUX
american_scientific_journal-591	71	12	the	the	DET
american_scientific_journal-591	71	13	same	same	ADJ
american_scientific_journal-591	71	14	as	as	ADP
american_scientific_journal-591	71	15	distance	distance	NOUN
american_scientific_journal-591	71	16	from	from	ADP
american_scientific_journal-591	71	17	a	a	DET
american_scientific_journal-591	71	18	to	to	PART
american_scientific_journal-591	71	19	bʹ	bʹ	NOUN
american_scientific_journal-591	71	20	since	since	SCONJ
american_scientific_journal-591	71	21	r	r	NOUN
american_scientific_journal-591	71	22	and	and	CCONJ
american_scientific_journal-591	71	23	p	p	NOUN
american_scientific_journal-591	71	24	refer	refer	NOUN
american_scientific_journal-591	71	25	to	to	ADP
american_scientific_journal-591	71	26	the	the	DET
american_scientific_journal-591	71	27	same	same	ADJ
american_scientific_journal-591	71	28	point	point	NOUN
american_scientific_journal-591	71	29	,	,	PUNCT
american_scientific_journal-591	71	30	d(a	d(a	PROPN
american_scientific_journal-591	71	31	,	,	PUNCT
american_scientific_journal-591	71	32	r)+d(r	r)+d(r	PROPN
american_scientific_journal-591	71	33	,	,	PUNCT
american_scientific_journal-591	71	34	b’)=d(a	b’)=d(a	PROPN
american_scientific_journal-591	71	35	,	,	PUNCT
american_scientific_journal-591	71	36	p)+d(p	p)+d(p	PROPN
american_scientific_journal-591	71	37	,	,	PUNCT
american_scientific_journal-591	71	38	b	b	NOUN
american_scientific_journal-591	71	39	’	'	PUNCT
american_scientific_journal-591	71	40	)	)	PUNCT
american_scientific_journal-591	71	41	.	.	PUNCT
american_scientific_journal-591	72	1	next	next	ADV
american_scientific_journal-591	72	2	,	,	PUNCT
american_scientific_journal-591	72	3	by	by	ADP
american_scientific_journal-591	72	4	constructing	construct	VERB
american_scientific_journal-591	72	5	another	another	DET
american_scientific_journal-591	72	6	point	point	NOUN
american_scientific_journal-591	72	7	bʹʹʹ	bʹʹʹ	NOUN
american_scientific_journal-591	72	8	,	,	PUNCT
american_scientific_journal-591	72	9	c	c	PROPN
american_scientific_journal-591	72	10	units	unit	NOUN
american_scientific_journal-591	72	11	away	away	ADV
american_scientific_journal-591	72	12	from	from	ADP
american_scientific_journal-591	72	13	bʹ	bʹ	PRON
american_scientific_journal-591	72	14	to	to	ADP
american_scientific_journal-591	72	15	the	the	DET
american_scientific_journal-591	72	16	left	left	NOUN
american_scientific_journal-591	72	17	,	,	PUNCT
american_scientific_journal-591	72	18	it	it	PRON
american_scientific_journal-591	72	19	can	can	AUX
american_scientific_journal-591	72	20	form	form	VERB
american_scientific_journal-591	72	21	a	a	DET
american_scientific_journal-591	72	22	right	right	ADJ
american_scientific_journal-591	72	23	triangle	triangle	NOUN
american_scientific_journal-591	72	24	with	with	ADP
american_scientific_journal-591	72	25	vertices	vertex	NOUN
american_scientific_journal-591	72	26	a	a	PRON
american_scientific_journal-591	72	27	,	,	PUNCT
american_scientific_journal-591	72	28	bʹ	bʹ	NOUN
american_scientific_journal-591	72	29	and	and	CCONJ
american_scientific_journal-591	72	30	bʹʹʹ	bʹʹʹ	NOUN
american_scientific_journal-591	72	31	(	(	PUNCT
american_scientific_journal-591	72	32	see	see	VERB
american_scientific_journal-591	72	33	figure	figure	NOUN
american_scientific_journal-591	72	34	6	6	NUM
american_scientific_journal-591	72	35	)	)	PUNCT
american_scientific_journal-591	72	36	.	.	PUNCT
american_scientific_journal-591	73	1	88	88	NUM
american_scientific_journal-591	73	2	american	american	ADJ
american_scientific_journal-591	73	3	scientific	scientific	ADJ
american_scientific_journal-591	73	4	research	research	NOUN
american_scientific_journal-591	73	5	journal	journal	NOUN
american_scientific_journal-591	73	6	for	for	ADP
american_scientific_journal-591	73	7	engineering	engineering	NOUN
american_scientific_journal-591	73	8	,	,	PUNCT
american_scientific_journal-591	73	9	technology	technology	NOUN
american_scientific_journal-591	73	10	,	,	PUNCT
american_scientific_journal-591	73	11	and	and	CCONJ
american_scientific_journal-591	73	12	sciences	science	NOUN
american_scientific_journal-591	73	13	(	(	PUNCT
american_scientific_journal-591	73	14	asrjets	asrjet	NOUN
american_scientific_journal-591	73	15	)	)	PUNCT
american_scientific_journal-591	73	16	(	(	PUNCT
american_scientific_journal-591	73	17	2015	2015	NUM
american_scientific_journal-591	73	18	)	)	PUNCT
american_scientific_journal-591	73	19	volume	volume	NOUN
american_scientific_journal-591	73	20	11	11	NUM
american_scientific_journal-591	73	21	,	,	PUNCT
american_scientific_journal-591	73	22	no	no	DET
american_scientific_journal-591	73	23	1	1	NUM
american_scientific_journal-591	73	24	,	,	PUNCT
american_scientific_journal-591	73	25	pp	pp	ADV
american_scientific_journal-591	73	26	84	84	NUM
american_scientific_journal-591	73	27	-	-	SYM
american_scientific_journal-591	73	28	95	95	NUM
american_scientific_journal-591	73	29	figure	figure	NOUN
american_scientific_journal-591	73	30	6	6	NUM
american_scientific_journal-591	73	31	:	:	PUNCT
american_scientific_journal-591	73	32	the	the	DET
american_scientific_journal-591	73	33	right	right	ADJ
american_scientific_journal-591	73	34	triangle	triangle	NOUN
american_scientific_journal-591	73	35	abʹbʹʹʹ	abʹbʹʹʹ	NOUN
american_scientific_journal-591	73	36	it	it	PRON
american_scientific_journal-591	73	37	can	can	AUX
american_scientific_journal-591	73	38	now	now	ADV
american_scientific_journal-591	73	39	be	be	AUX
american_scientific_journal-591	73	40	easily	easily	ADV
american_scientific_journal-591	73	41	seen	see	VERB
american_scientific_journal-591	73	42	that	that	SCONJ
american_scientific_journal-591	73	43	the	the	DET
american_scientific_journal-591	73	44	pythagorean	pythagorean	PROPN
american_scientific_journal-591	73	45	relation	relation	NOUN
american_scientific_journal-591	73	46	holds	hold	VERB
american_scientific_journal-591	73	47	and	and	CCONJ
american_scientific_journal-591	73	48	hence	hence	ADV
american_scientific_journal-591	73	49	,	,	PUNCT
american_scientific_journal-591	73	50	2	2	NUM
american_scientific_journal-591	73	51	2	2	NUM
american_scientific_journal-591	73	52	(	(	PUNCT
american_scientific_journal-591	73	53	,	,	PUNCT
american_scientific_journal-591	73	54	'	'	PUNCT
american_scientific_journal-591	73	55	)	)	PUNCT
american_scientific_journal-591	73	56	(	(	PUNCT
american_scientific_journal-591	73	57	)	)	PUNCT
american_scientific_journal-591	73	58	d	d	X
american_scientific_journal-591	73	59	d	d	NOUN
american_scientific_journal-591	73	60	a	a	DET
american_scientific_journal-591	73	61	b	b	NOUN
american_scientific_journal-591	73	62	a	a	DET
american_scientific_journal-591	73	63	b	b	NOUN
american_scientific_journal-591	73	64	c=	c=	NOUN
american_scientific_journal-591	73	65	=	=	PUNCT
american_scientific_journal-591	74	1	+	+	CCONJ
american_scientific_journal-591	75	1	+	+	CCONJ
american_scientific_journal-591	75	2	.	.	PUNCT
american_scientific_journal-591	76	1	in	in	ADP
american_scientific_journal-591	76	2	addition	addition	NOUN
american_scientific_journal-591	76	3	,	,	PUNCT
american_scientific_journal-591	76	4	the	the	DET
american_scientific_journal-591	76	5	location	location	NOUN
american_scientific_journal-591	76	6	of	of	ADP
american_scientific_journal-591	76	7	p	p	PROPN
american_scientific_journal-591	76	8	can	can	AUX
american_scientific_journal-591	76	9	also	also	ADV
american_scientific_journal-591	76	10	be	be	AUX
american_scientific_journal-591	76	11	determined	determine	VERB
american_scientific_journal-591	76	12	specifically	specifically	ADV
american_scientific_journal-591	76	13	by	by	ADP
american_scientific_journal-591	76	14	using	use	VERB
american_scientific_journal-591	76	15	the	the	DET
american_scientific_journal-591	76	16	formula	formula	NOUN
american_scientific_journal-591	76	17	ba	ba	PROPN
american_scientific_journal-591	76	18	acx	acx	PROPN
american_scientific_journal-591	77	1	+	+	CCONJ
american_scientific_journal-591	78	1	=	=	NOUN
american_scientific_journal-591	78	2	derived	derive	VERB
american_scientific_journal-591	78	3	as	as	SCONJ
american_scientific_journal-591	78	4	follows	follow	VERB
american_scientific_journal-591	78	5	:	:	PUNCT
american_scientific_journal-591	78	6	looking	look	VERB
american_scientific_journal-591	78	7	at	at	ADP
american_scientific_journal-591	78	8	figure	figure	NOUN
american_scientific_journal-591	78	9	7	7	NUM
american_scientific_journal-591	78	10	,	,	PUNCT
american_scientific_journal-591	78	11	since	since	SCONJ
american_scientific_journal-591	78	12	a	a	PRON
american_scientific_journal-591	78	13	,	,	PUNCT
american_scientific_journal-591	78	14	p	p	NOUN
american_scientific_journal-591	78	15	and	and	CCONJ
american_scientific_journal-591	78	16	b	b	NOUN
american_scientific_journal-591	78	17	’	'	PUNCT
american_scientific_journal-591	78	18	are	be	AUX
american_scientific_journal-591	78	19	in	in	ADP
american_scientific_journal-591	78	20	a	a	DET
american_scientific_journal-591	78	21	line	line	NOUN
american_scientific_journal-591	78	22	,	,	PUNCT
american_scientific_journal-591	78	23	∠apa	∠apa	PROPN
american_scientific_journal-591	78	24	”	"	PUNCT
american_scientific_journal-591	78	25	and	and	CCONJ
american_scientific_journal-591	78	26	∠	∠	PROPN
american_scientific_journal-591	78	27	b’pb	b’pb	PROPN
american_scientific_journal-591	78	28	’’	’'	PUNCT
american_scientific_journal-591	78	29	are	be	AUX
american_scientific_journal-591	78	30	vertical	vertical	ADJ
american_scientific_journal-591	78	31	angles	angle	NOUN
american_scientific_journal-591	78	32	.	.	PUNCT
american_scientific_journal-591	79	1	then	then	ADV
american_scientific_journal-591	79	2	,	,	PUNCT
american_scientific_journal-591	79	3	let	let	VERB
american_scientific_journal-591	79	4	x	x	PRON
american_scientific_journal-591	79	5	be	be	AUX
american_scientific_journal-591	79	6	the	the	DET
american_scientific_journal-591	79	7	distance	distance	NOUN
american_scientific_journal-591	79	8	from	from	ADP
american_scientific_journal-591	79	9	a	a	PRON
american_scientific_journal-591	79	10	”	"	PUNCT
american_scientific_journal-591	79	11	to	to	ADP
american_scientific_journal-591	79	12	p	p	NOUN
american_scientific_journal-591	79	13	and	and	CCONJ
american_scientific_journal-591	79	14	hence	hence	ADV
american_scientific_journal-591	79	15	,	,	PUNCT
american_scientific_journal-591	79	16	c	c	X
american_scientific_journal-591	79	17	–	–	PUNCT
american_scientific_journal-591	79	18	x	x	PUNCT
american_scientific_journal-591	79	19	is	be	AUX
american_scientific_journal-591	79	20	the	the	DET
american_scientific_journal-591	79	21	distance	distance	NOUN
american_scientific_journal-591	79	22	from	from	ADP
american_scientific_journal-591	79	23	p	p	NOUN
american_scientific_journal-591	79	24	to	to	ADP
american_scientific_journal-591	79	25	b	b	NOUN
american_scientific_journal-591	79	26	”	"	PUNCT
american_scientific_journal-591	79	27	.	.	PUNCT
american_scientific_journal-591	80	1	figure	figure	VERB
american_scientific_journal-591	80	2	7	7	NUM
american_scientific_journal-591	80	3	:	:	PUNCT
american_scientific_journal-591	80	4	the	the	DET
american_scientific_journal-591	80	5	location	location	NOUN
american_scientific_journal-591	80	6	of	of	ADP
american_scientific_journal-591	80	7	p	p	PROPN
american_scientific_journal-591	80	8	89	89	NUM
american_scientific_journal-591	80	9	american	american	ADJ
american_scientific_journal-591	80	10	scientific	scientific	ADJ
american_scientific_journal-591	80	11	research	research	NOUN
american_scientific_journal-591	80	12	journal	journal	NOUN
american_scientific_journal-591	80	13	for	for	ADP
american_scientific_journal-591	80	14	engineering	engineering	NOUN
american_scientific_journal-591	80	15	,	,	PUNCT
american_scientific_journal-591	80	16	technology	technology	NOUN
american_scientific_journal-591	80	17	,	,	PUNCT
american_scientific_journal-591	80	18	and	and	CCONJ
american_scientific_journal-591	80	19	sciences	science	NOUN
american_scientific_journal-591	80	20	(	(	PUNCT
american_scientific_journal-591	80	21	asrjets	asrjet	NOUN
american_scientific_journal-591	80	22	)	)	PUNCT
american_scientific_journal-591	80	23	(	(	PUNCT
american_scientific_journal-591	80	24	2015	2015	NUM
american_scientific_journal-591	80	25	)	)	PUNCT
american_scientific_journal-591	80	26	volume	volume	NOUN
american_scientific_journal-591	80	27	11	11	NUM
american_scientific_journal-591	80	28	,	,	PUNCT
american_scientific_journal-591	80	29	no	no	DET
american_scientific_journal-591	80	30	1	1	NUM
american_scientific_journal-591	80	31	,	,	PUNCT
american_scientific_journal-591	80	32	pp	pp	ADV
american_scientific_journal-591	80	33	84	84	NUM
american_scientific_journal-591	80	34	-	-	SYM
american_scientific_journal-591	80	35	95	95	NUM
american_scientific_journal-591	80	36	then	then	ADV
american_scientific_journal-591	80	37	,	,	PUNCT
american_scientific_journal-591	80	38	tan	tan	PROPN
american_scientific_journal-591	80	39	(	(	PUNCT
american_scientific_journal-591	80	40	apa	apa	PROPN
american_scientific_journal-591	80	41	”	"	PUNCT
american_scientific_journal-591	80	42	)	)	PUNCT
american_scientific_journal-591	80	43	=	=	SYM
american_scientific_journal-591	81	1	a	a	PRON
american_scientific_journal-591	81	2	x	x	X
american_scientific_journal-591	81	3	and	and	CCONJ
american_scientific_journal-591	81	4	tan	tan	PROPN
american_scientific_journal-591	81	5	(	(	PUNCT
american_scientific_journal-591	81	6	b’pb	b’pb	NOUN
american_scientific_journal-591	81	7	”	"	PUNCT
american_scientific_journal-591	81	8	)	)	PUNCT
american_scientific_journal-591	82	1	=	=	SYM
american_scientific_journal-591	82	2	b	b	PROPN
american_scientific_journal-591	82	3	c	c	X
american_scientific_journal-591	82	4	x−	x−	PROPN
american_scientific_journal-591	82	5	,	,	PUNCT
american_scientific_journal-591	82	6	and	and	CCONJ
american_scientific_journal-591	82	7	since	since	SCONJ
american_scientific_journal-591	82	8	the	the	DET
american_scientific_journal-591	82	9	measure	measure	NOUN
american_scientific_journal-591	82	10	of∠apa	of∠apa	VERB
american_scientific_journal-591	82	11	”	"	PUNCT
american_scientific_journal-591	82	12	is	be	AUX
american_scientific_journal-591	82	13	equal	equal	ADJ
american_scientific_journal-591	82	14	to	to	ADP
american_scientific_journal-591	82	15	that	that	PRON
american_scientific_journal-591	82	16	of	of	ADP
american_scientific_journal-591	82	17	∠	∠	PROPN
american_scientific_journal-591	82	18	b’pb	b’pb	PROPN
american_scientific_journal-591	82	19	”	"	PUNCT
american_scientific_journal-591	82	20	,	,	PUNCT
american_scientific_journal-591	82	21	tan	tan	PROPN
american_scientific_journal-591	82	22	(	(	PUNCT
american_scientific_journal-591	82	23	apa	apa	PROPN
american_scientific_journal-591	82	24	”	"	PUNCT
american_scientific_journal-591	82	25	)	)	PUNCT
american_scientific_journal-591	83	1	=	=	SYM
american_scientific_journal-591	83	2	tan	tan	PROPN
american_scientific_journal-591	83	3	(	(	PUNCT
american_scientific_journal-591	83	4	b’pb	b’pb	NOUN
american_scientific_journal-591	83	5	”	"	PUNCT
american_scientific_journal-591	83	6	)	)	PUNCT
american_scientific_journal-591	83	7	.	.	PUNCT
american_scientific_journal-591	84	1	hence	hence	ADV
american_scientific_journal-591	84	2	,	,	PUNCT
american_scientific_journal-591	84	3	a	a	DET
american_scientific_journal-591	84	4	b	b	NOUN
american_scientific_journal-591	84	5	x	x	NOUN
american_scientific_journal-591	84	6	c	c	NOUN
american_scientific_journal-591	84	7	x	x	SYM
american_scientific_journal-591	84	8	=	=	SYM
american_scientific_journal-591	84	9	−	−	PROPN
american_scientific_journal-591	84	10	and	and	CCONJ
american_scientific_journal-591	84	11	solving	solving	NOUN
american_scientific_journal-591	84	12	gives	give	VERB
american_scientific_journal-591	84	13	acx	acx	PROPN
american_scientific_journal-591	84	14	a	a	DET
american_scientific_journal-591	84	15	b	b	NOUN
american_scientific_journal-591	84	16	=	=	SYM
american_scientific_journal-591	84	17	+	+	CCONJ
american_scientific_journal-591	84	18	,	,	PUNCT
american_scientific_journal-591	84	19	which	which	PRON
american_scientific_journal-591	84	20	is	be	AUX
american_scientific_journal-591	84	21	used	use	VERB
american_scientific_journal-591	84	22	to	to	PART
american_scientific_journal-591	84	23	locate	locate	VERB
american_scientific_journal-591	84	24	p	p	NOUN
american_scientific_journal-591	84	25	in	in	ADP
american_scientific_journal-591	84	26	l	l	NOUN
american_scientific_journal-591	84	27	from	from	ADP
american_scientific_journal-591	84	28	a	a	PRON
american_scientific_journal-591	84	29	”	"	PUNCT
american_scientific_journal-591	84	30	.	.	PUNCT
american_scientific_journal-591	84	31	3.2	3.2	NUM
american_scientific_journal-591	84	32	.	.	PUNCT
american_scientific_journal-591	85	1	derivation	derivation	NOUN
american_scientific_journal-591	85	2	of	of	ADP
american_scientific_journal-591	85	3	the	the	DET
american_scientific_journal-591	85	4	formula	formula	NOUN
american_scientific_journal-591	85	5	by	by	ADP
american_scientific_journal-591	85	6	analytical	analytical	ADJ
american_scientific_journal-591	85	7	approach	approach	NOUN
american_scientific_journal-591	85	8	given	give	VERB
american_scientific_journal-591	85	9	two	two	NUM
american_scientific_journal-591	85	10	points	point	NOUN
american_scientific_journal-591	85	11	a	a	PRON
american_scientific_journal-591	85	12	and	and	CCONJ
american_scientific_journal-591	85	13	b	b	NOUN
american_scientific_journal-591	85	14	on	on	ADP
american_scientific_journal-591	85	15	the	the	DET
american_scientific_journal-591	85	16	same	same	ADJ
american_scientific_journal-591	85	17	side	side	NOUN
american_scientific_journal-591	85	18	of	of	ADP
american_scientific_journal-591	85	19	line	line	NOUN
american_scientific_journal-591	85	20	l	l	NOUN
american_scientific_journal-591	85	21	,	,	PUNCT
american_scientific_journal-591	85	22	derive	derive	VERB
american_scientific_journal-591	85	23	the	the	DET
american_scientific_journal-591	85	24	formula	formula	NOUN
american_scientific_journal-591	85	25	for	for	ADP
american_scientific_journal-591	85	26	the	the	DET
american_scientific_journal-591	85	27	minimum	minimum	ADJ
american_scientific_journal-591	85	28	distance	distance	NOUN
american_scientific_journal-591	85	29	from	from	ADP
american_scientific_journal-591	85	30	a	a	PRON
american_scientific_journal-591	85	31	to	to	ADP
american_scientific_journal-591	85	32	l	l	NOUN
american_scientific_journal-591	85	33	to	to	ADP
american_scientific_journal-591	85	34	b	b	NOUN
american_scientific_journal-591	85	35	using	use	VERB
american_scientific_journal-591	85	36	differentiation	differentiation	NOUN
american_scientific_journal-591	85	37	,	,	PUNCT
american_scientific_journal-591	85	38	in	in	ADP
american_scientific_journal-591	85	39	particular	particular	ADJ
american_scientific_journal-591	85	40	,	,	PUNCT
american_scientific_journal-591	85	41	applying	apply	VERB
american_scientific_journal-591	85	42	the	the	DET
american_scientific_journal-591	85	43	extreme	extreme	ADJ
american_scientific_journal-591	85	44	-	-	PUNCT
american_scientific_journal-591	85	45	value	value	NOUN
american_scientific_journal-591	85	46	theorem	theorem	NOUN
american_scientific_journal-591	85	47	.	.	PUNCT
american_scientific_journal-591	86	1	refer	refer	VERB
american_scientific_journal-591	86	2	to	to	PART
american_scientific_journal-591	86	3	figure	figure	VERB
american_scientific_journal-591	86	4	8	8	NUM
american_scientific_journal-591	86	5	for	for	ADP
american_scientific_journal-591	86	6	the	the	DET
american_scientific_journal-591	86	7	following	follow	VERB
american_scientific_journal-591	86	8	discussion	discussion	NOUN
american_scientific_journal-591	86	9	:	:	PUNCT
american_scientific_journal-591	86	10	figure	figure	NOUN
american_scientific_journal-591	86	11	8	8	NUM
american_scientific_journal-591	86	12	:	:	PUNCT
american_scientific_journal-591	86	13	minimum	minimum	ADJ
american_scientific_journal-591	86	14	distance	distance	NOUN
american_scientific_journal-591	86	15	problem	problem	NOUN
american_scientific_journal-591	86	16	in	in	ADP
american_scientific_journal-591	86	17	calculus	calculus	NOUN
american_scientific_journal-591	86	18	to	to	PART
american_scientific_journal-591	86	19	begin	begin	VERB
american_scientific_journal-591	86	20	with	with	ADP
american_scientific_journal-591	86	21	,	,	PUNCT
american_scientific_journal-591	86	22	let	let	VERB
american_scientific_journal-591	86	23	a	a	PRON
american_scientific_journal-591	86	24	be	be	AUX
american_scientific_journal-591	86	25	the	the	DET
american_scientific_journal-591	86	26	distance	distance	NOUN
american_scientific_journal-591	86	27	from	from	ADP
american_scientific_journal-591	86	28	a	a	PRON
american_scientific_journal-591	86	29	to	to	ADP
american_scientific_journal-591	86	30	l	l	NOUN
american_scientific_journal-591	86	31	and	and	CCONJ
american_scientific_journal-591	86	32	b	b	NOUN
american_scientific_journal-591	86	33	be	be	AUX
american_scientific_journal-591	86	34	the	the	DET
american_scientific_journal-591	86	35	distance	distance	NOUN
american_scientific_journal-591	86	36	from	from	ADP
american_scientific_journal-591	86	37	b	b	NOUN
american_scientific_journal-591	86	38	to	to	ADP
american_scientific_journal-591	86	39	l.	l.	PROPN
american_scientific_journal-591	86	40	then	then	ADV
american_scientific_journal-591	86	41	,	,	PUNCT
american_scientific_journal-591	86	42	let	let	VERB
american_scientific_journal-591	86	43	a	a	PRON
american_scientific_journal-591	86	44	”	"	PUNCT
american_scientific_journal-591	86	45	be	be	AUX
american_scientific_journal-591	86	46	the	the	DET
american_scientific_journal-591	86	47	point	point	NOUN
american_scientific_journal-591	86	48	in	in	ADP
american_scientific_journal-591	86	49	l	l	NOUN
american_scientific_journal-591	86	50	such	such	ADJ
american_scientific_journal-591	86	51	that	that	SCONJ
american_scientific_journal-591	86	52	d	d	NOUN
american_scientific_journal-591	86	53	(	(	PUNCT
american_scientific_journal-591	86	54	a	a	PRON
american_scientific_journal-591	86	55	,	,	PUNCT
american_scientific_journal-591	86	56	a	a	PRON
american_scientific_journal-591	86	57	”	"	PUNCT
american_scientific_journal-591	86	58	)	)	PUNCT
american_scientific_journal-591	86	59	=	=	SYM
american_scientific_journal-591	86	60	a	a	X
american_scientific_journal-591	86	61	;	;	PUNCT
american_scientific_journal-591	86	62	b	b	X
american_scientific_journal-591	86	63	”	"	PUNCT
american_scientific_journal-591	86	64	be	be	AUX
american_scientific_journal-591	86	65	the	the	DET
american_scientific_journal-591	86	66	point	point	NOUN
american_scientific_journal-591	86	67	in	in	ADP
american_scientific_journal-591	86	68	l	l	NOUN
american_scientific_journal-591	87	1	such	such	ADJ
american_scientific_journal-591	87	2	that	that	SCONJ
american_scientific_journal-591	87	3	d	d	NOUN
american_scientific_journal-591	87	4	(	(	PUNCT
american_scientific_journal-591	87	5	b	b	PROPN
american_scientific_journal-591	87	6	,	,	PUNCT
american_scientific_journal-591	87	7	b	b	NOUN
american_scientific_journal-591	87	8	”	"	PUNCT
american_scientific_journal-591	87	9	)	)	PUNCT
american_scientific_journal-591	87	10	=	=	SYM
american_scientific_journal-591	87	11	b	b	NOUN
american_scientific_journal-591	87	12	;	;	PUNCT
american_scientific_journal-591	87	13	and	and	CCONJ
american_scientific_journal-591	87	14	d	d	X
american_scientific_journal-591	87	15	(	(	PUNCT
american_scientific_journal-591	87	16	a	a	PRON
american_scientific_journal-591	87	17	”	"	PUNCT
american_scientific_journal-591	87	18	,	,	PUNCT
american_scientific_journal-591	87	19	b	b	NOUN
american_scientific_journal-591	87	20	”	"	PUNCT
american_scientific_journal-591	87	21	)	)	PUNCT
american_scientific_journal-591	88	1	=	=	SYM
american_scientific_journal-591	88	2	c.	c.	NOUN
american_scientific_journal-591	88	3	further	far	ADV
american_scientific_journal-591	88	4	,	,	PUNCT
american_scientific_journal-591	88	5	let	let	VERB
american_scientific_journal-591	88	6	p	p	PRON
american_scientific_journal-591	88	7	be	be	AUX
american_scientific_journal-591	88	8	a	a	DET
american_scientific_journal-591	88	9	point	point	NOUN
american_scientific_journal-591	88	10	in	in	ADP
american_scientific_journal-591	88	11	l	l	NOUN
american_scientific_journal-591	88	12	and	and	CCONJ
american_scientific_journal-591	88	13	let	let	VERB
american_scientific_journal-591	88	14	the	the	DET
american_scientific_journal-591	88	15	distance	distance	NOUN
american_scientific_journal-591	88	16	from	from	ADP
american_scientific_journal-591	88	17	a	a	PRON
american_scientific_journal-591	88	18	to	to	ADP
american_scientific_journal-591	88	19	p	p	NOUN
american_scientific_journal-591	88	20	to	to	AUX
american_scientific_journal-591	88	21	b	b	NOUN
american_scientific_journal-591	88	22	be	be	AUX
american_scientific_journal-591	88	23	minimized	minimize	VERB
american_scientific_journal-591	88	24	.	.	PUNCT
american_scientific_journal-591	89	1	also	also	ADV
american_scientific_journal-591	89	2	,	,	PUNCT
american_scientific_journal-591	89	3	let	let	VERB
american_scientific_journal-591	89	4	d	d	X
american_scientific_journal-591	89	5	(	(	PUNCT
american_scientific_journal-591	89	6	a	a	PRON
american_scientific_journal-591	89	7	,	,	PUNCT
american_scientific_journal-591	89	8	p	p	NOUN
american_scientific_journal-591	89	9	)	)	PUNCT
american_scientific_journal-591	90	1	=	=	SYM
american_scientific_journal-591	90	2	y	y	PROPN
american_scientific_journal-591	90	3	,	,	PUNCT
american_scientific_journal-591	90	4	d	d	X
american_scientific_journal-591	90	5	(	(	PUNCT
american_scientific_journal-591	90	6	p	p	X
american_scientific_journal-591	90	7	,	,	PUNCT
american_scientific_journal-591	90	8	b	b	NOUN
american_scientific_journal-591	90	9	)	)	PUNCT
american_scientific_journal-591	90	10	=	=	SYM
american_scientific_journal-591	91	1	z	z	PROPN
american_scientific_journal-591	91	2	and	and	CCONJ
american_scientific_journal-591	91	3	d	d	PROPN
american_scientific_journal-591	91	4	(	(	PUNCT
american_scientific_journal-591	91	5	a	a	PRON
american_scientific_journal-591	91	6	”	"	PUNCT
american_scientific_journal-591	91	7	,	,	PUNCT
american_scientific_journal-591	91	8	p	p	NOUN
american_scientific_journal-591	91	9	)	)	PUNCT
american_scientific_journal-591	92	1	=	=	PUNCT
american_scientific_journal-591	92	2	x.	x.	NOUN
american_scientific_journal-591	92	3	then	then	ADV
american_scientific_journal-591	92	4	,	,	PUNCT
american_scientific_journal-591	92	5	let	let	VERB
american_scientific_journal-591	92	6	d	d	X
american_scientific_journal-591	92	7	y	y	PROPN
american_scientific_journal-591	92	8	z=	z=	VERB
american_scientific_journal-591	92	9	+	+	CCONJ
american_scientific_journal-591	92	10	be	be	AUX
american_scientific_journal-591	92	11	the	the	DET
american_scientific_journal-591	92	12	distance	distance	NOUN
american_scientific_journal-591	92	13	from	from	ADP
american_scientific_journal-591	92	14	a	a	PRON
american_scientific_journal-591	92	15	to	to	ADP
american_scientific_journal-591	92	16	p	p	NOUN
american_scientific_journal-591	92	17	in	in	ADP
american_scientific_journal-591	92	18	l	l	NOUN
american_scientific_journal-591	92	19	to	to	ADP
american_scientific_journal-591	92	20	b	b	NOUN
american_scientific_journal-591	92	21	that	that	PRON
american_scientific_journal-591	92	22	needs	need	VERB
american_scientific_journal-591	92	23	to	to	PART
american_scientific_journal-591	92	24	be	be	AUX
american_scientific_journal-591	92	25	minimized	minimize	VERB
american_scientific_journal-591	92	26	.	.	PUNCT
american_scientific_journal-591	93	1	this	this	PRON
american_scientific_journal-591	93	2	is	be	AUX
american_scientific_journal-591	93	3	clearly	clearly	ADV
american_scientific_journal-591	93	4	an	an	DET
american_scientific_journal-591	93	5	application	application	NOUN
american_scientific_journal-591	93	6	of	of	ADP
american_scientific_journal-591	93	7	the	the	DET
american_scientific_journal-591	93	8	extreme	extreme	ADJ
american_scientific_journal-591	93	9	-	-	PUNCT
american_scientific_journal-591	93	10	value	value	NOUN
american_scientific_journal-591	93	11	theorem	theorem	NOUN
american_scientific_journal-591	93	12	.	.	PUNCT
american_scientific_journal-591	94	1	the	the	DET
american_scientific_journal-591	94	2	distance	distance	NOUN
american_scientific_journal-591	94	3	can	can	AUX
american_scientific_journal-591	94	4	be	be	AUX
american_scientific_journal-591	94	5	expressed	express	VERB
american_scientific_journal-591	94	6	as	as	ADP
american_scientific_journal-591	94	7	a	a	DET
american_scientific_journal-591	94	8	function	function	NOUN
american_scientific_journal-591	94	9	of	of	ADP
american_scientific_journal-591	94	10	x.	x.	NOUN
american_scientific_journal-591	94	11	since	since	SCONJ
american_scientific_journal-591	94	12	x	x	PRON
american_scientific_journal-591	94	13	is	be	AUX
american_scientific_journal-591	94	14	the	the	DET
american_scientific_journal-591	94	15	distance	distance	NOUN
american_scientific_journal-591	94	16	from	from	ADP
american_scientific_journal-591	94	17	a	a	PRON
american_scientific_journal-591	94	18	”	"	PUNCT
american_scientific_journal-591	94	19	to	to	ADP
american_scientific_journal-591	94	20	p	p	NOUN
american_scientific_journal-591	94	21	and	and	CCONJ
american_scientific_journal-591	94	22	p	p	NOUN
american_scientific_journal-591	94	23	can	can	AUX
american_scientific_journal-591	94	24	be	be	AUX
american_scientific_journal-591	94	25	anywhere	anywhere	ADV
american_scientific_journal-591	94	26	in	in	ADP
american_scientific_journal-591	94	27	l	l	NOUN
american_scientific_journal-591	94	28	from	from	ADP
american_scientific_journal-591	94	29	a	a	PRON
american_scientific_journal-591	94	30	”	"	PUNCT
american_scientific_journal-591	94	31	to	to	ADP
american_scientific_journal-591	94	32	b	b	NOUN
american_scientific_journal-591	94	33	”	"	PUNCT
american_scientific_journal-591	94	34	,	,	PUNCT
american_scientific_journal-591	94	35	the	the	DET
american_scientific_journal-591	94	36	value	value	NOUN
american_scientific_journal-591	94	37	of	of	ADP
american_scientific_journal-591	94	38	x	x	NOUN
american_scientific_journal-591	94	39	is	be	AUX
american_scientific_journal-591	94	40	in	in	ADP
american_scientific_journal-591	94	41	the	the	DET
american_scientific_journal-591	94	42	closed	closed	ADJ
american_scientific_journal-591	94	43	interval	interval	NOUN
american_scientific_journal-591	94	44	[	[	X
american_scientific_journal-591	94	45	0	0	NUM
american_scientific_journal-591	94	46	,	,	PUNCT
american_scientific_journal-591	94	47	c	c	NOUN
american_scientific_journal-591	94	48	]	]	PUNCT
american_scientific_journal-591	94	49	.	.	PUNCT
american_scientific_journal-591	95	1	note	note	VERB
american_scientific_journal-591	95	2	also	also	ADV
american_scientific_journal-591	95	3	that	that	SCONJ
american_scientific_journal-591	95	4	p	p	PRON
american_scientific_journal-591	95	5	should	should	AUX
american_scientific_journal-591	95	6	not	not	PART
american_scientific_journal-591	95	7	be	be	AUX
american_scientific_journal-591	95	8	at	at	ADP
american_scientific_journal-591	95	9	the	the	DET
american_scientific_journal-591	95	10	left	left	NOUN
american_scientific_journal-591	95	11	of	of	ADP
american_scientific_journal-591	95	12	a	a	PRON
american_scientific_journal-591	95	13	”	"	PUNCT
american_scientific_journal-591	95	14	in	in	ADP
american_scientific_journal-591	95	15	l	l	NOUN
american_scientific_journal-591	95	16	nor	nor	CCONJ
american_scientific_journal-591	95	17	be	be	AUX
american_scientific_journal-591	95	18	at	at	ADP
american_scientific_journal-591	95	19	the	the	DET
american_scientific_journal-591	95	20	right	right	NOUN
american_scientific_journal-591	95	21	of	of	ADP
american_scientific_journal-591	95	22	b	b	NOUN
american_scientific_journal-591	95	23	”	"	PUNCT
american_scientific_journal-591	95	24	in	in	ADP
american_scientific_journal-591	95	25	l	l	NOUN
american_scientific_journal-591	95	26	since	since	SCONJ
american_scientific_journal-591	95	27	the	the	DET
american_scientific_journal-591	95	28	distance	distance	NOUN
american_scientific_journal-591	95	29	is	be	AUX
american_scientific_journal-591	95	30	to	to	PART
american_scientific_journal-591	95	31	be	be	AUX
american_scientific_journal-591	95	32	minimized	minimize	VERB
american_scientific_journal-591	95	33	.	.	PUNCT
american_scientific_journal-591	96	1	it	it	PRON
american_scientific_journal-591	96	2	can	can	AUX
american_scientific_journal-591	96	3	be	be	AUX
american_scientific_journal-591	96	4	easily	easily	ADV
american_scientific_journal-591	96	5	shown	show	VERB
american_scientific_journal-591	96	6	,	,	PUNCT
american_scientific_journal-591	96	7	through	through	ADP
american_scientific_journal-591	96	8	the	the	DET
american_scientific_journal-591	96	9	use	use	NOUN
american_scientific_journal-591	96	10	of	of	ADP
american_scientific_journal-591	96	11	coordinate	coordinate	NOUN
american_scientific_journal-591	96	12	points	point	NOUN
american_scientific_journal-591	96	13	and	and	CCONJ
american_scientific_journal-591	96	14	the	the	DET
american_scientific_journal-591	96	15	distance	distance	NOUN
american_scientific_journal-591	96	16	formula	formula	NOUN
american_scientific_journal-591	96	17	in	in	ADP
american_scientific_journal-591	96	18	analytic	analytic	ADJ
american_scientific_journal-591	96	19	geometry	geometry	NOUN
american_scientific_journal-591	96	20	,	,	PUNCT
american_scientific_journal-591	96	21	2	2	NUM
american_scientific_journal-591	96	22	2	2	NUM
american_scientific_journal-591	96	23	2	2	NUM
american_scientific_journal-591	96	24	1	1	NUM
american_scientific_journal-591	96	25	2	2	NUM
american_scientific_journal-591	96	26	1	1	NUM
american_scientific_journal-591	96	27	(	(	PUNCT
american_scientific_journal-591	96	28	)	)	PUNCT
american_scientific_journal-591	96	29	(	(	PUNCT
american_scientific_journal-591	96	30	)	)	PUNCT
american_scientific_journal-591	96	31	d	d	X
american_scientific_journal-591	96	32	x	x	PUNCT
american_scientific_journal-591	96	33	x	x	PUNCT
american_scientific_journal-591	96	34	y	y	NOUN
american_scientific_journal-591	96	35	y=	y=	NUM
american_scientific_journal-591	96	36	−	−	PROPN
american_scientific_journal-591	97	1	+	+	CCONJ
american_scientific_journal-591	97	2	−	−	PROPN
american_scientific_journal-591	97	3	,	,	PUNCT
american_scientific_journal-591	98	1	that	that	SCONJ
american_scientific_journal-591	98	2	d(a	d(a	PROPN
american_scientific_journal-591	98	3	,	,	PUNCT
american_scientific_journal-591	98	4	a	a	PRON
american_scientific_journal-591	98	5	”	"	PUNCT
american_scientific_journal-591	98	6	)	)	PUNCT
american_scientific_journal-591	98	7	+	+	CCONJ
american_scientific_journal-591	98	8	d(a	d(a	PROPN
american_scientific_journal-591	98	9	”	"	PUNCT
american_scientific_journal-591	98	10	,	,	PUNCT
american_scientific_journal-591	98	11	b	b	X
american_scientific_journal-591	98	12	)	)	PUNCT
american_scientific_journal-591	98	13	<	<	X
american_scientific_journal-591	99	1	d(a	d(a	PROPN
american_scientific_journal-591	99	2	,	,	PUNCT
american_scientific_journal-591	99	3	p	p	NOUN
american_scientific_journal-591	99	4	at	at	ADP
american_scientific_journal-591	99	5	left	left	NOUN
american_scientific_journal-591	99	6	of	of	ADP
american_scientific_journal-591	99	7	a	a	PRON
american_scientific_journal-591	99	8	”	"	PUNCT
american_scientific_journal-591	99	9	)	)	PUNCT
american_scientific_journal-591	99	10	+	+	CCONJ
american_scientific_journal-591	99	11	d(p	d(p	PROPN
american_scientific_journal-591	99	12	at	at	ADP
american_scientific_journal-591	99	13	left	left	ADV
american_scientific_journal-591	99	14	of	of	ADP
american_scientific_journal-591	99	15	a	a	DET
american_scientific_journal-591	99	16	”	"	PUNCT
american_scientific_journal-591	99	17	,	,	PUNCT
american_scientific_journal-591	99	18	b	b	NOUN
american_scientific_journal-591	99	19	)	)	PUNCT
american_scientific_journal-591	99	20	and	and	CCONJ
american_scientific_journal-591	99	21	d(b	d(b	PROPN
american_scientific_journal-591	99	22	,	,	PUNCT
american_scientific_journal-591	99	23	b	b	NOUN
american_scientific_journal-591	99	24	”	"	PUNCT
american_scientific_journal-591	99	25	)	)	PUNCT
american_scientific_journal-591	99	26	+	+	CCONJ
american_scientific_journal-591	99	27	d(b	d(b	X
american_scientific_journal-591	99	28	”	"	PUNCT
american_scientific_journal-591	99	29	,	,	PUNCT
american_scientific_journal-591	99	30	a	a	PRON
american_scientific_journal-591	99	31	)	)	PUNCT
american_scientific_journal-591	99	32	<	<	X
american_scientific_journal-591	99	33	d(b	d(b	PROPN
american_scientific_journal-591	99	34	,	,	PUNCT
american_scientific_journal-591	99	35	p	p	NOUN
american_scientific_journal-591	99	36	at	at	ADP
american_scientific_journal-591	99	37	right	right	NOUN
american_scientific_journal-591	99	38	of	of	ADP
american_scientific_journal-591	99	39	b	b	NOUN
american_scientific_journal-591	99	40	”	"	PUNCT
american_scientific_journal-591	99	41	)	)	PUNCT
american_scientific_journal-591	100	1	+	+	CCONJ
american_scientific_journal-591	100	2	d(p	d(p	PROPN
american_scientific_journal-591	100	3	at	at	ADP
american_scientific_journal-591	100	4	right	right	NOUN
american_scientific_journal-591	100	5	of	of	ADP
american_scientific_journal-591	100	6	b	b	NOUN
american_scientific_journal-591	100	7	”	"	PUNCT
american_scientific_journal-591	100	8	,	,	PUNCT
american_scientific_journal-591	100	9	a	a	PRON
american_scientific_journal-591	100	10	)	)	PUNCT
american_scientific_journal-591	100	11	.	.	PUNCT
american_scientific_journal-591	101	1	90	90	NUM
american_scientific_journal-591	101	2	american	american	ADJ
american_scientific_journal-591	101	3	scientific	scientific	ADJ
american_scientific_journal-591	101	4	research	research	NOUN
american_scientific_journal-591	101	5	journal	journal	NOUN
american_scientific_journal-591	101	6	for	for	ADP
american_scientific_journal-591	101	7	engineering	engineering	NOUN
american_scientific_journal-591	101	8	,	,	PUNCT
american_scientific_journal-591	101	9	technology	technology	NOUN
american_scientific_journal-591	101	10	,	,	PUNCT
american_scientific_journal-591	101	11	and	and	CCONJ
american_scientific_journal-591	101	12	sciences	science	NOUN
american_scientific_journal-591	101	13	(	(	PUNCT
american_scientific_journal-591	101	14	asrjets	asrjet	NOUN
american_scientific_journal-591	101	15	)	)	PUNCT
american_scientific_journal-591	101	16	(	(	PUNCT
american_scientific_journal-591	101	17	2015	2015	NUM
american_scientific_journal-591	101	18	)	)	PUNCT
american_scientific_journal-591	101	19	volume	volume	NOUN
american_scientific_journal-591	101	20	11	11	NUM
american_scientific_journal-591	101	21	,	,	PUNCT
american_scientific_journal-591	101	22	no	no	DET
american_scientific_journal-591	101	23	1	1	NUM
american_scientific_journal-591	101	24	,	,	PUNCT
american_scientific_journal-591	101	25	pp	pp	ADV
american_scientific_journal-591	101	26	84	84	NUM
american_scientific_journal-591	101	27	-	-	SYM
american_scientific_journal-591	101	28	95	95	NUM
american_scientific_journal-591	101	29	for	for	ADP
american_scientific_journal-591	101	30	d	d	PROPN
american_scientific_journal-591	101	31	=	=	SYM
american_scientific_journal-591	101	32	y	y	PROPN
american_scientific_journal-591	101	33	+	+	PROPN
american_scientific_journal-591	101	34	z	z	PROPN
american_scientific_journal-591	101	35	,	,	PUNCT
american_scientific_journal-591	101	36	the	the	DET
american_scientific_journal-591	101	37	application	application	NOUN
american_scientific_journal-591	101	38	of	of	ADP
american_scientific_journal-591	101	39	the	the	DET
american_scientific_journal-591	101	40	pythagorean	pythagorean	PROPN
american_scientific_journal-591	101	41	theorem	theorem	NOUN
american_scientific_journal-591	101	42	results	result	NOUN
american_scientific_journal-591	101	43	to	to	ADP
american_scientific_journal-591	101	44	2222	2222	NUM
american_scientific_journal-591	101	45	)	)	PUNCT
american_scientific_journal-591	101	46	(	(	PUNCT
american_scientific_journal-591	101	47	bxcaxd	bxcaxd	NOUN
american_scientific_journal-591	101	48	+	+	PROPN
american_scientific_journal-591	101	49	−++=	−++=	PROPN
american_scientific_journal-591	101	50	,	,	PUNCT
american_scientific_journal-591	101	51	the	the	DET
american_scientific_journal-591	101	52	derivative	derivative	NOUN
american_scientific_journal-591	101	53	of	of	ADP
american_scientific_journal-591	101	54	which	which	PRON
american_scientific_journal-591	101	55	is	be	AUX
american_scientific_journal-591	101	56	2222	2222	NUM
american_scientific_journal-591	101	57	)	)	PUNCT
american_scientific_journal-591	101	58	(	(	PUNCT
american_scientific_journal-591	101	59	)	)	PUNCT
american_scientific_journal-591	101	60	(	(	PUNCT
american_scientific_journal-591	101	61	bxc	bxc	NOUN
american_scientific_journal-591	101	62	cx	cx	NOUN
american_scientific_journal-591	101	63	ax	ax	NOUN
american_scientific_journal-591	102	1	x	x	X
american_scientific_journal-591	102	2	dx	dx	PROPN
american_scientific_journal-591	102	3	dd	dd	VERB
american_scientific_journal-591	103	1	+	+	NOUN
american_scientific_journal-591	103	2	−	−	NOUN
american_scientific_journal-591	103	3	−	−	PROPN
american_scientific_journal-591	104	1	+	+	SYM
american_scientific_journal-591	104	2	+	+	CCONJ
american_scientific_journal-591	104	3	=	=	NOUN
american_scientific_journal-591	104	4	.	.	PUNCT
american_scientific_journal-591	105	1	notice	notice	NOUN
american_scientific_journal-591	105	2	also	also	ADV
american_scientific_journal-591	105	3	that	that	SCONJ
american_scientific_journal-591	105	4	since	since	SCONJ
american_scientific_journal-591	105	5	d	d	NOUN
american_scientific_journal-591	105	6	is	be	AUX
american_scientific_journal-591	105	7	a	a	DET
american_scientific_journal-591	105	8	sum	sum	NOUN
american_scientific_journal-591	105	9	of	of	ADP
american_scientific_journal-591	105	10	two	two	NUM
american_scientific_journal-591	105	11	radical	radical	ADJ
american_scientific_journal-591	105	12	functions	function	NOUN
american_scientific_journal-591	105	13	with	with	ADP
american_scientific_journal-591	105	14	positive	positive	ADJ
american_scientific_journal-591	105	15	even	even	ADJ
american_scientific_journal-591	105	16	index	index	NOUN
american_scientific_journal-591	105	17	2	2	NUM
american_scientific_journal-591	105	18	and	and	CCONJ
american_scientific_journal-591	105	19	whose	whose	DET
american_scientific_journal-591	105	20	radicands	radicand	NOUN
american_scientific_journal-591	105	21	are	be	AUX
american_scientific_journal-591	105	22	polynomials	polynomial	NOUN
american_scientific_journal-591	105	23	,	,	PUNCT
american_scientific_journal-591	105	24	it	it	PRON
american_scientific_journal-591	105	25	is	be	AUX
american_scientific_journal-591	105	26	continuous	continuous	ADJ
american_scientific_journal-591	105	27	on	on	ADP
american_scientific_journal-591	105	28	the	the	DET
american_scientific_journal-591	105	29	closed	closed	ADJ
american_scientific_journal-591	105	30	interval	interval	NOUN
american_scientific_journal-591	105	31	[	[	X
american_scientific_journal-591	105	32	0	0	NUM
american_scientific_journal-591	105	33	,	,	PUNCT
american_scientific_journal-591	105	34	c	c	NOUN
american_scientific_journal-591	105	35	]	]	X
american_scientific_journal-591	105	36	,	,	PUNCT
american_scientific_journal-591	105	37	which	which	PRON
american_scientific_journal-591	105	38	can	can	AUX
american_scientific_journal-591	105	39	be	be	AUX
american_scientific_journal-591	105	40	shown	show	VERB
american_scientific_journal-591	105	41	through	through	ADP
american_scientific_journal-591	105	42	the	the	DET
american_scientific_journal-591	105	43	application	application	NOUN
american_scientific_journal-591	105	44	of	of	ADP
american_scientific_journal-591	105	45	the	the	DET
american_scientific_journal-591	105	46	theorem	theorem	NOUN
american_scientific_journal-591	105	47	on	on	ADP
american_scientific_journal-591	105	48	the	the	DET
american_scientific_journal-591	105	49	continuity	continuity	NOUN
american_scientific_journal-591	105	50	of	of	ADP
american_scientific_journal-591	105	51	a	a	DET
american_scientific_journal-591	105	52	composite	composite	ADJ
american_scientific_journal-591	105	53	function	function	NOUN
american_scientific_journal-591	105	54	,	,	PUNCT
american_scientific_journal-591	105	55	theorem	theorem	VERB
american_scientific_journal-591	105	56	on	on	ADP
american_scientific_journal-591	105	57	the	the	DET
american_scientific_journal-591	105	58	addition	addition	NOUN
american_scientific_journal-591	105	59	of	of	ADP
american_scientific_journal-591	105	60	two	two	NUM
american_scientific_journal-591	105	61	continuous	continuous	ADJ
american_scientific_journal-591	105	62	functions	function	NOUN
american_scientific_journal-591	105	63	,	,	PUNCT
american_scientific_journal-591	105	64	definitions	definition	NOUN
american_scientific_journal-591	105	65	of	of	ADP
american_scientific_journal-591	105	66	continuity	continuity	NOUN
american_scientific_journal-591	105	67	,	,	PUNCT
american_scientific_journal-591	105	68	and	and	CCONJ
american_scientific_journal-591	105	69	theorems	theorem	NOUN
american_scientific_journal-591	105	70	on	on	ADP
american_scientific_journal-591	105	71	limits	limit	NOUN
american_scientific_journal-591	105	72	.	.	PUNCT
american_scientific_journal-591	106	1	for	for	ADP
american_scientific_journal-591	106	2	instance	instance	NOUN
american_scientific_journal-591	106	3	,	,	PUNCT
american_scientific_journal-591	106	4	if	if	SCONJ
american_scientific_journal-591	106	5	(	(	PUNCT
american_scientific_journal-591	106	6	)	)	PUNCT
american_scientific_journal-591	106	7	f	f	NOUN
american_scientific_journal-591	106	8	x	x	PUNCT
american_scientific_journal-591	106	9	x=	x=	PROPN
american_scientific_journal-591	106	10	and	and	CCONJ
american_scientific_journal-591	106	11	2	2	NUM
american_scientific_journal-591	106	12	2	2	NUM
american_scientific_journal-591	106	13	(	(	PUNCT
american_scientific_journal-591	106	14	)	)	PUNCT
american_scientific_journal-591	106	15	g	g	NOUN
american_scientific_journal-591	106	16	x	x	X
american_scientific_journal-591	106	17	x	x	X
american_scientific_journal-591	106	18	a=	a=	PROPN
american_scientific_journal-591	106	19	+	+	CCONJ
american_scientific_journal-591	106	20	,	,	PUNCT
american_scientific_journal-591	106	21	then	then	ADV
american_scientific_journal-591	106	22	2	2	NUM
american_scientific_journal-591	106	23	2	2	NUM
american_scientific_journal-591	106	24	(	(	PUNCT
american_scientific_journal-591	106	25	(	(	PUNCT
american_scientific_journal-591	106	26	)	)	PUNCT
american_scientific_journal-591	106	27	)	)	PUNCT
american_scientific_journal-591	106	28	f	f	PROPN
american_scientific_journal-591	107	1	g	g	NOUN
american_scientific_journal-591	107	2	x	x	X
american_scientific_journal-591	107	3	x	x	X
american_scientific_journal-591	107	4	a=	a=	VERB
american_scientific_journal-591	107	5	+	+	CCONJ
american_scientific_journal-591	107	6	.	.	PUNCT
american_scientific_journal-591	108	1	recall	recall	VERB
american_scientific_journal-591	108	2	that	that	PRON
american_scientific_journal-591	108	3	(	(	PUNCT
american_scientific_journal-591	108	4	)	)	PUNCT
american_scientific_journal-591	108	5	g	g	NOUN
american_scientific_journal-591	108	6	x	x	PUNCT
american_scientific_journal-591	108	7	being	be	AUX
american_scientific_journal-591	108	8	a	a	DET
american_scientific_journal-591	108	9	polynomial	polynomial	ADJ
american_scientific_journal-591	108	10	function	function	NOUN
american_scientific_journal-591	108	11	2	2	NUM
american_scientific_journal-591	108	12	2x	2x	NOUN
american_scientific_journal-591	108	13	a+	a+	PUNCT
american_scientific_journal-591	108	14	is	be	AUX
american_scientific_journal-591	108	15	continuous	continuous	ADJ
american_scientific_journal-591	108	16	at	at	ADP
american_scientific_journal-591	108	17	every	every	DET
american_scientific_journal-591	108	18	number	number	NOUN
american_scientific_journal-591	108	19	while	while	SCONJ
american_scientific_journal-591	108	20	(	(	PUNCT
american_scientific_journal-591	108	21	)	)	PUNCT
american_scientific_journal-591	108	22	f	f	X
american_scientific_journal-591	109	1	x	x	X
american_scientific_journal-591	109	2	x=	x=	PROPN
american_scientific_journal-591	109	3	is	be	AUX
american_scientific_journal-591	109	4	continuous	continuous	ADJ
american_scientific_journal-591	109	5	at	at	ADP
american_scientific_journal-591	109	6	every	every	DET
american_scientific_journal-591	109	7	positive	positive	ADJ
american_scientific_journal-591	109	8	number	number	NOUN
american_scientific_journal-591	109	9	,	,	PUNCT
american_scientific_journal-591	109	10	hence	hence	ADV
american_scientific_journal-591	109	11	2	2	NUM
american_scientific_journal-591	109	12	2x	2x	NOUN
american_scientific_journal-591	109	13	a+	a+	PUNCT
american_scientific_journal-591	109	14	is	be	AUX
american_scientific_journal-591	109	15	continuous	continuous	ADJ
american_scientific_journal-591	109	16	at	at	ADP
american_scientific_journal-591	109	17	2	2	NUM
american_scientific_journal-591	109	18	2	2	NUM
american_scientific_journal-591	109	19	0x	0x	X
american_scientific_journal-591	109	20	a+	a+	PUNCT
american_scientific_journal-591	109	21	>	>	X
american_scientific_journal-591	109	22	.	.	PUNCT
american_scientific_journal-591	110	1	then	then	ADV
american_scientific_journal-591	110	2	,	,	PUNCT
american_scientific_journal-591	110	3	using	use	VERB
american_scientific_journal-591	110	4	the	the	DET
american_scientific_journal-591	110	5	definition	definition	NOUN
american_scientific_journal-591	110	6	of	of	ADP
american_scientific_journal-591	110	7	right	right	ADJ
american_scientific_journal-591	110	8	-	-	PUNCT
american_scientific_journal-591	110	9	hand	hand	NOUN
american_scientific_journal-591	110	10	continuity	continuity	NOUN
american_scientific_journal-591	110	11	and	and	CCONJ
american_scientific_journal-591	110	12	left	left	ADJ
american_scientific_journal-591	110	13	-	-	PUNCT
american_scientific_journal-591	110	14	hand	hand	NOUN
american_scientific_journal-591	110	15	continuity	continuity	NOUN
american_scientific_journal-591	110	16	it	it	PRON
american_scientific_journal-591	110	17	can	can	AUX
american_scientific_journal-591	110	18	be	be	AUX
american_scientific_journal-591	110	19	shown	show	VERB
american_scientific_journal-591	110	20	that	that	PRON
american_scientific_journal-591	110	21	is	be	AUX
american_scientific_journal-591	110	22	continuous	continuous	ADJ
american_scientific_journal-591	110	23	on	on	ADP
american_scientific_journal-591	110	24	[	[	X
american_scientific_journal-591	110	25	0	0	NUM
american_scientific_journal-591	110	26	,	,	PUNCT
american_scientific_journal-591	110	27	c	c	NOUN
american_scientific_journal-591	110	28	]	]	PUNCT
american_scientific_journal-591	110	29	.	.	PUNCT
american_scientific_journal-591	111	1	the	the	DET
american_scientific_journal-591	111	2	same	same	ADJ
american_scientific_journal-591	111	3	process	process	NOUN
american_scientific_journal-591	111	4	can	can	AUX
american_scientific_journal-591	111	5	be	be	AUX
american_scientific_journal-591	111	6	done	do	VERB
american_scientific_journal-591	111	7	for	for	ADP
american_scientific_journal-591	111	8	the	the	DET
american_scientific_journal-591	111	9	second	second	ADJ
american_scientific_journal-591	111	10	radical	radical	ADJ
american_scientific_journal-591	111	11	function	function	NOUN
american_scientific_journal-591	111	12	2	2	NUM
american_scientific_journal-591	111	13	2	2	NUM
american_scientific_journal-591	111	14	(	(	PUNCT
american_scientific_journal-591	111	15	)	)	PUNCT
american_scientific_journal-591	111	16	c	c	NOUN
american_scientific_journal-591	111	17	x	x	PUNCT
american_scientific_journal-591	111	18	b−	b−	PROPN
american_scientific_journal-591	111	19	+	+	CCONJ
american_scientific_journal-591	111	20	.	.	PUNCT
american_scientific_journal-591	112	1	finally	finally	ADV
american_scientific_journal-591	112	2	,	,	PUNCT
american_scientific_journal-591	112	3	recall	recall	VERB
american_scientific_journal-591	112	4	that	that	SCONJ
american_scientific_journal-591	112	5	the	the	DET
american_scientific_journal-591	112	6	sum	sum	NOUN
american_scientific_journal-591	112	7	of	of	ADP
american_scientific_journal-591	112	8	two	two	NUM
american_scientific_journal-591	112	9	continuous	continuous	ADJ
american_scientific_journal-591	112	10	functions	function	NOUN
american_scientific_journal-591	112	11	is	be	AUX
american_scientific_journal-591	112	12	continuous	continuous	ADJ
american_scientific_journal-591	112	13	.	.	PUNCT
american_scientific_journal-591	113	1	next	next	ADJ
american_scientific_journal-591	113	2	is	be	AUX
american_scientific_journal-591	113	3	to	to	PART
american_scientific_journal-591	113	4	find	find	VERB
american_scientific_journal-591	113	5	relative	relative	ADJ
american_scientific_journal-591	113	6	extremum	extremum	ADJ
american_scientific_journal-591	113	7	by	by	ADP
american_scientific_journal-591	113	8	equating	equate	VERB
american_scientific_journal-591	113	9	the	the	DET
american_scientific_journal-591	113	10	derivative	derivative	NOUN
american_scientific_journal-591	113	11	to	to	ADP
american_scientific_journal-591	113	12	zero	zero	NUM
american_scientific_journal-591	113	13	,	,	PUNCT
american_scientific_journal-591	113	14	i.e.	i.e.	X
american_scientific_journal-591	113	15	0	0	NUM
american_scientific_journal-591	113	16	)	)	PUNCT
american_scientific_journal-591	113	17	(	(	PUNCT
american_scientific_journal-591	113	18	2222	2222	NUM
american_scientific_journal-591	113	19	=	=	PUNCT
american_scientific_journal-591	114	1	+	+	NOUN
american_scientific_journal-591	114	2	−	−	NOUN
american_scientific_journal-591	114	3	−	−	PROPN
american_scientific_journal-591	115	1	+	+	CCONJ
american_scientific_journal-591	115	2	+	+	CCONJ
american_scientific_journal-591	115	3	bxc	bxc	ADJ
american_scientific_journal-591	115	4	cx	cx	NOUN
american_scientific_journal-591	115	5	ax	ax	NOUN
american_scientific_journal-591	115	6	x	x	X
american_scientific_journal-591	115	7	,	,	PUNCT
american_scientific_journal-591	115	8	which	which	PRON
american_scientific_journal-591	115	9	,	,	PUNCT
american_scientific_journal-591	115	10	by	by	ADP
american_scientific_journal-591	115	11	series	series	NOUN
american_scientific_journal-591	115	12	of	of	ADP
american_scientific_journal-591	115	13	algebraic	algebraic	PROPN
american_scientific_journal-591	115	14	manipulations	manipulation	NOUN
american_scientific_journal-591	115	15	,	,	PUNCT
american_scientific_journal-591	115	16	can	can	AUX
american_scientific_journal-591	115	17	be	be	AUX
american_scientific_journal-591	115	18	simplified	simplify	VERB
american_scientific_journal-591	115	19	into	into	ADP
american_scientific_journal-591	115	20	0)2	0)2	PROPN
american_scientific_journal-591	115	21	(	(	PUNCT
american_scientific_journal-591	115	22	)	)	PUNCT
american_scientific_journal-591	115	23	(	(	PUNCT
american_scientific_journal-591	115	24	222222	222222	NUM
american_scientific_journal-591	115	25	=	=	SYM
american_scientific_journal-591	115	26	+	+	ADP
american_scientific_journal-591	115	27	−−	−−	NOUN
american_scientific_journal-591	115	28	acxcaxba	acxcaxba	NOUN
american_scientific_journal-591	115	29	.	.	PUNCT
american_scientific_journal-591	116	1	then	then	ADV
american_scientific_journal-591	116	2	,	,	PUNCT
american_scientific_journal-591	116	3	by	by	ADP
american_scientific_journal-591	116	4	quadratic	quadratic	ADJ
american_scientific_journal-591	116	5	formula	formula	NOUN
american_scientific_journal-591	116	6	,	,	PUNCT
american_scientific_journal-591	116	7	the	the	DET
american_scientific_journal-591	116	8	roots	root	NOUN
american_scientific_journal-591	116	9	of	of	ADP
american_scientific_journal-591	116	10	the	the	DET
american_scientific_journal-591	116	11	equation	equation	NOUN
american_scientific_journal-591	116	12	or	or	CCONJ
american_scientific_journal-591	116	13	the	the	DET
american_scientific_journal-591	116	14	values	value	NOUN
american_scientific_journal-591	116	15	of	of	ADP
american_scientific_journal-591	116	16	x	x	SYM
american_scientific_journal-591	116	17	are	be	AUX
american_scientific_journal-591	116	18	acx	acx	NOUN
american_scientific_journal-591	116	19	a	a	DET
american_scientific_journal-591	116	20	b	b	NOUN
american_scientific_journal-591	116	21	=	=	PUNCT
american_scientific_journal-591	116	22	−	−	PROPN
american_scientific_journal-591	116	23	and	and	CCONJ
american_scientific_journal-591	116	24	acx	acx	PROPN
american_scientific_journal-591	116	25	a	a	DET
american_scientific_journal-591	116	26	b	b	NOUN
american_scientific_journal-591	116	27	=	=	SYM
american_scientific_journal-591	117	1	+	+	CCONJ
american_scientific_journal-591	117	2	.	.	PUNCT
american_scientific_journal-591	118	1	the	the	DET
american_scientific_journal-591	118	2	first	first	ADJ
american_scientific_journal-591	118	3	root	root	NOUN
american_scientific_journal-591	118	4	,	,	PUNCT
american_scientific_journal-591	118	5	however	however	ADV
american_scientific_journal-591	118	6	,	,	PUNCT
american_scientific_journal-591	118	7	is	be	AUX
american_scientific_journal-591	118	8	an	an	DET
american_scientific_journal-591	118	9	extraneous	extraneous	ADJ
american_scientific_journal-591	118	10	root	root	NOUN
american_scientific_journal-591	118	11	and	and	CCONJ
american_scientific_journal-591	118	12	is	be	AUX
american_scientific_journal-591	118	13	therefore	therefore	ADV
american_scientific_journal-591	118	14	rejected	reject	VERB
american_scientific_journal-591	118	15	.	.	PUNCT
american_scientific_journal-591	119	1	recall	recall	VERB
american_scientific_journal-591	119	2	that	that	SCONJ
american_scientific_journal-591	119	3	x	x	PRON
american_scientific_journal-591	119	4	should	should	AUX
american_scientific_journal-591	119	5	be	be	AUX
american_scientific_journal-591	119	6	in	in	ADP
american_scientific_journal-591	119	7	the	the	DET
american_scientific_journal-591	119	8	closed	closed	ADJ
american_scientific_journal-591	119	9	interval	interval	NOUN
american_scientific_journal-591	119	10	[	[	X
american_scientific_journal-591	119	11	0	0	NUM
american_scientific_journal-591	119	12	,	,	PUNCT
american_scientific_journal-591	119	13	c	c	NOUN
american_scientific_journal-591	119	14	]	]	PUNCT
american_scientific_journal-591	119	15	.	.	PUNCT
american_scientific_journal-591	120	1	in	in	ADP
american_scientific_journal-591	120	2	examining	examine	VERB
american_scientific_journal-591	120	3	the	the	DET
american_scientific_journal-591	120	4	root	root	NOUN
american_scientific_journal-591	120	5	ac	ac	ADP
american_scientific_journal-591	120	6	a	a	DET
american_scientific_journal-591	120	7	b−	b−	NOUN
american_scientific_journal-591	120	8	,	,	PUNCT
american_scientific_journal-591	120	9	there	there	PRON
american_scientific_journal-591	120	10	are	be	VERB
american_scientific_journal-591	120	11	three	three	NUM
american_scientific_journal-591	120	12	cases	case	NOUN
american_scientific_journal-591	120	13	:	:	PUNCT
american_scientific_journal-591	120	14	(	(	PUNCT
american_scientific_journal-591	120	15	1	1	X
american_scientific_journal-591	120	16	)	)	PUNCT
american_scientific_journal-591	120	17	a	a	DET
american_scientific_journal-591	120	18	b=	b=	NOUN
american_scientific_journal-591	120	19	,	,	PUNCT
american_scientific_journal-591	120	20	(	(	PUNCT
american_scientific_journal-591	120	21	2	2	X
american_scientific_journal-591	120	22	)	)	PUNCT
american_scientific_journal-591	120	23	a	a	DET
american_scientific_journal-591	120	24	b	b	NOUN
american_scientific_journal-591	120	25	<	<	X
american_scientific_journal-591	120	26	,	,	PUNCT
american_scientific_journal-591	120	27	and	and	CCONJ
american_scientific_journal-591	120	28	(	(	PUNCT
american_scientific_journal-591	120	29	3	3	X
american_scientific_journal-591	120	30	)	)	PUNCT
american_scientific_journal-591	120	31	a	a	DET
american_scientific_journal-591	120	32	b	b	NOUN
american_scientific_journal-591	120	33	>	>	X
american_scientific_journal-591	120	34	.	.	PUNCT
american_scientific_journal-591	121	1	if	if	SCONJ
american_scientific_journal-591	121	2	a	a	DET
american_scientific_journal-591	121	3	b=	b=	NOUN
american_scientific_journal-591	121	4	,	,	PUNCT
american_scientific_journal-591	121	5	then	then	ADV
american_scientific_journal-591	121	6	obviously	obviously	ADV
american_scientific_journal-591	121	7	ac	ac	VERB
american_scientific_journal-591	121	8	a	a	DET
american_scientific_journal-591	121	9	b−	b−	NOUN
american_scientific_journal-591	121	10	is	be	AUX
american_scientific_journal-591	121	11	undetermined	undetermined	ADJ
american_scientific_journal-591	121	12	.	.	PUNCT
american_scientific_journal-591	122	1	if	if	SCONJ
american_scientific_journal-591	122	2	a	a	DET
american_scientific_journal-591	122	3	b	b	NOUN
american_scientific_journal-591	122	4	<	<	X
american_scientific_journal-591	122	5	,	,	PUNCT
american_scientific_journal-591	122	6	then	then	ADV
american_scientific_journal-591	122	7	0ac	0ac	VERB
american_scientific_journal-591	122	8	a	a	DET
american_scientific_journal-591	122	9	b	b	NOUN
american_scientific_journal-591	122	10	<	<	X
american_scientific_journal-591	122	11	−	−	PROPN
american_scientific_journal-591	122	12	,	,	PUNCT
american_scientific_journal-591	122	13	which	which	PRON
american_scientific_journal-591	122	14	is	be	AUX
american_scientific_journal-591	122	15	not	not	PART
american_scientific_journal-591	122	16	in	in	ADP
american_scientific_journal-591	122	17	[	[	X
american_scientific_journal-591	122	18	0	0	NUM
american_scientific_journal-591	122	19	,	,	PUNCT
american_scientific_journal-591	122	20	c	c	NOUN
american_scientific_journal-591	122	21	]	]	PUNCT
american_scientific_journal-591	122	22	.	.	PUNCT
american_scientific_journal-591	123	1	if	if	SCONJ
american_scientific_journal-591	123	2	a	a	DET
american_scientific_journal-591	123	3	b	b	X
american_scientific_journal-591	123	4	>	>	X
american_scientific_journal-591	123	5	,	,	PUNCT
american_scientific_journal-591	123	6	then	then	ADV
american_scientific_journal-591	123	7	there	there	PRON
american_scientific_journal-591	123	8	exists	exist	VERB
american_scientific_journal-591	123	9	a	a	DET
american_scientific_journal-591	123	10	positive	positive	ADJ
american_scientific_journal-591	123	11	number	number	NOUN
american_scientific_journal-591	123	12	r	r	NOUN
american_scientific_journal-591	123	13	such	such	DET
american_scientific_journal-591	123	14	that	that	SCONJ
american_scientific_journal-591	123	15	a	a	DET
american_scientific_journal-591	123	16	b	b	NOUN
american_scientific_journal-591	123	17	r=	r=	ADJ
american_scientific_journal-591	123	18	+	+	CCONJ
american_scientific_journal-591	123	19	or	or	CCONJ
american_scientific_journal-591	123	20	r	r	NOUN
american_scientific_journal-591	123	21	a	a	DET
american_scientific_journal-591	123	22	b=	b=	NOUN
american_scientific_journal-591	123	23	−	−	NOUN
american_scientific_journal-591	123	24	and	and	CCONJ
american_scientific_journal-591	123	25	hence	hence	ADV
american_scientific_journal-591	123	26	(	(	PUNCT
american_scientific_journal-591	123	27	)	)	PUNCT
american_scientific_journal-591	124	1	ac	ac	PROPN
american_scientific_journal-591	125	1	b	b	NOUN
american_scientific_journal-591	126	1	r	r	NOUN
american_scientific_journal-591	126	2	c	c	PROPN
american_scientific_journal-591	126	3	bc	bc	PROPN
american_scientific_journal-591	126	4	c	c	PROPN
american_scientific_journal-591	126	5	a	a	DET
american_scientific_journal-591	126	6	b	b	NOUN
american_scientific_journal-591	126	7	r	r	NOUN
american_scientific_journal-591	126	8	r	r	NOUN
american_scientific_journal-591	126	9	+	+	NOUN
american_scientific_journal-591	126	10	=	=	SYM
american_scientific_journal-591	126	11	=	=	SYM
american_scientific_journal-591	127	1	+	+	NUM
american_scientific_journal-591	127	2	−	−	PROPN
american_scientific_journal-591	127	3	,	,	PUNCT
american_scientific_journal-591	127	4	which	which	PRON
american_scientific_journal-591	127	5	is	be	AUX
american_scientific_journal-591	127	6	obviously	obviously	ADV
american_scientific_journal-591	127	7	greater	great	ADJ
american_scientific_journal-591	127	8	than	than	ADP
american_scientific_journal-591	127	9	c	c	NOUN
american_scientific_journal-591	127	10	and	and	CCONJ
american_scientific_journal-591	127	11	so	so	ADV
american_scientific_journal-591	127	12	,	,	PUNCT
american_scientific_journal-591	127	13	not	not	PART
american_scientific_journal-591	127	14	in	in	ADP
american_scientific_journal-591	127	15	[	[	X
american_scientific_journal-591	127	16	0	0	NUM
american_scientific_journal-591	127	17	,	,	PUNCT
american_scientific_journal-591	127	18	c	c	NOUN
american_scientific_journal-591	127	19	]	]	PUNCT
american_scientific_journal-591	127	20	.	.	PUNCT
american_scientific_journal-591	128	1	91	91	NUM
american_scientific_journal-591	128	2	american	american	ADJ
american_scientific_journal-591	128	3	scientific	scientific	ADJ
american_scientific_journal-591	128	4	research	research	NOUN
american_scientific_journal-591	128	5	journal	journal	NOUN
american_scientific_journal-591	128	6	for	for	ADP
american_scientific_journal-591	128	7	engineering	engineering	NOUN
american_scientific_journal-591	128	8	,	,	PUNCT
american_scientific_journal-591	128	9	technology	technology	NOUN
american_scientific_journal-591	128	10	,	,	PUNCT
american_scientific_journal-591	128	11	and	and	CCONJ
american_scientific_journal-591	128	12	sciences	science	NOUN
american_scientific_journal-591	128	13	(	(	PUNCT
american_scientific_journal-591	128	14	asrjets	asrjet	NOUN
american_scientific_journal-591	128	15	)	)	PUNCT
american_scientific_journal-591	128	16	(	(	PUNCT
american_scientific_journal-591	128	17	2015	2015	NUM
american_scientific_journal-591	128	18	)	)	PUNCT
american_scientific_journal-591	128	19	volume	volume	NOUN
american_scientific_journal-591	128	20	11	11	NUM
american_scientific_journal-591	128	21	,	,	PUNCT
american_scientific_journal-591	128	22	no	no	DET
american_scientific_journal-591	128	23	1	1	NUM
american_scientific_journal-591	128	24	,	,	PUNCT
american_scientific_journal-591	128	25	pp	pp	ADV
american_scientific_journal-591	128	26	84	84	NUM
american_scientific_journal-591	128	27	-	-	SYM
american_scientific_journal-591	128	28	95	95	NUM
american_scientific_journal-591	128	29	hence	hence	ADV
american_scientific_journal-591	128	30	,	,	PUNCT
american_scientific_journal-591	128	31	the	the	DET
american_scientific_journal-591	128	32	relative	relative	ADJ
american_scientific_journal-591	128	33	extremum	extremum	NOUN
american_scientific_journal-591	128	34	is	be	AUX
american_scientific_journal-591	128	35	acx	acx	PROPN
american_scientific_journal-591	128	36	a	a	DET
american_scientific_journal-591	128	37	b	b	NOUN
american_scientific_journal-591	128	38	=	=	SYM
american_scientific_journal-591	129	1	+	+	CCONJ
american_scientific_journal-591	129	2	.	.	PUNCT
american_scientific_journal-591	130	1	looking	look	VERB
american_scientific_journal-591	130	2	back	back	ADV
american_scientific_journal-591	130	3	at	at	ADP
american_scientific_journal-591	130	4	figure	figure	NOUN
american_scientific_journal-591	130	5	8	8	NUM
american_scientific_journal-591	130	6	,	,	PUNCT
american_scientific_journal-591	130	7	this	this	PRON
american_scientific_journal-591	130	8	can	can	AUX
american_scientific_journal-591	130	9	be	be	AUX
american_scientific_journal-591	130	10	considered	consider	VERB
american_scientific_journal-591	130	11	as	as	ADP
american_scientific_journal-591	130	12	the	the	DET
american_scientific_journal-591	130	13	formula	formula	NOUN
american_scientific_journal-591	130	14	for	for	ADP
american_scientific_journal-591	130	15	determining	determine	VERB
american_scientific_journal-591	130	16	the	the	DET
american_scientific_journal-591	130	17	location	location	NOUN
american_scientific_journal-591	130	18	of	of	ADP
american_scientific_journal-591	130	19	p	p	NOUN
american_scientific_journal-591	130	20	in	in	ADP
american_scientific_journal-591	130	21	l	l	NOUN
american_scientific_journal-591	130	22	from	from	ADP
american_scientific_journal-591	130	23	a	a	PRON
american_scientific_journal-591	130	24	”	"	PUNCT
american_scientific_journal-591	130	25	.	.	PUNCT
american_scientific_journal-591	131	1	notice	notice	VERB
american_scientific_journal-591	131	2	that	that	SCONJ
american_scientific_journal-591	131	3	if	if	SCONJ
american_scientific_journal-591	131	4	a	a	DET
american_scientific_journal-591	131	5	b=	b=	NOUN
american_scientific_journal-591	131	6	,	,	PUNCT
american_scientific_journal-591	131	7	i.e.	i.e.	X
american_scientific_journal-591	131	8	when	when	SCONJ
american_scientific_journal-591	131	9	a	a	PRON
american_scientific_journal-591	131	10	and	and	CCONJ
american_scientific_journal-591	131	11	b	b	NOUN
american_scientific_journal-591	131	12	have	have	VERB
american_scientific_journal-591	131	13	equal	equal	ADJ
american_scientific_journal-591	131	14	distances	distance	NOUN
american_scientific_journal-591	131	15	from	from	ADP
american_scientific_journal-591	131	16	l	l	NOUN
american_scientific_journal-591	131	17	,	,	PUNCT
american_scientific_journal-591	131	18	then	then	ADV
american_scientific_journal-591	131	19	2	2	NUM
american_scientific_journal-591	131	20	cx	cx	NOUN
american_scientific_journal-591	131	21	=	=	NOUN
american_scientific_journal-591	131	22	or	or	CCONJ
american_scientific_journal-591	131	23	p	p	NOUN
american_scientific_journal-591	131	24	is	be	AUX
american_scientific_journal-591	131	25	in	in	ADP
american_scientific_journal-591	131	26	the	the	DET
american_scientific_journal-591	131	27	middle	middle	NOUN
american_scientific_journal-591	131	28	of	of	ADP
american_scientific_journal-591	131	29	a	a	PRON
american_scientific_journal-591	131	30	”	"	PUNCT
american_scientific_journal-591	131	31	and	and	CCONJ
american_scientific_journal-591	131	32	b	b	NOUN
american_scientific_journal-591	131	33	”	"	PUNCT
american_scientific_journal-591	131	34	.	.	PUNCT
american_scientific_journal-591	132	1	it	it	PRON
american_scientific_journal-591	132	2	can	can	AUX
american_scientific_journal-591	132	3	be	be	AUX
american_scientific_journal-591	132	4	shown	show	VERB
american_scientific_journal-591	132	5	also	also	ADV
american_scientific_journal-591	132	6	that	that	SCONJ
american_scientific_journal-591	132	7	p	p	NOUN
american_scientific_journal-591	132	8	is	be	AUX
american_scientific_journal-591	132	9	always	always	ADV
american_scientific_journal-591	132	10	nearer	near	ADJ
american_scientific_journal-591	132	11	the	the	DET
american_scientific_journal-591	132	12	point	point	NOUN
american_scientific_journal-591	132	13	with	with	ADP
american_scientific_journal-591	132	14	shorter	short	ADJ
american_scientific_journal-591	132	15	distance	distance	NOUN
american_scientific_journal-591	132	16	from	from	ADP
american_scientific_journal-591	132	17	l.	l.	PROPN
american_scientific_journal-591	132	18	the	the	DET
american_scientific_journal-591	132	19	distance	distance	NOUN
american_scientific_journal-591	132	20	d	d	NOUN
american_scientific_journal-591	132	21	can	can	AUX
american_scientific_journal-591	132	22	now	now	ADV
american_scientific_journal-591	132	23	be	be	AUX
american_scientific_journal-591	132	24	expressed	express	VERB
american_scientific_journal-591	132	25	in	in	ADP
american_scientific_journal-591	132	26	terms	term	NOUN
american_scientific_journal-591	132	27	of	of	ADP
american_scientific_journal-591	132	28	the	the	DET
american_scientific_journal-591	132	29	distances	distance	NOUN
american_scientific_journal-591	132	30	a	a	DET
american_scientific_journal-591	132	31	,	,	PUNCT
american_scientific_journal-591	132	32	b	b	PROPN
american_scientific_journal-591	132	33	and	and	CCONJ
american_scientific_journal-591	132	34	c	c	NOUN
american_scientific_journal-591	132	35	,	,	PUNCT
american_scientific_journal-591	132	36	i.e.	i.e.	X
american_scientific_journal-591	133	1	2	2	NUM
american_scientific_journal-591	133	2	2	2	NUM
american_scientific_journal-591	133	3	2	2	NUM
american_scientific_journal-591	133	4	2	2	NUM
american_scientific_journal-591	133	5	b	b	NOUN
american_scientific_journal-591	133	6	ba	ba	NOUN
american_scientific_journal-591	133	7	acca	acca	NOUN
american_scientific_journal-591	133	8	ba	ba	PROPN
american_scientific_journal-591	133	9	acd	acd	NOUN
american_scientific_journal-591	133	10	+	+	NOUN
american_scientific_journal-591	133	11			NOUN
american_scientific_journal-591	133	12			PUNCT
american_scientific_journal-591	134	1			PROPN
american_scientific_journal-591	134	2			NOUN
american_scientific_journal-591	134	3			NOUN
american_scientific_journal-591	134	4			NOUN
american_scientific_journal-591	134	5	+	+	CCONJ
american_scientific_journal-591	134	6	−++	−++	PROPN
american_scientific_journal-591	134	7			PUNCT
american_scientific_journal-591	135	1			PROPN
american_scientific_journal-591	135	2			NOUN
american_scientific_journal-591	135	3			NOUN
american_scientific_journal-591	135	4			VERB
american_scientific_journal-591	135	5	+	+	PUNCT
american_scientific_journal-591	135	6	=	=	PUNCT
american_scientific_journal-591	135	7	that	that	SCONJ
american_scientific_journal-591	135	8	when	when	SCONJ
american_scientific_journal-591	135	9	simplified	simplified	ADJ
american_scientific_journal-591	135	10	will	will	AUX
american_scientific_journal-591	135	11	result	result	VERB
american_scientific_journal-591	135	12	to	to	ADP
american_scientific_journal-591	135	13	2	2	NUM
american_scientific_journal-591	135	14	2	2	NUM
american_scientific_journal-591	135	15	(	(	PUNCT
american_scientific_journal-591	135	16	)	)	PUNCT
american_scientific_journal-591	135	17	d	d	NOUN
american_scientific_journal-591	135	18	a	a	DET
american_scientific_journal-591	135	19	b	b	NOUN
american_scientific_journal-591	135	20	c=	c=	NOUN
american_scientific_journal-591	135	21	+	+	X
american_scientific_journal-591	135	22	+	+	CCONJ
american_scientific_journal-591	135	23	,	,	PUNCT
american_scientific_journal-591	135	24	and	and	CCONJ
american_scientific_journal-591	135	25	which	which	PRON
american_scientific_journal-591	135	26	is	be	AUX
american_scientific_journal-591	135	27	the	the	DET
american_scientific_journal-591	135	28	distance	distance	NOUN
american_scientific_journal-591	135	29	from	from	ADP
american_scientific_journal-591	135	30	a	a	PRON
american_scientific_journal-591	135	31	to	to	ADP
american_scientific_journal-591	135	32	p	p	NOUN
american_scientific_journal-591	135	33	in	in	ADP
american_scientific_journal-591	135	34	l	l	NOUN
american_scientific_journal-591	135	35	to	to	ADP
american_scientific_journal-591	135	36	b	b	NOUN
american_scientific_journal-591	135	37	at	at	ADP
american_scientific_journal-591	135	38	the	the	DET
american_scientific_journal-591	135	39	relative	relative	ADJ
american_scientific_journal-591	135	40	extremum	extremum	ADJ
american_scientific_journal-591	135	41	acx	acx	PROPN
american_scientific_journal-591	135	42	a	a	DET
american_scientific_journal-591	135	43	b	b	NOUN
american_scientific_journal-591	135	44	=	=	SYM
american_scientific_journal-591	135	45	+	+	CCONJ
american_scientific_journal-591	135	46	.	.	PUNCT
american_scientific_journal-591	136	1	with	with	ADP
american_scientific_journal-591	136	2	the	the	DET
american_scientific_journal-591	136	3	extreme	extreme	ADJ
american_scientific_journal-591	136	4	-	-	PUNCT
american_scientific_journal-591	136	5	value	value	NOUN
american_scientific_journal-591	136	6	theorem	theorem	NOUN
american_scientific_journal-591	136	7	in	in	ADP
american_scientific_journal-591	136	8	mind	mind	NOUN
american_scientific_journal-591	136	9	,	,	PUNCT
american_scientific_journal-591	136	10	the	the	DET
american_scientific_journal-591	136	11	next	next	ADJ
american_scientific_journal-591	136	12	step	step	NOUN
american_scientific_journal-591	136	13	is	be	AUX
american_scientific_journal-591	136	14	to	to	PART
american_scientific_journal-591	136	15	compute	compute	VERB
american_scientific_journal-591	136	16	the	the	DET
american_scientific_journal-591	136	17	distance	distance	NOUN
american_scientific_journal-591	136	18	at	at	ADP
american_scientific_journal-591	136	19	the	the	DET
american_scientific_journal-591	136	20	endpoints	endpoint	NOUN
american_scientific_journal-591	136	21	of	of	ADP
american_scientific_journal-591	136	22	[	[	X
american_scientific_journal-591	136	23	0	0	NUM
american_scientific_journal-591	136	24	,	,	PUNCT
american_scientific_journal-591	136	25	c	c	NOUN
american_scientific_journal-591	136	26	]	]	PUNCT
american_scientific_journal-591	136	27	.	.	PUNCT
american_scientific_journal-591	137	1	that	that	PRON
american_scientific_journal-591	137	2	is	be	AUX
american_scientific_journal-591	137	3	,	,	PUNCT
american_scientific_journal-591	137	4	if	if	SCONJ
american_scientific_journal-591	137	5	0x	0x	NUM
american_scientific_journal-591	137	6	=	=	SYM
american_scientific_journal-591	137	7	,	,	PUNCT
american_scientific_journal-591	137	8	then	then	ADV
american_scientific_journal-591	137	9	2	2	NUM
american_scientific_journal-591	137	10	2d	2d	NOUN
american_scientific_journal-591	137	11	a	a	DET
american_scientific_journal-591	137	12	b	b	NOUN
american_scientific_journal-591	137	13	c=	c=	NOUN
american_scientific_journal-591	137	14	+	+	X
american_scientific_journal-591	138	1	+	+	CCONJ
american_scientific_journal-591	138	2	and	and	CCONJ
american_scientific_journal-591	138	3	if	if	SCONJ
american_scientific_journal-591	138	4	x	x	PRON
american_scientific_journal-591	138	5	c=	c=	NOUN
american_scientific_journal-591	138	6	,	,	PUNCT
american_scientific_journal-591	138	7	then	then	ADV
american_scientific_journal-591	138	8	2	2	NUM
american_scientific_journal-591	138	9	2d	2d	NOUN
american_scientific_journal-591	138	10	b	b	NOUN
american_scientific_journal-591	138	11	a	a	DET
american_scientific_journal-591	138	12	c=	c=	NOUN
american_scientific_journal-591	138	13	+	+	X
american_scientific_journal-591	139	1	+	+	CCONJ
american_scientific_journal-591	139	2	.	.	PUNCT
american_scientific_journal-591	140	1	to	to	PART
american_scientific_journal-591	140	2	determine	determine	VERB
american_scientific_journal-591	140	3	if	if	SCONJ
american_scientific_journal-591	140	4	2	2	NUM
american_scientific_journal-591	140	5	2	2	NUM
american_scientific_journal-591	140	6	(	(	PUNCT
american_scientific_journal-591	140	7	)	)	PUNCT
american_scientific_journal-591	140	8	d	d	NOUN
american_scientific_journal-591	140	9	a	a	DET
american_scientific_journal-591	140	10	b	b	NOUN
american_scientific_journal-591	140	11	c=	c=	NOUN
american_scientific_journal-591	141	1	+	+	CCONJ
american_scientific_journal-591	141	2	+	+	CCONJ
american_scientific_journal-591	141	3	is	be	AUX
american_scientific_journal-591	141	4	the	the	DET
american_scientific_journal-591	141	5	absolute	absolute	ADJ
american_scientific_journal-591	141	6	minimum	minimum	NOUN
american_scientific_journal-591	141	7	,	,	PUNCT
american_scientific_journal-591	141	8	there	there	PRON
american_scientific_journal-591	141	9	is	be	VERB
american_scientific_journal-591	141	10	a	a	DET
american_scientific_journal-591	141	11	need	need	NOUN
american_scientific_journal-591	141	12	to	to	PART
american_scientific_journal-591	141	13	show	show	VERB
american_scientific_journal-591	141	14	that	that	SCONJ
american_scientific_journal-591	141	15	2	2	NUM
american_scientific_journal-591	141	16	2	2	NUM
american_scientific_journal-591	141	17	(	(	PUNCT
american_scientific_journal-591	141	18	)	)	PUNCT
american_scientific_journal-591	141	19	a	a	DET
american_scientific_journal-591	141	20	b	b	NOUN
american_scientific_journal-591	141	21	c+	c+	NOUN
american_scientific_journal-591	141	22	+	+	X
american_scientific_journal-591	141	23	is	be	AUX
american_scientific_journal-591	141	24	less	less	ADJ
american_scientific_journal-591	141	25	than	than	ADP
american_scientific_journal-591	141	26	both	both	DET
american_scientific_journal-591	141	27	2	2	NUM
american_scientific_journal-591	141	28	2a	2a	NUM
american_scientific_journal-591	141	29	b	b	NOUN
american_scientific_journal-591	141	30	c+	c+	NOUN
american_scientific_journal-591	141	31	+	+	PUNCT
american_scientific_journal-591	141	32	and	and	CCONJ
american_scientific_journal-591	141	33	2	2	NUM
american_scientific_journal-591	141	34	2b	2b	NOUN
american_scientific_journal-591	141	35	a	a	DET
american_scientific_journal-591	141	36	c+	c+	NOUN
american_scientific_journal-591	141	37	+	+	X
american_scientific_journal-591	141	38	.	.	PUNCT
american_scientific_journal-591	142	1	hence	hence	ADV
american_scientific_journal-591	142	2	,	,	PUNCT
american_scientific_journal-591	142	3	2	2	NUM
american_scientific_journal-591	142	4	2	2	NUM
american_scientific_journal-591	142	5	2	2	NUM
american_scientific_journal-591	142	6	2	2	NUM
american_scientific_journal-591	142	7	(	(	PUNCT
american_scientific_journal-591	142	8	)	)	PUNCT
american_scientific_journal-591	142	9	a	a	DET
american_scientific_journal-591	142	10	b	b	NOUN
american_scientific_journal-591	142	11	c	c	NOUN
american_scientific_journal-591	142	12	a	a	DET
american_scientific_journal-591	142	13	b	b	NOUN
american_scientific_journal-591	142	14	c+	c+	NOUN
american_scientific_journal-591	142	15	+	+	X
american_scientific_journal-591	142	16	<	<	X
american_scientific_journal-591	143	1	+	+	X
american_scientific_journal-591	143	2	+	+	CCONJ
american_scientific_journal-591	143	3	,	,	PUNCT
american_scientific_journal-591	144	1	which	which	PRON
american_scientific_journal-591	144	2	when	when	SCONJ
american_scientific_journal-591	144	3	both	both	DET
american_scientific_journal-591	144	4	sides	side	NOUN
american_scientific_journal-591	144	5	are	be	AUX
american_scientific_journal-591	144	6	squared	square	VERB
american_scientific_journal-591	144	7	and	and	CCONJ
american_scientific_journal-591	144	8	the	the	DET
american_scientific_journal-591	144	9	inequality	inequality	NOUN
american_scientific_journal-591	144	10	is	be	AUX
american_scientific_journal-591	144	11	simplified	simplify	VERB
american_scientific_journal-591	144	12	results	result	NOUN
american_scientific_journal-591	144	13	to	to	ADP
american_scientific_journal-591	144	14	2	2	NUM
american_scientific_journal-591	144	15	2b	2b	NOUN
american_scientific_journal-591	144	16	b	b	NOUN
american_scientific_journal-591	144	17	c	c	X
american_scientific_journal-591	144	18	<	<	X
american_scientific_journal-591	144	19	+	+	X
american_scientific_journal-591	144	20	and	and	CCONJ
american_scientific_journal-591	144	21	squaring	square	VERB
american_scientific_journal-591	144	22	again	again	ADV
american_scientific_journal-591	144	23	gives	give	VERB
american_scientific_journal-591	144	24	the	the	DET
american_scientific_journal-591	144	25	obviously	obviously	ADV
american_scientific_journal-591	144	26	true	true	ADJ
american_scientific_journal-591	144	27	inequality	inequality	NOUN
american_scientific_journal-591	144	28	2	2	NUM
american_scientific_journal-591	144	29	2	2	NUM
american_scientific_journal-591	144	30	2b	2b	NUM
american_scientific_journal-591	145	1	b	b	NOUN
american_scientific_journal-591	145	2	c	c	X
american_scientific_journal-591	145	3	<	<	X
american_scientific_journal-591	145	4	+	+	X
american_scientific_journal-591	145	5	.	.	PUNCT
american_scientific_journal-591	146	1	similarly	similarly	ADV
american_scientific_journal-591	146	2	,	,	PUNCT
american_scientific_journal-591	146	3	2	2	NUM
american_scientific_journal-591	146	4	2	2	NUM
american_scientific_journal-591	146	5	2	2	NUM
american_scientific_journal-591	146	6	2	2	NUM
american_scientific_journal-591	146	7	(	(	PUNCT
american_scientific_journal-591	146	8	)	)	PUNCT
american_scientific_journal-591	146	9	a	a	DET
american_scientific_journal-591	146	10	b	b	NOUN
american_scientific_journal-591	146	11	c	c	PROPN
american_scientific_journal-591	146	12	b	b	PROPN
american_scientific_journal-591	146	13	a	a	DET
american_scientific_journal-591	146	14	c+	c+	NOUN
american_scientific_journal-591	146	15	+	+	X
american_scientific_journal-591	146	16	<	<	X
american_scientific_journal-591	147	1	+	+	X
american_scientific_journal-591	147	2	+	+	CCONJ
american_scientific_journal-591	147	3	,	,	PUNCT
american_scientific_journal-591	147	4	which	which	PRON
american_scientific_journal-591	147	5	when	when	SCONJ
american_scientific_journal-591	147	6	also	also	ADV
american_scientific_journal-591	147	7	squared	square	VERB
american_scientific_journal-591	147	8	and	and	CCONJ
american_scientific_journal-591	147	9	simplified	simplified	ADJ
american_scientific_journal-591	147	10	will	will	AUX
american_scientific_journal-591	147	11	have	have	VERB
american_scientific_journal-591	147	12	2	2	NUM
american_scientific_journal-591	147	13	2a	2a	NUM
american_scientific_journal-591	147	14	a	a	DET
american_scientific_journal-591	147	15	c	c	NOUN
american_scientific_journal-591	147	16	<	<	X
american_scientific_journal-591	147	17	+	+	X
american_scientific_journal-591	147	18	and	and	CCONJ
american_scientific_journal-591	147	19	squaring	square	VERB
american_scientific_journal-591	147	20	again	again	ADV
american_scientific_journal-591	147	21	gives	give	VERB
american_scientific_journal-591	147	22	also	also	ADV
american_scientific_journal-591	147	23	a	a	DET
american_scientific_journal-591	147	24	true	true	ADJ
american_scientific_journal-591	147	25	inequality	inequality	NOUN
american_scientific_journal-591	147	26	2	2	NUM
american_scientific_journal-591	147	27	2	2	NUM
american_scientific_journal-591	147	28	2a	2a	NUM
american_scientific_journal-591	147	29	a	a	DET
american_scientific_journal-591	147	30	c	c	NOUN
american_scientific_journal-591	147	31	<	<	X
american_scientific_journal-591	148	1	+	+	X
american_scientific_journal-591	148	2	.	.	PUNCT
american_scientific_journal-591	149	1	it	it	PRON
american_scientific_journal-591	149	2	is	be	AUX
american_scientific_journal-591	149	3	now	now	ADV
american_scientific_journal-591	149	4	very	very	ADV
american_scientific_journal-591	149	5	clear	clear	ADJ
american_scientific_journal-591	149	6	that	that	SCONJ
american_scientific_journal-591	149	7	22	22	NUM
american_scientific_journal-591	149	8	)	)	PUNCT
american_scientific_journal-591	149	9	(	(	PUNCT
american_scientific_journal-591	149	10	cbad	cbad	VERB
american_scientific_journal-591	149	11	+	+	PROPN
american_scientific_journal-591	149	12	+	+	NOUN
american_scientific_journal-591	149	13	=	=	PRON
american_scientific_journal-591	149	14	is	be	AUX
american_scientific_journal-591	149	15	a	a	DET
american_scientific_journal-591	149	16	formula	formula	NOUN
american_scientific_journal-591	149	17	that	that	PRON
american_scientific_journal-591	149	18	will	will	AUX
american_scientific_journal-591	149	19	surely	surely	ADV
american_scientific_journal-591	149	20	give	give	VERB
american_scientific_journal-591	149	21	the	the	DET
american_scientific_journal-591	149	22	minimum	minimum	ADJ
american_scientific_journal-591	149	23	distance	distance	NOUN
american_scientific_journal-591	149	24	from	from	ADP
american_scientific_journal-591	149	25	a	a	DET
american_scientific_journal-591	149	26	point	point	NOUN
american_scientific_journal-591	149	27	to	to	ADP
american_scientific_journal-591	149	28	a	a	DET
american_scientific_journal-591	149	29	line	line	NOUN
american_scientific_journal-591	149	30	to	to	ADP
american_scientific_journal-591	149	31	another	another	DET
american_scientific_journal-591	149	32	point	point	NOUN
american_scientific_journal-591	149	33	on	on	ADP
american_scientific_journal-591	149	34	the	the	DET
american_scientific_journal-591	149	35	same	same	ADJ
american_scientific_journal-591	149	36	side	side	NOUN
american_scientific_journal-591	149	37	of	of	ADP
american_scientific_journal-591	149	38	the	the	DET
american_scientific_journal-591	149	39	line	line	NOUN
american_scientific_journal-591	149	40	.	.	PUNCT
american_scientific_journal-591	150	1	the	the	DET
american_scientific_journal-591	150	2	formula	formula	NOUN
american_scientific_journal-591	150	3	,	,	PUNCT
american_scientific_journal-591	150	4	being	be	AUX
american_scientific_journal-591	150	5	a	a	DET
american_scientific_journal-591	150	6	pythagorean	pythagorean	ADJ
american_scientific_journal-591	150	7	relation	relation	NOUN
american_scientific_journal-591	150	8	and	and	CCONJ
american_scientific_journal-591	150	9	as	as	SCONJ
american_scientific_journal-591	150	10	shown	show	VERB
american_scientific_journal-591	150	11	in	in	ADP
american_scientific_journal-591	150	12	the	the	DET
american_scientific_journal-591	150	13	geometrical	geometrical	ADJ
american_scientific_journal-591	150	14	derivation	derivation	NOUN
american_scientific_journal-591	150	15	,	,	PUNCT
american_scientific_journal-591	150	16	is	be	AUX
american_scientific_journal-591	150	17	also	also	ADV
american_scientific_journal-591	150	18	applicable	applicable	ADJ
american_scientific_journal-591	150	19	for	for	ADP
american_scientific_journal-591	150	20	the	the	DET
american_scientific_journal-591	150	21	minimum	minimum	ADJ
american_scientific_journal-591	150	22	distance	distance	NOUN
american_scientific_journal-591	150	23	from	from	ADP
american_scientific_journal-591	150	24	a	a	DET
american_scientific_journal-591	150	25	point	point	NOUN
american_scientific_journal-591	150	26	to	to	ADP
american_scientific_journal-591	150	27	a	a	DET
american_scientific_journal-591	150	28	line	line	NOUN
american_scientific_journal-591	150	29	to	to	ADP
american_scientific_journal-591	150	30	another	another	DET
american_scientific_journal-591	150	31	point	point	NOUN
american_scientific_journal-591	150	32	on	on	ADP
american_scientific_journal-591	150	33	the	the	DET
american_scientific_journal-591	150	34	other	other	ADJ
american_scientific_journal-591	150	35	side	side	NOUN
american_scientific_journal-591	150	36	of	of	ADP
american_scientific_journal-591	150	37	the	the	DET
american_scientific_journal-591	150	38	line	line	NOUN
american_scientific_journal-591	150	39	.	.	PUNCT
american_scientific_journal-591	151	1	3.3	3.3	NUM
american_scientific_journal-591	151	2	.	.	PUNCT
american_scientific_journal-591	151	3	problems	problem	NOUN
american_scientific_journal-591	151	4	and	and	CCONJ
american_scientific_journal-591	151	5	solutions	solution	NOUN
american_scientific_journal-591	151	6	sample	sample	NOUN
american_scientific_journal-591	151	7	problems	problem	NOUN
american_scientific_journal-591	151	8	and	and	CCONJ
american_scientific_journal-591	151	9	solutions	solution	NOUN
american_scientific_journal-591	151	10	to	to	PART
american_scientific_journal-591	151	11	illustrate	illustrate	VERB
american_scientific_journal-591	151	12	the	the	DET
american_scientific_journal-591	151	13	use	use	NOUN
american_scientific_journal-591	151	14	of	of	ADP
american_scientific_journal-591	151	15	the	the	DET
american_scientific_journal-591	151	16	derived	derive	VERB
american_scientific_journal-591	151	17	formulas	formula	NOUN
american_scientific_journal-591	151	18	are	be	AUX
american_scientific_journal-591	151	19	presented	present	VERB
american_scientific_journal-591	151	20	here	here	ADV
american_scientific_journal-591	151	21	.	.	PUNCT
american_scientific_journal-591	152	1	in	in	ADP
american_scientific_journal-591	152	2	solving	solve	VERB
american_scientific_journal-591	152	3	the	the	DET
american_scientific_journal-591	152	4	following	follow	VERB
american_scientific_journal-591	152	5	problems	problem	NOUN
american_scientific_journal-591	152	6	,	,	PUNCT
american_scientific_journal-591	152	7	figures	figure	NOUN
american_scientific_journal-591	152	8	or	or	CCONJ
american_scientific_journal-591	152	9	illustrations	illustration	NOUN
american_scientific_journal-591	152	10	may	may	AUX
american_scientific_journal-591	152	11	or	or	CCONJ
american_scientific_journal-591	152	12	may	may	AUX
american_scientific_journal-591	152	13	not	not	PART
american_scientific_journal-591	152	14	be	be	AUX
american_scientific_journal-591	152	15	used	use	VERB
american_scientific_journal-591	152	16	,	,	PUNCT
american_scientific_journal-591	152	17	as	as	ADV
american_scientific_journal-591	152	18	long	long	ADV
american_scientific_journal-591	152	19	as	as	SCONJ
american_scientific_journal-591	152	20	the	the	DET
american_scientific_journal-591	152	21	distances	distance	NOUN
american_scientific_journal-591	152	22	,	,	PUNCT
american_scientific_journal-591	152	23	a	a	DET
american_scientific_journal-591	152	24	,	,	PUNCT
american_scientific_journal-591	152	25	b	b	NOUN
american_scientific_journal-591	152	26	and	and	CCONJ
american_scientific_journal-591	152	27	c	c	NOUN
american_scientific_journal-591	152	28	,	,	PUNCT
american_scientific_journal-591	152	29	are	be	AUX
american_scientific_journal-591	152	30	clear	clear	ADJ
american_scientific_journal-591	152	31	for	for	SCONJ
american_scientific_journal-591	152	32	the	the	DET
american_scientific_journal-591	152	33	problem	problem	NOUN
american_scientific_journal-591	152	34	solver	solver	ADV
american_scientific_journal-591	152	35	.	.	PUNCT
american_scientific_journal-591	153	1	92	92	NUM
american_scientific_journal-591	153	2	american	american	ADJ
american_scientific_journal-591	153	3	scientific	scientific	ADJ
american_scientific_journal-591	153	4	research	research	NOUN
american_scientific_journal-591	153	5	journal	journal	NOUN
american_scientific_journal-591	153	6	for	for	ADP
american_scientific_journal-591	153	7	engineering	engineering	NOUN
american_scientific_journal-591	153	8	,	,	PUNCT
american_scientific_journal-591	153	9	technology	technology	NOUN
american_scientific_journal-591	153	10	,	,	PUNCT
american_scientific_journal-591	153	11	and	and	CCONJ
american_scientific_journal-591	153	12	sciences	science	NOUN
american_scientific_journal-591	153	13	(	(	PUNCT
american_scientific_journal-591	153	14	asrjets	asrjet	NOUN
american_scientific_journal-591	153	15	)	)	PUNCT
american_scientific_journal-591	153	16	(	(	PUNCT
american_scientific_journal-591	153	17	2015	2015	NUM
american_scientific_journal-591	153	18	)	)	PUNCT
american_scientific_journal-591	153	19	volume	volume	NOUN
american_scientific_journal-591	153	20	11	11	NUM
american_scientific_journal-591	153	21	,	,	PUNCT
american_scientific_journal-591	153	22	no	no	DET
american_scientific_journal-591	153	23	1	1	NUM
american_scientific_journal-591	153	24	,	,	PUNCT
american_scientific_journal-591	153	25	pp	pp	ADV
american_scientific_journal-591	153	26	84	84	NUM
american_scientific_journal-591	153	27	-	-	SYM
american_scientific_journal-591	153	28	95	95	NUM
american_scientific_journal-591	153	29	problem	problem	NOUN
american_scientific_journal-591	153	30	1	1	NUM
american_scientific_journal-591	153	31	.	.	PUNCT
american_scientific_journal-591	153	32	towns	town	NOUN
american_scientific_journal-591	153	33	a	a	PRON
american_scientific_journal-591	153	34	and	and	CCONJ
american_scientific_journal-591	153	35	b	b	NOUN
american_scientific_journal-591	153	36	,	,	PUNCT
american_scientific_journal-591	153	37	situated	situate	VERB
american_scientific_journal-591	153	38	inland	inland	ADV
american_scientific_journal-591	153	39	on	on	ADP
american_scientific_journal-591	153	40	the	the	DET
american_scientific_journal-591	153	41	same	same	ADJ
american_scientific_journal-591	153	42	side	side	NOUN
american_scientific_journal-591	153	43	of	of	ADP
american_scientific_journal-591	153	44	a	a	DET
american_scientific_journal-591	153	45	straight	straight	ADJ
american_scientific_journal-591	153	46	river	river	NOUN
american_scientific_journal-591	153	47	,	,	PUNCT
american_scientific_journal-591	153	48	want	want	VERB
american_scientific_journal-591	153	49	to	to	PART
american_scientific_journal-591	153	50	erect	erect	VERB
american_scientific_journal-591	153	51	a	a	DET
american_scientific_journal-591	153	52	jointly	jointly	ADV
american_scientific_journal-591	153	53	owned	own	VERB
american_scientific_journal-591	153	54	pumping	pumping	NOUN
american_scientific_journal-591	153	55	station	station	NOUN
american_scientific_journal-591	153	56	p	p	NOUN
american_scientific_journal-591	153	57	on	on	ADP
american_scientific_journal-591	153	58	the	the	DET
american_scientific_journal-591	153	59	bank	bank	NOUN
american_scientific_journal-591	153	60	of	of	ADP
american_scientific_journal-591	153	61	the	the	DET
american_scientific_journal-591	153	62	river	river	NOUN
american_scientific_journal-591	153	63	.	.	PUNCT
american_scientific_journal-591	154	1	if	if	SCONJ
american_scientific_journal-591	154	2	town	town	NOUN
american_scientific_journal-591	154	3	a	a	PRON
american_scientific_journal-591	154	4	is	be	AUX
american_scientific_journal-591	154	5	12	12	NUM
american_scientific_journal-591	154	6	km	km	NOUN
american_scientific_journal-591	154	7	from	from	ADP
american_scientific_journal-591	154	8	the	the	DET
american_scientific_journal-591	154	9	river	river	NOUN
american_scientific_journal-591	154	10	,	,	PUNCT
american_scientific_journal-591	154	11	town	town	NOUN
american_scientific_journal-591	154	12	b	b	PROPN
american_scientific_journal-591	154	13	is	be	AUX
american_scientific_journal-591	154	14	28	28	NUM
american_scientific_journal-591	154	15	km	km	NOUN
american_scientific_journal-591	154	16	from	from	ADP
american_scientific_journal-591	154	17	the	the	DET
american_scientific_journal-591	154	18	river	river	NOUN
american_scientific_journal-591	154	19	,	,	PUNCT
american_scientific_journal-591	154	20	and	and	CCONJ
american_scientific_journal-591	154	21	the	the	DET
american_scientific_journal-591	154	22	points	point	NOUN
american_scientific_journal-591	154	23	on	on	ADP
american_scientific_journal-591	154	24	the	the	DET
american_scientific_journal-591	154	25	river	river	NOUN
american_scientific_journal-591	154	26	nearest	near	ADJ
american_scientific_journal-591	154	27	to	to	ADP
american_scientific_journal-591	154	28	a	a	PRON
american_scientific_journal-591	154	29	and	and	CCONJ
american_scientific_journal-591	154	30	b	b	NOUN
american_scientific_journal-591	154	31	are	be	AUX
american_scientific_journal-591	154	32	30	30	NUM
american_scientific_journal-591	154	33	km	km	NOUN
american_scientific_journal-591	154	34	apart	apart	ADV
american_scientific_journal-591	154	35	,	,	PUNCT
american_scientific_journal-591	154	36	where	where	SCONJ
american_scientific_journal-591	154	37	should	should	AUX
american_scientific_journal-591	154	38	p	p	NOUN
american_scientific_journal-591	154	39	be	be	AUX
american_scientific_journal-591	154	40	located	locate	VERB
american_scientific_journal-591	154	41	if	if	SCONJ
american_scientific_journal-591	154	42	the	the	DET
american_scientific_journal-591	154	43	length	length	NOUN
american_scientific_journal-591	154	44	of	of	ADP
american_scientific_journal-591	154	45	the	the	DET
american_scientific_journal-591	154	46	pipe	pipe	NOUN
american_scientific_journal-591	154	47	to	to	PART
american_scientific_journal-591	154	48	be	be	AUX
american_scientific_journal-591	154	49	used	use	VERB
american_scientific_journal-591	154	50	from	from	ADP
american_scientific_journal-591	154	51	p	p	NOUN
american_scientific_journal-591	154	52	to	to	ADP
american_scientific_journal-591	154	53	a	a	PRON
american_scientific_journal-591	154	54	and	and	CCONJ
american_scientific_journal-591	154	55	from	from	ADP
american_scientific_journal-591	154	56	p	p	NOUN
american_scientific_journal-591	154	57	to	to	ADP
american_scientific_journal-591	154	58	b	b	NOUN
american_scientific_journal-591	154	59	is	be	AUX
american_scientific_journal-591	154	60	to	to	PART
american_scientific_journal-591	154	61	be	be	AUX
american_scientific_journal-591	154	62	a	a	DET
american_scientific_journal-591	154	63	minimum	minimum	NOUN
american_scientific_journal-591	154	64	?	?	PUNCT
american_scientific_journal-591	155	1	what	what	PRON
american_scientific_journal-591	155	2	will	will	AUX
american_scientific_journal-591	155	3	be	be	AUX
american_scientific_journal-591	155	4	the	the	DET
american_scientific_journal-591	155	5	minimum	minimum	ADJ
american_scientific_journal-591	155	6	length	length	NOUN
american_scientific_journal-591	155	7	of	of	ADP
american_scientific_journal-591	155	8	the	the	DET
american_scientific_journal-591	155	9	pipe	pipe	NOUN
american_scientific_journal-591	155	10	?	?	PUNCT
american_scientific_journal-591	156	1	solution	solution	NOUN
american_scientific_journal-591	156	2	:	:	PUNCT
american_scientific_journal-591	156	3	using	use	VERB
american_scientific_journal-591	156	4	the	the	DET
american_scientific_journal-591	156	5	derived	derive	VERB
american_scientific_journal-591	156	6	formula	formula	NOUN
american_scientific_journal-591	156	7	for	for	ADP
american_scientific_journal-591	156	8	the	the	DET
american_scientific_journal-591	156	9	relative	relative	ADJ
american_scientific_journal-591	156	10	extremum	extremum	ADJ
american_scientific_journal-591	156	11	value	value	NOUN
american_scientific_journal-591	156	12	of	of	ADP
american_scientific_journal-591	156	13	x	x	PRON
american_scientific_journal-591	156	14	,	,	PUNCT
american_scientific_journal-591	156	15	the	the	DET
american_scientific_journal-591	156	16	location	location	NOUN
american_scientific_journal-591	156	17	of	of	ADP
american_scientific_journal-591	156	18	p	p	PROPN
american_scientific_journal-591	156	19	can	can	AUX
american_scientific_journal-591	156	20	be	be	AUX
american_scientific_journal-591	156	21	easily	easily	ADV
american_scientific_journal-591	156	22	found	find	VERB
american_scientific_journal-591	156	23	with	with	ADP
american_scientific_journal-591	156	24	a	a	DET
american_scientific_journal-591	156	25	=	=	SYM
american_scientific_journal-591	156	26	12	12	NUM
american_scientific_journal-591	156	27	km	km	NOUN
american_scientific_journal-591	156	28	,	,	PUNCT
american_scientific_journal-591	156	29	b	b	NOUN
american_scientific_journal-591	156	30	=	=	SYM
american_scientific_journal-591	156	31	28	28	NUM
american_scientific_journal-591	156	32	km	km	NOUN
american_scientific_journal-591	156	33	and	and	CCONJ
american_scientific_journal-591	156	34	c	c	NOUN
american_scientific_journal-591	156	35	=	=	SYM
american_scientific_journal-591	156	36	30	30	NUM
american_scientific_journal-591	156	37	km	km	NOUN
american_scientific_journal-591	156	38	as	as	SCONJ
american_scientific_journal-591	156	39	follows	follow	VERB
american_scientific_journal-591	156	40	:	:	PUNCT
american_scientific_journal-591	156	41	12(30	12(30	NUM
american_scientific_journal-591	156	42	)	)	PUNCT
american_scientific_journal-591	156	43	9	9	NUM
american_scientific_journal-591	156	44	12	12	NUM
american_scientific_journal-591	156	45	28	28	NUM
american_scientific_journal-591	156	46	acx	acx	NOUN
american_scientific_journal-591	156	47	a	a	DET
american_scientific_journal-591	156	48	b	b	NOUN
american_scientific_journal-591	156	49	=	=	SYM
american_scientific_journal-591	156	50	=	=	PUNCT
american_scientific_journal-591	157	1	=	=	PUNCT
american_scientific_journal-591	158	1	+	+	PUNCT
american_scientific_journal-591	158	2	+	+	CCONJ
american_scientific_journal-591	158	3	.	.	PUNCT
american_scientific_journal-591	159	1	for	for	SCONJ
american_scientific_journal-591	159	2	minimum	minimum	ADJ
american_scientific_journal-591	159	3	length	length	NOUN
american_scientific_journal-591	159	4	of	of	ADP
american_scientific_journal-591	159	5	pipe	pipe	NOUN
american_scientific_journal-591	159	6	to	to	PART
american_scientific_journal-591	159	7	be	be	AUX
american_scientific_journal-591	159	8	used	use	VERB
american_scientific_journal-591	159	9	,	,	PUNCT
american_scientific_journal-591	159	10	the	the	DET
american_scientific_journal-591	159	11	derived	derive	VERB
american_scientific_journal-591	159	12	minimum	minimum	NOUN
american_scientific_journal-591	159	13	distance	distance	NOUN
american_scientific_journal-591	159	14	formula	formula	NOUN
american_scientific_journal-591	159	15	can	can	AUX
american_scientific_journal-591	159	16	be	be	AUX
american_scientific_journal-591	159	17	used	use	VERB
american_scientific_journal-591	159	18	,	,	PUNCT
american_scientific_journal-591	159	19	i.e.	i.e.	X
american_scientific_journal-591	159	20	2	2	NUM
american_scientific_journal-591	159	21	2	2	NUM
american_scientific_journal-591	159	22	2	2	NUM
american_scientific_journal-591	159	23	2	2	NUM
american_scientific_journal-591	159	24	(	(	PUNCT
american_scientific_journal-591	159	25	)	)	PUNCT
american_scientific_journal-591	159	26	(	(	PUNCT
american_scientific_journal-591	159	27	12	12	NUM
american_scientific_journal-591	159	28	28	28	NUM
american_scientific_journal-591	159	29	)	)	PUNCT
american_scientific_journal-591	159	30	30	30	NUM
american_scientific_journal-591	159	31	50d	50d	NOUN
american_scientific_journal-591	159	32	a	a	DET
american_scientific_journal-591	159	33	b	b	NOUN
american_scientific_journal-591	159	34	c=	c=	NOUN
american_scientific_journal-591	159	35	+	+	X
american_scientific_journal-591	160	1	+	+	PUNCT
american_scientific_journal-591	160	2	=	=	SYM
american_scientific_journal-591	161	1	+	+	PUNCT
american_scientific_journal-591	161	2	+	+	CCONJ
american_scientific_journal-591	161	3	=	=	NOUN
american_scientific_journal-591	161	4	.	.	PUNCT
american_scientific_journal-591	162	1	therefore	therefore	ADV
american_scientific_journal-591	162	2	,	,	PUNCT
american_scientific_journal-591	162	3	the	the	DET
american_scientific_journal-591	162	4	location	location	NOUN
american_scientific_journal-591	162	5	of	of	ADP
american_scientific_journal-591	162	6	p	p	PROPN
american_scientific_journal-591	162	7	is	be	AUX
american_scientific_journal-591	162	8	9	9	NUM
american_scientific_journal-591	162	9	km	km	NOUN
american_scientific_journal-591	162	10	from	from	ADP
american_scientific_journal-591	162	11	the	the	DET
american_scientific_journal-591	162	12	point	point	NOUN
american_scientific_journal-591	162	13	on	on	ADP
american_scientific_journal-591	162	14	the	the	DET
american_scientific_journal-591	162	15	river	river	NOUN
american_scientific_journal-591	162	16	nearest	nearest	ADP
american_scientific_journal-591	162	17	a	a	PRON
american_scientific_journal-591	162	18	and	and	CCONJ
american_scientific_journal-591	162	19	the	the	DET
american_scientific_journal-591	162	20	minimum	minimum	ADJ
american_scientific_journal-591	162	21	length	length	NOUN
american_scientific_journal-591	162	22	of	of	ADP
american_scientific_journal-591	162	23	the	the	DET
american_scientific_journal-591	162	24	pipe	pipe	NOUN
american_scientific_journal-591	162	25	to	to	PART
american_scientific_journal-591	162	26	be	be	AUX
american_scientific_journal-591	162	27	used	use	VERB
american_scientific_journal-591	162	28	is	be	AUX
american_scientific_journal-591	162	29	50	50	NUM
american_scientific_journal-591	162	30	km	km	NOUN
american_scientific_journal-591	162	31	.	.	PUNCT
american_scientific_journal-591	163	1	the	the	DET
american_scientific_journal-591	163	2	illustration	illustration	NOUN
american_scientific_journal-591	163	3	of	of	ADP
american_scientific_journal-591	163	4	the	the	DET
american_scientific_journal-591	163	5	above	above	ADJ
american_scientific_journal-591	163	6	problem	problem	NOUN
american_scientific_journal-591	163	7	is	be	AUX
american_scientific_journal-591	163	8	given	give	VERB
american_scientific_journal-591	163	9	in	in	ADP
american_scientific_journal-591	163	10	figure	figure	NOUN
american_scientific_journal-591	163	11	9	9	NUM
american_scientific_journal-591	163	12	.	.	PUNCT
american_scientific_journal-591	164	1	figure	figure	NOUN
american_scientific_journal-591	164	2	9	9	NUM
american_scientific_journal-591	164	3	:	:	PUNCT
american_scientific_journal-591	164	4	problem	problem	NOUN
american_scientific_journal-591	164	5	1	1	NUM
american_scientific_journal-591	164	6	illustration	illustration	NOUN
american_scientific_journal-591	164	7	problem	problem	NOUN
american_scientific_journal-591	164	8	2	2	NUM
american_scientific_journal-591	164	9	.	.	PUNCT
american_scientific_journal-591	164	10	suppose	suppose	VERB
american_scientific_journal-591	164	11	that	that	SCONJ
american_scientific_journal-591	164	12	light	light	NOUN
american_scientific_journal-591	164	13	reflects	reflect	VERB
american_scientific_journal-591	164	14	off	off	ADP
american_scientific_journal-591	164	15	a	a	DET
american_scientific_journal-591	164	16	flat	flat	ADJ
american_scientific_journal-591	164	17	mirror	mirror	NOUN
american_scientific_journal-591	164	18	to	to	PART
american_scientific_journal-591	164	19	get	get	VERB
american_scientific_journal-591	164	20	from	from	ADP
american_scientific_journal-591	164	21	point	point	NOUN
american_scientific_journal-591	164	22	a	a	PRON
american_scientific_journal-591	164	23	to	to	PART
american_scientific_journal-591	164	24	point	point	VERB
american_scientific_journal-591	164	25	b.	b.	PROPN
american_scientific_journal-591	164	26	assuming	assume	VERB
american_scientific_journal-591	164	27	a	a	DET
american_scientific_journal-591	164	28	constant	constant	ADJ
american_scientific_journal-591	164	29	velocity	velocity	NOUN
american_scientific_journal-591	164	30	of	of	ADP
american_scientific_journal-591	164	31	light	light	NOUN
american_scientific_journal-591	164	32	,	,	PUNCT
american_scientific_journal-591	164	33	time	time	NOUN
american_scientific_journal-591	164	34	can	can	AUX
american_scientific_journal-591	164	35	be	be	AUX
american_scientific_journal-591	164	36	minimized	minimize	VERB
american_scientific_journal-591	164	37	by	by	ADP
american_scientific_journal-591	164	38	minimizing	minimize	VERB
american_scientific_journal-591	164	39	the	the	DET
american_scientific_journal-591	164	40	distance	distance	NOUN
american_scientific_journal-591	164	41	traveled	travel	VERB
american_scientific_journal-591	164	42	.	.	PUNCT
american_scientific_journal-591	165	1	if	if	SCONJ
american_scientific_journal-591	165	2	a	a	PRON
american_scientific_journal-591	165	3	is	be	AUX
american_scientific_journal-591	165	4	2	2	NUM
american_scientific_journal-591	165	5	units	unit	NOUN
american_scientific_journal-591	165	6	and	and	CCONJ
american_scientific_journal-591	165	7	b	b	NOUN
american_scientific_journal-591	165	8	is	be	AUX
american_scientific_journal-591	165	9	1	1	NUM
american_scientific_journal-591	165	10	unit	unit	NOUN
american_scientific_journal-591	165	11	from	from	ADP
american_scientific_journal-591	165	12	the	the	DET
american_scientific_journal-591	165	13	mirror	mirror	NOUN
american_scientific_journal-591	165	14	and	and	CCONJ
american_scientific_journal-591	165	15	the	the	DET
american_scientific_journal-591	165	16	points	point	NOUN
american_scientific_journal-591	165	17	on	on	ADP
american_scientific_journal-591	165	18	the	the	DET
american_scientific_journal-591	165	19	mirror	mirror	NOUN
american_scientific_journal-591	165	20	nearest	near	ADJ
american_scientific_journal-591	165	21	a	a	PRON
american_scientific_journal-591	165	22	and	and	CCONJ
american_scientific_journal-591	165	23	b	b	NOUN
american_scientific_journal-591	165	24	are	be	AUX
american_scientific_journal-591	165	25	4	4	NUM
american_scientific_journal-591	165	26	units	unit	NOUN
american_scientific_journal-591	165	27	apart	apart	ADV
american_scientific_journal-591	165	28	,	,	PUNCT
american_scientific_journal-591	165	29	find	find	VERB
american_scientific_journal-591	165	30	the	the	DET
american_scientific_journal-591	165	31	location	location	NOUN
american_scientific_journal-591	165	32	of	of	ADP
american_scientific_journal-591	165	33	point	point	NOUN
american_scientific_journal-591	165	34	p	p	NOUN
american_scientific_journal-591	165	35	on	on	ADP
american_scientific_journal-591	165	36	the	the	DET
american_scientific_journal-591	165	37	mirror	mirror	NOUN
american_scientific_journal-591	165	38	that	that	PRON
american_scientific_journal-591	165	39	minimizes	minimize	VERB
american_scientific_journal-591	165	40	the	the	DET
american_scientific_journal-591	165	41	distance	distance	NOUN
american_scientific_journal-591	165	42	traveled	travel	VERB
american_scientific_journal-591	165	43	.	.	PUNCT
american_scientific_journal-591	166	1	solution	solution	NOUN
american_scientific_journal-591	166	2	:	:	PUNCT
american_scientific_journal-591	166	3	given	give	VERB
american_scientific_journal-591	166	4	that	that	SCONJ
american_scientific_journal-591	166	5	a	a	DET
american_scientific_journal-591	166	6	=	=	SYM
american_scientific_journal-591	166	7	2	2	NUM
american_scientific_journal-591	166	8	,	,	PUNCT
american_scientific_journal-591	166	9	b	b	NOUN
american_scientific_journal-591	166	10	=	=	SYM
american_scientific_journal-591	166	11	1	1	NUM
american_scientific_journal-591	166	12	and	and	CCONJ
american_scientific_journal-591	166	13	c	c	NOUN
american_scientific_journal-591	166	14	=	=	SYM
american_scientific_journal-591	166	15	4	4	NUM
american_scientific_journal-591	166	16	,	,	PUNCT
american_scientific_journal-591	166	17	the	the	DET
american_scientific_journal-591	166	18	location	location	NOUN
american_scientific_journal-591	166	19	of	of	ADP
american_scientific_journal-591	166	20	p	p	NOUN
american_scientific_journal-591	166	21	that	that	PRON
american_scientific_journal-591	166	22	minimizes	minimize	VERB
american_scientific_journal-591	166	23	the	the	DET
american_scientific_journal-591	166	24	distance	distance	NOUN
american_scientific_journal-591	166	25	traveled	travel	VERB
american_scientific_journal-591	166	26	by	by	ADP
american_scientific_journal-591	166	27	the	the	DET
american_scientific_journal-591	166	28	light	light	NOUN
american_scientific_journal-591	166	29	is	be	AUX
american_scientific_journal-591	166	30	2(4	2(4	NUM
american_scientific_journal-591	166	31	)	)	PUNCT
american_scientific_journal-591	166	32	2.667	2.667	NUM
american_scientific_journal-591	166	33	2	2	NUM
american_scientific_journal-591	166	34	1	1	NUM
american_scientific_journal-591	166	35	acx	acx	NOUN
american_scientific_journal-591	166	36	a	a	DET
american_scientific_journal-591	166	37	b	b	NOUN
american_scientific_journal-591	166	38	=	=	SYM
american_scientific_journal-591	166	39	=	=	SYM
american_scientific_journal-591	167	1	≈	≈	PROPN
american_scientific_journal-591	167	2	+	+	CCONJ
american_scientific_journal-591	167	3	+	+	NUM
american_scientific_journal-591	167	4	units	unit	NOUN
american_scientific_journal-591	167	5	from	from	ADP
american_scientific_journal-591	167	6	the	the	DET
american_scientific_journal-591	167	7	point	point	NOUN
american_scientific_journal-591	167	8	on	on	ADP
american_scientific_journal-591	167	9	the	the	DET
american_scientific_journal-591	167	10	mirror	mirror	NOUN
american_scientific_journal-591	167	11	nearest	near	ADJ
american_scientific_journal-591	167	12	a.	a.	NOUN
american_scientific_journal-591	167	13	problem	problem	NOUN
american_scientific_journal-591	167	14	3	3	NUM
american_scientific_journal-591	167	15	.	.	PUNCT
american_scientific_journal-591	167	16	two	two	NUM
american_scientific_journal-591	167	17	posts	post	NOUN
american_scientific_journal-591	167	18	,	,	PUNCT
american_scientific_journal-591	167	19	both	both	DET
american_scientific_journal-591	167	20	15	15	NUM
american_scientific_journal-591	167	21	feet	foot	NOUN
american_scientific_journal-591	167	22	high	high	ADJ
american_scientific_journal-591	167	23	,	,	PUNCT
american_scientific_journal-591	167	24	stand	stand	VERB
american_scientific_journal-591	167	25	24	24	NUM
american_scientific_journal-591	167	26	feet	foot	NOUN
american_scientific_journal-591	167	27	apart	apart	ADV
american_scientific_journal-591	167	28	.	.	PUNCT
american_scientific_journal-591	168	1	they	they	PRON
american_scientific_journal-591	168	2	are	be	AUX
american_scientific_journal-591	168	3	to	to	PART
american_scientific_journal-591	168	4	be	be	AUX
american_scientific_journal-591	168	5	stayed	stay	VERB
american_scientific_journal-591	168	6	by	by	ADP
american_scientific_journal-591	168	7	two	two	NUM
american_scientific_journal-591	168	8	wires	wire	NOUN
american_scientific_journal-591	168	9	,	,	PUNCT
american_scientific_journal-591	168	10	attached	attach	VERB
american_scientific_journal-591	168	11	to	to	ADP
american_scientific_journal-591	168	12	a	a	DET
american_scientific_journal-591	168	13	single	single	ADJ
american_scientific_journal-591	168	14	stake	stake	NOUN
american_scientific_journal-591	168	15	,	,	PUNCT
american_scientific_journal-591	168	16	running	run	VERB
american_scientific_journal-591	168	17	from	from	ADP
american_scientific_journal-591	168	18	ground	ground	NOUN
american_scientific_journal-591	168	19	level	level	NOUN
american_scientific_journal-591	168	20	to	to	ADP
american_scientific_journal-591	168	21	the	the	DET
american_scientific_journal-591	168	22	top	top	NOUN
american_scientific_journal-591	168	23	of	of	ADP
american_scientific_journal-591	168	24	each	each	DET
american_scientific_journal-591	168	25	post	post	NOUN
american_scientific_journal-591	168	26	.	.	PUNCT
american_scientific_journal-591	169	1	what	what	PRON
american_scientific_journal-591	169	2	is	be	AUX
american_scientific_journal-591	169	3	the	the	DET
american_scientific_journal-591	169	4	minimum	minimum	ADJ
american_scientific_journal-591	169	5	total	total	ADJ
american_scientific_journal-591	169	6	length	length	NOUN
american_scientific_journal-591	169	7	of	of	ADP
american_scientific_journal-591	169	8	wire	wire	NOUN
american_scientific_journal-591	169	9	possible	possible	ADJ
american_scientific_journal-591	169	10	if	if	SCONJ
american_scientific_journal-591	169	11	the	the	DET
american_scientific_journal-591	169	12	stake	stake	NOUN
american_scientific_journal-591	169	13	can	can	AUX
american_scientific_journal-591	169	14	be	be	AUX
american_scientific_journal-591	169	15	placed	place	VERB
american_scientific_journal-591	169	16	anywhere	anywhere	ADV
american_scientific_journal-591	169	17	on	on	ADP
american_scientific_journal-591	169	18	the	the	DET
american_scientific_journal-591	169	19	ground	ground	NOUN
american_scientific_journal-591	169	20	?	?	PUNCT
american_scientific_journal-591	170	1	93	93	NUM
american_scientific_journal-591	170	2	american	american	ADJ
american_scientific_journal-591	170	3	scientific	scientific	ADJ
american_scientific_journal-591	170	4	research	research	NOUN
american_scientific_journal-591	170	5	journal	journal	NOUN
american_scientific_journal-591	170	6	for	for	ADP
american_scientific_journal-591	170	7	engineering	engineering	NOUN
american_scientific_journal-591	170	8	,	,	PUNCT
american_scientific_journal-591	170	9	technology	technology	NOUN
american_scientific_journal-591	170	10	,	,	PUNCT
american_scientific_journal-591	170	11	and	and	CCONJ
american_scientific_journal-591	170	12	sciences	science	NOUN
american_scientific_journal-591	170	13	(	(	PUNCT
american_scientific_journal-591	170	14	asrjets	asrjet	NOUN
american_scientific_journal-591	170	15	)	)	PUNCT
american_scientific_journal-591	170	16	(	(	PUNCT
american_scientific_journal-591	170	17	2015	2015	NUM
american_scientific_journal-591	170	18	)	)	PUNCT
american_scientific_journal-591	170	19	volume	volume	NOUN
american_scientific_journal-591	170	20	11	11	NUM
american_scientific_journal-591	170	21	,	,	PUNCT
american_scientific_journal-591	170	22	no	no	DET
american_scientific_journal-591	170	23	1	1	NUM
american_scientific_journal-591	170	24	,	,	PUNCT
american_scientific_journal-591	170	25	pp	pp	ADV
american_scientific_journal-591	170	26	84	84	NUM
american_scientific_journal-591	170	27	-	-	SYM
american_scientific_journal-591	170	28	95	95	NUM
american_scientific_journal-591	170	29	solution	solution	NOUN
american_scientific_journal-591	170	30	:	:	PUNCT
american_scientific_journal-591	170	31	since	since	SCONJ
american_scientific_journal-591	170	32	the	the	DET
american_scientific_journal-591	170	33	two	two	NUM
american_scientific_journal-591	170	34	posts	post	NOUN
american_scientific_journal-591	170	35	are	be	AUX
american_scientific_journal-591	170	36	both	both	PRON
american_scientific_journal-591	170	37	15	15	NUM
american_scientific_journal-591	170	38	ft	ft	NOUN
american_scientific_journal-591	170	39	high	high	ADJ
american_scientific_journal-591	170	40	and	and	CCONJ
american_scientific_journal-591	170	41	24	24	NUM
american_scientific_journal-591	170	42	ft	ft	NOUN
american_scientific_journal-591	170	43	apart	apart	ADV
american_scientific_journal-591	170	44	,	,	PUNCT
american_scientific_journal-591	170	45	the	the	DET
american_scientific_journal-591	170	46	minimum	minimum	ADJ
american_scientific_journal-591	170	47	length	length	NOUN
american_scientific_journal-591	170	48	of	of	ADP
american_scientific_journal-591	170	49	wire	wire	NOUN
american_scientific_journal-591	170	50	possible	possible	ADJ
american_scientific_journal-591	170	51	is	be	AUX
american_scientific_journal-591	170	52	2	2	NUM
american_scientific_journal-591	170	53	2	2	NUM
american_scientific_journal-591	170	54	2	2	NUM
american_scientific_journal-591	170	55	2	2	NUM
american_scientific_journal-591	170	56	(	(	PUNCT
american_scientific_journal-591	170	57	)	)	PUNCT
american_scientific_journal-591	170	58	(	(	PUNCT
american_scientific_journal-591	170	59	15	15	NUM
american_scientific_journal-591	170	60	15	15	NUM
american_scientific_journal-591	170	61	)	)	PUNCT
american_scientific_journal-591	170	62	24	24	NUM
american_scientific_journal-591	170	63	38.419d	38.419d	NUM
american_scientific_journal-591	170	64	a	a	DET
american_scientific_journal-591	170	65	b	b	NOUN
american_scientific_journal-591	170	66	c=	c=	NOUN
american_scientific_journal-591	170	67	+	+	X
american_scientific_journal-591	171	1	+	+	PUNCT
american_scientific_journal-591	171	2	=	=	SYM
american_scientific_journal-591	172	1	+	+	PUNCT
american_scientific_journal-591	172	2	+	+	CCONJ
american_scientific_journal-591	172	3	≈	≈	PROPN
american_scientific_journal-591	172	4	ft	ft	PROPN
american_scientific_journal-591	172	5	.	.	PROPN
american_scientific_journal-591	172	6	4	4	NUM
american_scientific_journal-591	172	7	.	.	NOUN
american_scientific_journal-591	172	8	conclusion	conclusion	NOUN
american_scientific_journal-591	172	9	and	and	CCONJ
american_scientific_journal-591	172	10	directions	direction	NOUN
american_scientific_journal-591	172	11	for	for	ADP
american_scientific_journal-591	172	12	future	future	ADJ
american_scientific_journal-591	172	13	works	work	NOUN
american_scientific_journal-591	172	14	solving	solve	VERB
american_scientific_journal-591	172	15	optimization	optimization	NOUN
american_scientific_journal-591	172	16	problems	problem	NOUN
american_scientific_journal-591	172	17	is	be	AUX
american_scientific_journal-591	172	18	a	a	DET
american_scientific_journal-591	172	19	very	very	ADV
american_scientific_journal-591	172	20	important	important	ADJ
american_scientific_journal-591	172	21	application	application	NOUN
american_scientific_journal-591	172	22	of	of	ADP
american_scientific_journal-591	172	23	differential	differential	ADJ
american_scientific_journal-591	172	24	calculus	calculus	NOUN
american_scientific_journal-591	172	25	.	.	PUNCT
american_scientific_journal-591	173	1	this	this	DET
american_scientific_journal-591	173	2	application	application	NOUN
american_scientific_journal-591	173	3	is	be	AUX
american_scientific_journal-591	173	4	extended	extend	VERB
american_scientific_journal-591	173	5	to	to	ADP
american_scientific_journal-591	173	6	actual	actual	ADJ
american_scientific_journal-591	173	7	business	business	NOUN
american_scientific_journal-591	173	8	undertakings	undertaking	NOUN
american_scientific_journal-591	173	9	and	and	CCONJ
american_scientific_journal-591	173	10	engineering	engineering	NOUN
american_scientific_journal-591	173	11	works	work	NOUN
american_scientific_journal-591	173	12	,	,	PUNCT
american_scientific_journal-591	173	13	where	where	SCONJ
american_scientific_journal-591	173	14	most	most	ADV
american_scientific_journal-591	173	15	often	often	ADV
american_scientific_journal-591	173	16	,	,	PUNCT
american_scientific_journal-591	173	17	the	the	DET
american_scientific_journal-591	173	18	main	main	ADJ
american_scientific_journal-591	173	19	goal	goal	NOUN
american_scientific_journal-591	173	20	is	be	AUX
american_scientific_journal-591	173	21	maximizing	maximize	VERB
american_scientific_journal-591	173	22	profit	profit	NOUN
american_scientific_journal-591	173	23	and	and	CCONJ
american_scientific_journal-591	173	24	minimizing	minimize	VERB
american_scientific_journal-591	173	25	cost	cost	NOUN
american_scientific_journal-591	173	26	.	.	PUNCT
american_scientific_journal-591	174	1	minimizing	minimize	VERB
american_scientific_journal-591	174	2	length	length	NOUN
american_scientific_journal-591	174	3	or	or	CCONJ
american_scientific_journal-591	174	4	distance	distance	NOUN
american_scientific_journal-591	174	5	,	,	PUNCT
american_scientific_journal-591	174	6	and	and	CCONJ
american_scientific_journal-591	174	7	in	in	ADP
american_scientific_journal-591	174	8	a	a	DET
american_scientific_journal-591	174	9	way	way	NOUN
american_scientific_journal-591	174	10	,	,	PUNCT
american_scientific_journal-591	174	11	minimizing	minimize	VERB
american_scientific_journal-591	174	12	the	the	DET
american_scientific_journal-591	174	13	cost	cost	NOUN
american_scientific_journal-591	174	14	of	of	ADP
american_scientific_journal-591	174	15	materials	material	NOUN
american_scientific_journal-591	174	16	for	for	ADP
american_scientific_journal-591	174	17	projects	project	NOUN
american_scientific_journal-591	174	18	involving	involve	VERB
american_scientific_journal-591	174	19	lengths	length	NOUN
american_scientific_journal-591	174	20	or	or	CCONJ
american_scientific_journal-591	174	21	distances	distance	NOUN
american_scientific_journal-591	174	22	,	,	PUNCT
american_scientific_journal-591	174	23	is	be	AUX
american_scientific_journal-591	174	24	an	an	DET
american_scientific_journal-591	174	25	example	example	NOUN
american_scientific_journal-591	174	26	of	of	ADP
american_scientific_journal-591	174	27	such	such	ADJ
american_scientific_journal-591	174	28	application	application	NOUN
american_scientific_journal-591	174	29	.	.	PUNCT
american_scientific_journal-591	175	1	to	to	PART
american_scientific_journal-591	175	2	solve	solve	VERB
american_scientific_journal-591	175	3	problems	problem	NOUN
american_scientific_journal-591	175	4	of	of	ADP
american_scientific_journal-591	175	5	minimizing	minimize	VERB
american_scientific_journal-591	175	6	distance	distance	NOUN
american_scientific_journal-591	175	7	,	,	PUNCT
american_scientific_journal-591	175	8	the	the	DET
american_scientific_journal-591	175	9	extreme	extreme	ADJ
american_scientific_journal-591	175	10	-	-	PUNCT
american_scientific_journal-591	175	11	value	value	NOUN
american_scientific_journal-591	175	12	theorem	theorem	NOUN
american_scientific_journal-591	175	13	is	be	AUX
american_scientific_journal-591	175	14	usually	usually	ADV
american_scientific_journal-591	175	15	applied	apply	VERB
american_scientific_journal-591	175	16	.	.	PUNCT
american_scientific_journal-591	176	1	this	this	PRON
american_scientific_journal-591	176	2	involves	involve	VERB
american_scientific_journal-591	176	3	finding	find	VERB
american_scientific_journal-591	176	4	the	the	DET
american_scientific_journal-591	176	5	derivative	derivative	NOUN
american_scientific_journal-591	176	6	of	of	ADP
american_scientific_journal-591	176	7	a	a	DET
american_scientific_journal-591	176	8	function	function	NOUN
american_scientific_journal-591	176	9	,	,	PUNCT
american_scientific_journal-591	176	10	finding	find	VERB
american_scientific_journal-591	176	11	critical	critical	ADJ
american_scientific_journal-591	176	12	points	point	NOUN
american_scientific_journal-591	176	13	or	or	CCONJ
american_scientific_journal-591	176	14	relative	relative	ADJ
american_scientific_journal-591	176	15	extrema	extrema	NOUN
american_scientific_journal-591	176	16	,	,	PUNCT
american_scientific_journal-591	176	17	and	and	CCONJ
american_scientific_journal-591	176	18	calculating	calculate	VERB
american_scientific_journal-591	176	19	the	the	DET
american_scientific_journal-591	176	20	distance	distance	NOUN
american_scientific_journal-591	176	21	as	as	ADP
american_scientific_journal-591	176	22	a	a	DET
american_scientific_journal-591	176	23	function	function	NOUN
american_scientific_journal-591	176	24	value	value	NOUN
american_scientific_journal-591	176	25	at	at	ADP
american_scientific_journal-591	176	26	the	the	DET
american_scientific_journal-591	176	27	critical	critical	ADJ
american_scientific_journal-591	176	28	points	point	NOUN
american_scientific_journal-591	176	29	and	and	CCONJ
american_scientific_journal-591	176	30	at	at	ADP
american_scientific_journal-591	176	31	the	the	DET
american_scientific_journal-591	176	32	endpoints	endpoint	NOUN
american_scientific_journal-591	176	33	of	of	ADP
american_scientific_journal-591	176	34	the	the	DET
american_scientific_journal-591	176	35	closed	closed	ADJ
american_scientific_journal-591	176	36	interval	interval	NOUN
american_scientific_journal-591	176	37	and	and	CCONJ
american_scientific_journal-591	176	38	then	then	ADV
american_scientific_journal-591	176	39	comparing	compare	VERB
american_scientific_journal-591	176	40	the	the	DET
american_scientific_journal-591	176	41	results	result	NOUN
american_scientific_journal-591	176	42	to	to	PART
american_scientific_journal-591	176	43	find	find	VERB
american_scientific_journal-591	176	44	the	the	DET
american_scientific_journal-591	176	45	minimum	minimum	NOUN
american_scientific_journal-591	176	46	.	.	PUNCT
american_scientific_journal-591	177	1	however	however	ADV
american_scientific_journal-591	177	2	,	,	PUNCT
american_scientific_journal-591	177	3	such	such	ADJ
american_scientific_journal-591	177	4	solution	solution	NOUN
american_scientific_journal-591	177	5	is	be	AUX
american_scientific_journal-591	177	6	somewhat	somewhat	ADV
american_scientific_journal-591	177	7	lengthy	lengthy	ADJ
american_scientific_journal-591	177	8	and	and	CCONJ
american_scientific_journal-591	177	9	prone	prone	ADJ
american_scientific_journal-591	177	10	to	to	ADP
american_scientific_journal-591	177	11	computational	computational	ADJ
american_scientific_journal-591	177	12	errors	error	NOUN
american_scientific_journal-591	177	13	.	.	PUNCT
american_scientific_journal-591	178	1	thus	thus	ADV
american_scientific_journal-591	178	2	,	,	PUNCT
american_scientific_journal-591	178	3	using	use	VERB
american_scientific_journal-591	178	4	a	a	DET
american_scientific_journal-591	178	5	formula	formula	NOUN
american_scientific_journal-591	178	6	in	in	ADP
american_scientific_journal-591	178	7	solving	solve	VERB
american_scientific_journal-591	178	8	minimum	minimum	ADJ
american_scientific_journal-591	178	9	distance	distance	NOUN
american_scientific_journal-591	178	10	problems	problem	NOUN
american_scientific_journal-591	178	11	is	be	AUX
american_scientific_journal-591	178	12	a	a	DET
american_scientific_journal-591	178	13	better	well	ADJ
american_scientific_journal-591	178	14	alternative	alternative	NOUN
american_scientific_journal-591	178	15	;	;	PUNCT
american_scientific_journal-591	178	16	the	the	DET
american_scientific_journal-591	178	17	solution	solution	NOUN
american_scientific_journal-591	178	18	is	be	AUX
american_scientific_journal-591	178	19	direct	direct	ADJ
american_scientific_journal-591	178	20	and	and	CCONJ
american_scientific_journal-591	178	21	can	can	AUX
american_scientific_journal-591	178	22	be	be	AUX
american_scientific_journal-591	178	23	done	do	VERB
american_scientific_journal-591	178	24	with	with	ADP
american_scientific_journal-591	178	25	greater	great	ADJ
american_scientific_journal-591	178	26	ease	ease	NOUN
american_scientific_journal-591	178	27	,	,	PUNCT
american_scientific_journal-591	178	28	accuracy	accuracy	NOUN
american_scientific_journal-591	178	29	and	and	CCONJ
american_scientific_journal-591	178	30	speed	speed	NOUN
american_scientific_journal-591	178	31	.	.	PUNCT
american_scientific_journal-591	179	1	in	in	ADP
american_scientific_journal-591	179	2	particular	particular	ADJ
american_scientific_journal-591	179	3	,	,	PUNCT
american_scientific_journal-591	179	4	the	the	DET
american_scientific_journal-591	179	5	minimum	minimum	ADJ
american_scientific_journal-591	179	6	distance	distance	NOUN
american_scientific_journal-591	179	7	from	from	ADP
american_scientific_journal-591	179	8	a	a	DET
american_scientific_journal-591	179	9	point	point	NOUN
american_scientific_journal-591	179	10	to	to	ADP
american_scientific_journal-591	179	11	a	a	DET
american_scientific_journal-591	179	12	line	line	NOUN
american_scientific_journal-591	179	13	to	to	ADP
american_scientific_journal-591	179	14	another	another	DET
american_scientific_journal-591	179	15	point	point	NOUN
american_scientific_journal-591	179	16	on	on	ADP
american_scientific_journal-591	179	17	the	the	DET
american_scientific_journal-591	179	18	same	same	ADJ
american_scientific_journal-591	179	19	side	side	NOUN
american_scientific_journal-591	179	20	of	of	ADP
american_scientific_journal-591	179	21	the	the	DET
american_scientific_journal-591	179	22	line	line	NOUN
american_scientific_journal-591	179	23	can	can	AUX
american_scientific_journal-591	179	24	be	be	AUX
american_scientific_journal-591	179	25	determined	determine	VERB
american_scientific_journal-591	179	26	by	by	ADP
american_scientific_journal-591	179	27	the	the	DET
american_scientific_journal-591	179	28	formula	formula	NOUN
american_scientific_journal-591	179	29	2	2	NUM
american_scientific_journal-591	179	30	2	2	NUM
american_scientific_journal-591	179	31	(	(	PUNCT
american_scientific_journal-591	179	32	)	)	PUNCT
american_scientific_journal-591	180	1	d	d	NOUN
american_scientific_journal-591	180	2	a	a	DET
american_scientific_journal-591	180	3	b	b	NOUN
american_scientific_journal-591	180	4	c=	c=	NOUN
american_scientific_journal-591	180	5	+	+	X
american_scientific_journal-591	180	6	+	+	CCONJ
american_scientific_journal-591	180	7	,	,	PUNCT
american_scientific_journal-591	180	8	where	where	SCONJ
american_scientific_journal-591	180	9	d	d	NOUN
american_scientific_journal-591	180	10	is	be	AUX
american_scientific_journal-591	180	11	the	the	DET
american_scientific_journal-591	180	12	minimum	minimum	ADJ
american_scientific_journal-591	180	13	distance	distance	NOUN
american_scientific_journal-591	180	14	,	,	PUNCT
american_scientific_journal-591	180	15	a	a	PRON
american_scientific_journal-591	180	16	is	be	AUX
american_scientific_journal-591	180	17	the	the	DET
american_scientific_journal-591	180	18	distance	distance	NOUN
american_scientific_journal-591	180	19	from	from	ADP
american_scientific_journal-591	180	20	one	one	NUM
american_scientific_journal-591	180	21	point	point	NOUN
american_scientific_journal-591	180	22	to	to	ADP
american_scientific_journal-591	180	23	the	the	DET
american_scientific_journal-591	180	24	line	line	NOUN
american_scientific_journal-591	180	25	,	,	PUNCT
american_scientific_journal-591	180	26	b	b	NOUN
american_scientific_journal-591	180	27	is	be	AUX
american_scientific_journal-591	180	28	the	the	DET
american_scientific_journal-591	180	29	distance	distance	NOUN
american_scientific_journal-591	180	30	from	from	ADP
american_scientific_journal-591	180	31	the	the	DET
american_scientific_journal-591	180	32	other	other	ADJ
american_scientific_journal-591	180	33	point	point	NOUN
american_scientific_journal-591	180	34	to	to	ADP
american_scientific_journal-591	180	35	the	the	DET
american_scientific_journal-591	180	36	line	line	NOUN
american_scientific_journal-591	180	37	,	,	PUNCT
american_scientific_journal-591	180	38	and	and	CCONJ
american_scientific_journal-591	180	39	c	c	NOUN
american_scientific_journal-591	180	40	is	be	AUX
american_scientific_journal-591	180	41	the	the	DET
american_scientific_journal-591	180	42	distance	distance	NOUN
american_scientific_journal-591	180	43	between	between	ADP
american_scientific_journal-591	180	44	the	the	DET
american_scientific_journal-591	180	45	two	two	NUM
american_scientific_journal-591	180	46	points	point	NOUN
american_scientific_journal-591	180	47	in	in	ADP
american_scientific_journal-591	180	48	the	the	DET
american_scientific_journal-591	180	49	line	line	NOUN
american_scientific_journal-591	180	50	nearest	nearest	ADP
american_scientific_journal-591	180	51	the	the	DET
american_scientific_journal-591	180	52	two	two	NUM
american_scientific_journal-591	180	53	given	give	VERB
american_scientific_journal-591	180	54	points	point	NOUN
american_scientific_journal-591	180	55	.	.	PUNCT
american_scientific_journal-591	181	1	this	this	DET
american_scientific_journal-591	181	2	formula	formula	NOUN
american_scientific_journal-591	181	3	is	be	AUX
american_scientific_journal-591	181	4	derived	derive	VERB
american_scientific_journal-591	181	5	using	use	VERB
american_scientific_journal-591	181	6	two	two	NUM
american_scientific_journal-591	181	7	different	different	ADJ
american_scientific_journal-591	181	8	approaches	approach	NOUN
american_scientific_journal-591	181	9	:	:	PUNCT
american_scientific_journal-591	181	10	(	(	PUNCT
american_scientific_journal-591	181	11	1	1	X
american_scientific_journal-591	181	12	)	)	PUNCT
american_scientific_journal-591	181	13	geometrical	geometrical	ADJ
american_scientific_journal-591	181	14	construction	construction	NOUN
american_scientific_journal-591	181	15	and	and	CCONJ
american_scientific_journal-591	181	16	reasoning	reasoning	NOUN
american_scientific_journal-591	181	17	and	and	CCONJ
american_scientific_journal-591	181	18	(	(	PUNCT
american_scientific_journal-591	181	19	2	2	X
american_scientific_journal-591	181	20	)	)	PUNCT
american_scientific_journal-591	181	21	analytical	analytical	ADJ
american_scientific_journal-591	181	22	application	application	NOUN
american_scientific_journal-591	181	23	of	of	ADP
american_scientific_journal-591	181	24	extreme	extreme	ADJ
american_scientific_journal-591	181	25	-	-	PUNCT
american_scientific_journal-591	181	26	value	value	NOUN
american_scientific_journal-591	181	27	theorem	theorem	NOUN
american_scientific_journal-591	181	28	.	.	PUNCT
american_scientific_journal-591	182	1	in	in	ADP
american_scientific_journal-591	182	2	the	the	DET
american_scientific_journal-591	182	3	derivation	derivation	NOUN
american_scientific_journal-591	182	4	process	process	NOUN
american_scientific_journal-591	182	5	,	,	PUNCT
american_scientific_journal-591	182	6	the	the	DET
american_scientific_journal-591	182	7	formula	formula	NOUN
american_scientific_journal-591	182	8	for	for	ADP
american_scientific_journal-591	182	9	finding	find	VERB
american_scientific_journal-591	182	10	the	the	DET
american_scientific_journal-591	182	11	location	location	NOUN
american_scientific_journal-591	182	12	of	of	ADP
american_scientific_journal-591	182	13	the	the	DET
american_scientific_journal-591	182	14	point	point	NOUN
american_scientific_journal-591	182	15	in	in	ADP
american_scientific_journal-591	182	16	the	the	DET
american_scientific_journal-591	182	17	line	line	NOUN
american_scientific_journal-591	182	18	that	that	PRON
american_scientific_journal-591	182	19	will	will	AUX
american_scientific_journal-591	182	20	lead	lead	VERB
american_scientific_journal-591	182	21	to	to	ADP
american_scientific_journal-591	182	22	having	have	VERB
american_scientific_journal-591	182	23	minimum	minimum	ADJ
american_scientific_journal-591	182	24	distance	distance	NOUN
american_scientific_journal-591	182	25	was	be	AUX
american_scientific_journal-591	182	26	also	also	ADV
american_scientific_journal-591	182	27	determined	determine	VERB
american_scientific_journal-591	182	28	i.e.	i.e.	X
american_scientific_journal-591	182	29	/	/	SYM
american_scientific_journal-591	182	30	(	(	PUNCT
american_scientific_journal-591	182	31	)	)	PUNCT
american_scientific_journal-591	182	32	x	x	SYM
american_scientific_journal-591	182	33	ac	ac	ADP
american_scientific_journal-591	182	34	a	a	DET
american_scientific_journal-591	182	35	b=	b=	NOUN
american_scientific_journal-591	182	36	+	+	X
american_scientific_journal-591	182	37	.	.	PUNCT
american_scientific_journal-591	183	1	with	with	ADP
american_scientific_journal-591	183	2	the	the	DET
american_scientific_journal-591	183	3	use	use	NOUN
american_scientific_journal-591	183	4	of	of	ADP
american_scientific_journal-591	183	5	the	the	DET
american_scientific_journal-591	183	6	derived	derive	VERB
american_scientific_journal-591	183	7	formulas	formula	NOUN
american_scientific_journal-591	183	8	,	,	PUNCT
american_scientific_journal-591	183	9	the	the	DET
american_scientific_journal-591	183	10	problem	problem	NOUN
american_scientific_journal-591	183	11	solver	solver	NOUN
american_scientific_journal-591	183	12	will	will	AUX
american_scientific_journal-591	183	13	no	no	ADV
american_scientific_journal-591	183	14	longer	long	ADV
american_scientific_journal-591	183	15	need	need	VERB
american_scientific_journal-591	183	16	to	to	PART
american_scientific_journal-591	183	17	repeat	repeat	VERB
american_scientific_journal-591	183	18	the	the	DET
american_scientific_journal-591	183	19	same	same	ADJ
american_scientific_journal-591	183	20	reasoning	reasoning	NOUN
american_scientific_journal-591	183	21	process	process	NOUN
american_scientific_journal-591	183	22	in	in	ADP
american_scientific_journal-591	183	23	geometry	geometry	NOUN
american_scientific_journal-591	183	24	,	,	PUNCT
american_scientific_journal-591	183	25	or	or	CCONJ
american_scientific_journal-591	183	26	the	the	DET
american_scientific_journal-591	183	27	same	same	ADJ
american_scientific_journal-591	183	28	lengthy	lengthy	ADJ
american_scientific_journal-591	183	29	computations	computation	NOUN
american_scientific_journal-591	183	30	in	in	ADP
american_scientific_journal-591	183	31	differentiation	differentiation	NOUN
american_scientific_journal-591	183	32	,	,	PUNCT
american_scientific_journal-591	183	33	over	over	ADV
american_scientific_journal-591	183	34	and	and	CCONJ
american_scientific_journal-591	183	35	over	over	ADV
american_scientific_journal-591	183	36	again	again	ADV
american_scientific_journal-591	183	37	whenever	whenever	SCONJ
american_scientific_journal-591	183	38	there	there	PRON
american_scientific_journal-591	183	39	is	be	VERB
american_scientific_journal-591	183	40	a	a	DET
american_scientific_journal-591	183	41	need	need	NOUN
american_scientific_journal-591	183	42	to	to	PART
american_scientific_journal-591	183	43	solve	solve	VERB
american_scientific_journal-591	183	44	a	a	DET
american_scientific_journal-591	183	45	minimum	minimum	ADJ
american_scientific_journal-591	183	46	distance	distance	NOUN
american_scientific_journal-591	183	47	problem	problem	NOUN
american_scientific_journal-591	183	48	of	of	ADP
american_scientific_journal-591	183	49	this	this	DET
american_scientific_journal-591	183	50	kind	kind	NOUN
american_scientific_journal-591	183	51	.	.	PUNCT
american_scientific_journal-591	184	1	in	in	ADP
american_scientific_journal-591	184	2	practical	practical	ADJ
american_scientific_journal-591	184	3	applications	application	NOUN
american_scientific_journal-591	184	4	,	,	PUNCT
american_scientific_journal-591	184	5	if	if	SCONJ
american_scientific_journal-591	184	6	the	the	DET
american_scientific_journal-591	184	7	minimum	minimum	ADJ
american_scientific_journal-591	184	8	distance	distance	NOUN
american_scientific_journal-591	184	9	was	be	AUX
american_scientific_journal-591	184	10	accurately	accurately	ADV
american_scientific_journal-591	184	11	determined	determine	VERB
american_scientific_journal-591	184	12	then	then	ADV
american_scientific_journal-591	184	13	waste	waste	NOUN
american_scientific_journal-591	184	14	of	of	ADP
american_scientific_journal-591	184	15	materials	material	NOUN
american_scientific_journal-591	184	16	can	can	AUX
american_scientific_journal-591	184	17	be	be	AUX
american_scientific_journal-591	184	18	avoided	avoid	VERB
american_scientific_journal-591	184	19	and	and	CCONJ
american_scientific_journal-591	184	20	hence	hence	ADV
american_scientific_journal-591	184	21	,	,	PUNCT
american_scientific_journal-591	184	22	minimizing	minimize	VERB
american_scientific_journal-591	184	23	cost	cost	NOUN
american_scientific_journal-591	184	24	.	.	PUNCT
american_scientific_journal-591	185	1	also	also	ADV
american_scientific_journal-591	185	2	,	,	PUNCT
american_scientific_journal-591	185	3	finding	find	VERB
american_scientific_journal-591	185	4	the	the	DET
american_scientific_journal-591	185	5	minimum	minimum	ADJ
american_scientific_journal-591	185	6	distance	distance	NOUN
american_scientific_journal-591	185	7	directly	directly	ADV
american_scientific_journal-591	185	8	through	through	ADP
american_scientific_journal-591	185	9	the	the	DET
american_scientific_journal-591	185	10	use	use	NOUN
american_scientific_journal-591	185	11	of	of	ADP
american_scientific_journal-591	185	12	formula	formula	NOUN
american_scientific_journal-591	185	13	will	will	AUX
american_scientific_journal-591	185	14	greatly	greatly	ADV
american_scientific_journal-591	185	15	reduce	reduce	VERB
american_scientific_journal-591	185	16	time	time	NOUN
american_scientific_journal-591	185	17	and	and	CCONJ
american_scientific_journal-591	185	18	manpower	manpower	NOUN
american_scientific_journal-591	185	19	requirement	requirement	NOUN
american_scientific_journal-591	185	20	thereby	thereby	ADV
american_scientific_journal-591	185	21	reducing	reduce	VERB
american_scientific_journal-591	185	22	project	project	NOUN
american_scientific_journal-591	185	23	cost	cost	NOUN
american_scientific_journal-591	185	24	.	.	PUNCT
american_scientific_journal-591	186	1	future	future	ADJ
american_scientific_journal-591	186	2	works	work	NOUN
american_scientific_journal-591	186	3	to	to	PART
american_scientific_journal-591	186	4	be	be	AUX
american_scientific_journal-591	186	5	done	do	VERB
american_scientific_journal-591	186	6	by	by	ADP
american_scientific_journal-591	186	7	other	other	ADJ
american_scientific_journal-591	186	8	research	research	NOUN
american_scientific_journal-591	186	9	mathematicians	mathematician	NOUN
american_scientific_journal-591	186	10	may	may	AUX
american_scientific_journal-591	186	11	include	include	VERB
american_scientific_journal-591	186	12	(	(	PUNCT
american_scientific_journal-591	186	13	1	1	X
american_scientific_journal-591	186	14	)	)	PUNCT
american_scientific_journal-591	186	15	determining	determine	VERB
american_scientific_journal-591	186	16	the	the	DET
american_scientific_journal-591	186	17	minimum	minimum	ADJ
american_scientific_journal-591	186	18	distance	distance	NOUN
american_scientific_journal-591	186	19	formula	formula	NOUN
american_scientific_journal-591	186	20	from	from	ADP
american_scientific_journal-591	186	21	a	a	DET
american_scientific_journal-591	186	22	point	point	NOUN
american_scientific_journal-591	186	23	to	to	ADP
american_scientific_journal-591	186	24	a	a	DET
american_scientific_journal-591	186	25	line	line	NOUN
american_scientific_journal-591	186	26	to	to	ADP
american_scientific_journal-591	186	27	another	another	DET
american_scientific_journal-591	186	28	point	point	NOUN
american_scientific_journal-591	186	29	to	to	ADP
american_scientific_journal-591	186	30	the	the	DET
american_scientific_journal-591	186	31	same	same	ADJ
american_scientific_journal-591	186	32	line	line	NOUN
american_scientific_journal-591	186	33	to	to	ADP
american_scientific_journal-591	186	34	a	a	DET
american_scientific_journal-591	186	35	third	third	ADJ
american_scientific_journal-591	186	36	point	point	NOUN
american_scientific_journal-591	186	37	and	and	CCONJ
american_scientific_journal-591	186	38	so	so	ADV
american_scientific_journal-591	186	39	on	on	ADV
american_scientific_journal-591	186	40	,	,	PUNCT
american_scientific_journal-591	186	41	i.e.	i.e.	X
american_scientific_journal-591	186	42	minimum	minimum	ADJ
american_scientific_journal-591	186	43	distance	distance	NOUN
american_scientific_journal-591	186	44	formula	formula	NOUN
american_scientific_journal-591	186	45	that	that	PRON
american_scientific_journal-591	186	46	involves	involve	VERB
american_scientific_journal-591	186	47	a	a	DET
american_scientific_journal-591	186	48	line	line	NOUN
american_scientific_journal-591	186	49	and	and	CCONJ
american_scientific_journal-591	186	50	more	more	ADJ
american_scientific_journal-591	186	51	than	than	ADP
american_scientific_journal-591	186	52	two	two	NUM
american_scientific_journal-591	186	53	points	point	NOUN
american_scientific_journal-591	186	54	on	on	ADP
american_scientific_journal-591	186	55	one	one	NUM
american_scientific_journal-591	186	56	side	side	NOUN
american_scientific_journal-591	186	57	or	or	CCONJ
american_scientific_journal-591	186	58	both	both	DET
american_scientific_journal-591	186	59	sides	side	NOUN
american_scientific_journal-591	186	60	of	of	ADP
american_scientific_journal-591	186	61	the	the	DET
american_scientific_journal-591	186	62	line	line	NOUN
american_scientific_journal-591	186	63	and	and	CCONJ
american_scientific_journal-591	186	64	(	(	PUNCT
american_scientific_journal-591	186	65	2	2	X
american_scientific_journal-591	186	66	)	)	PUNCT
american_scientific_journal-591	186	67	deriving	derive	VERB
american_scientific_journal-591	186	68	formulas	formula	NOUN
american_scientific_journal-591	186	69	for	for	ADP
american_scientific_journal-591	186	70	other	other	ADJ
american_scientific_journal-591	186	71	optimization	optimization	NOUN
american_scientific_journal-591	186	72	applications	application	NOUN
american_scientific_journal-591	186	73	of	of	ADP
american_scientific_journal-591	186	74	differential	differential	ADJ
american_scientific_journal-591	186	75	calculus	calculus	NOUN
american_scientific_journal-591	186	76	.	.	PUNCT
american_scientific_journal-591	187	1	practitioners	practitioner	NOUN
american_scientific_journal-591	187	2	in	in	ADP
american_scientific_journal-591	187	3	the	the	DET
american_scientific_journal-591	187	4	fields	field	NOUN
american_scientific_journal-591	187	5	of	of	ADP
american_scientific_journal-591	187	6	business	business	NOUN
american_scientific_journal-591	187	7	and	and	CCONJ
american_scientific_journal-591	187	8	engineering	engineering	NOUN
american_scientific_journal-591	187	9	may	may	AUX
american_scientific_journal-591	187	10	further	far	ADV
american_scientific_journal-591	187	11	develop	develop	VERB
american_scientific_journal-591	187	12	the	the	DET
american_scientific_journal-591	187	13	utilization	utilization	NOUN
american_scientific_journal-591	187	14	of	of	ADP
american_scientific_journal-591	187	15	the	the	DET
american_scientific_journal-591	187	16	derived	derive	VERB
american_scientific_journal-591	187	17	formula	formula	NOUN
american_scientific_journal-591	187	18	or	or	CCONJ
american_scientific_journal-591	187	19	of	of	ADP
american_scientific_journal-591	187	20	future	future	ADJ
american_scientific_journal-591	187	21	similar	similar	ADJ
american_scientific_journal-591	187	22	mathematical	mathematical	ADJ
american_scientific_journal-591	187	23	models	model	NOUN
american_scientific_journal-591	187	24	in	in	ADP
american_scientific_journal-591	187	25	bigger	big	ADJ
american_scientific_journal-591	187	26	construction	construction	NOUN
american_scientific_journal-591	187	27	and	and	CCONJ
american_scientific_journal-591	187	28	business	business	NOUN
american_scientific_journal-591	187	29	projects	project	NOUN
american_scientific_journal-591	187	30	for	for	ADP
american_scientific_journal-591	187	31	example	example	NOUN
american_scientific_journal-591	187	32	,	,	PUNCT
american_scientific_journal-591	187	33	a	a	DET
american_scientific_journal-591	187	34	new	new	ADJ
american_scientific_journal-591	187	35	business	business	NOUN
american_scientific_journal-591	187	36	center	center	NOUN
american_scientific_journal-591	187	37	to	to	PART
american_scientific_journal-591	187	38	be	be	AUX
american_scientific_journal-591	187	39	located	locate	VERB
american_scientific_journal-591	187	40	in	in	ADP
american_scientific_journal-591	187	41	a	a	DET
american_scientific_journal-591	187	42	highway	highway	NOUN
american_scientific_journal-591	187	43	from	from	ADP
american_scientific_journal-591	187	44	where	where	SCONJ
american_scientific_journal-591	187	45	road	road	NOUN
american_scientific_journal-591	187	46	projects	project	NOUN
american_scientific_journal-591	187	47	with	with	ADP
american_scientific_journal-591	187	48	least	least	ADJ
american_scientific_journal-591	187	49	possible	possible	ADJ
american_scientific_journal-591	187	50	distances	distance	NOUN
american_scientific_journal-591	187	51	are	be	AUX
american_scientific_journal-591	187	52	to	to	PART
american_scientific_journal-591	187	53	be	be	AUX
american_scientific_journal-591	187	54	built	build	VERB
american_scientific_journal-591	187	55	going	go	VERB
american_scientific_journal-591	187	56	to	to	ADP
american_scientific_journal-591	187	57	urban	urban	ADJ
american_scientific_journal-591	187	58	centers	center	NOUN
american_scientific_journal-591	187	59	,	,	PUNCT
american_scientific_journal-591	187	60	an	an	DET
american_scientific_journal-591	187	61	airfield	airfield	NOUN
american_scientific_journal-591	187	62	to	to	PART
american_scientific_journal-591	187	63	be	be	AUX
american_scientific_journal-591	187	64	developed	develop	VERB
american_scientific_journal-591	187	65	in	in	ADP
american_scientific_journal-591	187	66	a	a	DET
american_scientific_journal-591	187	67	tourism	tourism	NOUN
american_scientific_journal-591	187	68	zone	zone	NOUN
american_scientific_journal-591	187	69	whereby	whereby	SCONJ
american_scientific_journal-591	187	70	also	also	ADV
american_scientific_journal-591	187	71	minimizing	minimize	VERB
american_scientific_journal-591	187	72	the	the	DET
american_scientific_journal-591	187	73	distances	distance	NOUN
american_scientific_journal-591	187	74	to	to	ADP
american_scientific_journal-591	187	75	different	different	ADJ
american_scientific_journal-591	187	76	tourism	tourism	NOUN
american_scientific_journal-591	187	77	establishments	establishment	NOUN
american_scientific_journal-591	187	78	,	,	PUNCT
american_scientific_journal-591	187	79	or	or	CCONJ
american_scientific_journal-591	187	80	a	a	DET
american_scientific_journal-591	187	81	bullet	bullet	NOUN
american_scientific_journal-591	187	82	train	train	NOUN
american_scientific_journal-591	187	83	central	central	ADJ
american_scientific_journal-591	187	84	station	station	NOUN
american_scientific_journal-591	187	85	connecting	connect	VERB
american_scientific_journal-591	187	86	various	various	ADJ
american_scientific_journal-591	187	87	destinations	destination	NOUN
american_scientific_journal-591	187	88	in	in	ADP
american_scientific_journal-591	187	89	the	the	DET
american_scientific_journal-591	187	90	shortest	short	ADJ
american_scientific_journal-591	187	91	possible	possible	ADJ
american_scientific_journal-591	187	92	distance	distance	NOUN
american_scientific_journal-591	187	93	and	and	CCONJ
american_scientific_journal-591	187	94	time	time	NOUN
american_scientific_journal-591	187	95	.	.	PUNCT
american_scientific_journal-591	188	1	94	94	NUM
american_scientific_journal-591	188	2	american	american	ADJ
american_scientific_journal-591	188	3	scientific	scientific	ADJ
american_scientific_journal-591	188	4	research	research	NOUN
american_scientific_journal-591	188	5	journal	journal	NOUN
american_scientific_journal-591	188	6	for	for	ADP
american_scientific_journal-591	188	7	engineering	engineering	NOUN
american_scientific_journal-591	188	8	,	,	PUNCT
american_scientific_journal-591	188	9	technology	technology	NOUN
american_scientific_journal-591	188	10	,	,	PUNCT
american_scientific_journal-591	188	11	and	and	CCONJ
american_scientific_journal-591	188	12	sciences	science	NOUN
american_scientific_journal-591	188	13	(	(	PUNCT
american_scientific_journal-591	188	14	asrjets	asrjet	NOUN
american_scientific_journal-591	188	15	)	)	PUNCT
american_scientific_journal-591	188	16	(	(	PUNCT
american_scientific_journal-591	188	17	2015	2015	NUM
american_scientific_journal-591	188	18	)	)	PUNCT
american_scientific_journal-591	188	19	volume	volume	NOUN
american_scientific_journal-591	188	20	11	11	NUM
american_scientific_journal-591	188	21	,	,	PUNCT
american_scientific_journal-591	188	22	no	no	DET
american_scientific_journal-591	188	23	1	1	NUM
american_scientific_journal-591	188	24	,	,	PUNCT
american_scientific_journal-591	188	25	pp	pp	ADV
american_scientific_journal-591	188	26	84	84	NUM
american_scientific_journal-591	188	27	-	-	SYM
american_scientific_journal-591	188	28	95	95	NUM
american_scientific_journal-591	188	29	references	reference	NOUN
american_scientific_journal-591	188	30	[	[	X
american_scientific_journal-591	188	31	1	1	NUM
american_scientific_journal-591	188	32	]	]	X
american_scientific_journal-591	188	33	r.t	r.t	PROPN
american_scientific_journal-591	188	34	.	.	PROPN
american_scientific_journal-591	188	35	smith	smith	PROPN
american_scientific_journal-591	188	36	and	and	CCONJ
american_scientific_journal-591	188	37	r.b	r.b	PROPN
american_scientific_journal-591	188	38	.	.	PROPN
american_scientific_journal-591	188	39	minton	minton	PROPN
american_scientific_journal-591	188	40	.	.	PUNCT
american_scientific_journal-591	189	1	calculus	calculus	PROPN
american_scientific_journal-591	189	2	,	,	PUNCT
american_scientific_journal-591	189	3	third	third	ADJ
american_scientific_journal-591	189	4	edition	edition	NOUN
american_scientific_journal-591	189	5	.	.	PUNCT
american_scientific_journal-591	190	1	new	new	PROPN
american_scientific_journal-591	190	2	york	york	PROPN
american_scientific_journal-591	190	3	:	:	PUNCT
american_scientific_journal-591	190	4	mcgraw	mcgraw	PROPN
american_scientific_journal-591	190	5	-	-	PUNCT
american_scientific_journal-591	190	6	hill	hill	PROPN
american_scientific_journal-591	190	7	,	,	PUNCT
american_scientific_journal-591	190	8	2008	2008	NUM
american_scientific_journal-591	190	9	.	.	PUNCT
american_scientific_journal-591	191	1	[	[	X
american_scientific_journal-591	191	2	2	2	NUM
american_scientific_journal-591	191	3	]	]	X
american_scientific_journal-591	191	4	j.l	j.l	PROPN
american_scientific_journal-591	191	5	.	.	PROPN
american_scientific_journal-591	191	6	berggren	berggren	PROPN
american_scientific_journal-591	191	7	.	.	PUNCT
american_scientific_journal-591	192	1	“	"	PUNCT
american_scientific_journal-591	192	2	mathematics	mathematic	NOUN
american_scientific_journal-591	192	3	”	"	PUNCT
american_scientific_journal-591	192	4	in	in	ADP
american_scientific_journal-591	192	5	funk	funk	NOUN
american_scientific_journal-591	192	6	&	&	CCONJ
american_scientific_journal-591	192	7	wagnalls	wagnall	VERB
american_scientific_journal-591	192	8	new	new	ADJ
american_scientific_journal-591	192	9	encyclopedia	encyclopedia	NOUN
american_scientific_journal-591	192	10	,	,	PUNCT
american_scientific_journal-591	192	11	vol	vol	NOUN
american_scientific_journal-591	192	12	.	.	PROPN
american_scientific_journal-591	192	13	17	17	NUM
american_scientific_journal-591	192	14	,	,	PUNCT
american_scientific_journal-591	192	15	p.	p.	NOUN
american_scientific_journal-591	192	16	97	97	NUM
american_scientific_journal-591	192	17	,	,	PUNCT
american_scientific_journal-591	192	18	1990	1990	NUM
american_scientific_journal-591	192	19	.	.	PUNCT
american_scientific_journal-591	193	1	[	[	X
american_scientific_journal-591	193	2	3	3	NUM
american_scientific_journal-591	193	3	]	]	X
american_scientific_journal-591	193	4	r.t	r.t	PROPN
american_scientific_journal-591	193	5	.	.	PROPN
american_scientific_journal-591	193	6	seeley	seeley	PROPN
american_scientific_journal-591	193	7	.	.	PUNCT
american_scientific_journal-591	194	1	calculus	calculus	NOUN
american_scientific_journal-591	194	2	of	of	ADP
american_scientific_journal-591	194	3	one	one	NUM
american_scientific_journal-591	194	4	variable	variable	NOUN
american_scientific_journal-591	194	5	.	.	PUNCT
american_scientific_journal-591	195	1	illinois	illinois	PROPN
american_scientific_journal-591	195	2	:	:	PUNCT
american_scientific_journal-591	195	3	scott	scott	PROPN
american_scientific_journal-591	195	4	,	,	PUNCT
american_scientific_journal-591	195	5	foresman	foresman	NOUN
american_scientific_journal-591	195	6	and	and	CCONJ
american_scientific_journal-591	195	7	company	company	NOUN
american_scientific_journal-591	195	8	,	,	PUNCT
american_scientific_journal-591	195	9	1968	1968	NUM
american_scientific_journal-591	195	10	.	.	PUNCT
american_scientific_journal-591	196	1	[	[	X
american_scientific_journal-591	196	2	4	4	X
american_scientific_journal-591	196	3	]	]	PUNCT
american_scientific_journal-591	196	4	k.	k.	PROPN
american_scientific_journal-591	196	5	kalmanson	kalmanson	PROPN
american_scientific_journal-591	196	6	and	and	CCONJ
american_scientific_journal-591	196	7	p.c	p.c	PROPN
american_scientific_journal-591	196	8	.	.	PROPN
american_scientific_journal-591	196	9	kenschaft	kenschaft	PROPN
american_scientific_journal-591	196	10	.	.	PUNCT
american_scientific_journal-591	197	1	calculus	calculus	NOUN
american_scientific_journal-591	197	2	:	:	PUNCT
american_scientific_journal-591	197	3	a	a	DET
american_scientific_journal-591	197	4	practical	practical	ADJ
american_scientific_journal-591	197	5	approach	approach	NOUN
american_scientific_journal-591	197	6	.	.	PUNCT
american_scientific_journal-591	198	1	new	new	PROPN
american_scientific_journal-591	198	2	york	york	PROPN
american_scientific_journal-591	198	3	:	:	PUNCT
american_scientific_journal-591	198	4	worth	worth	ADJ
american_scientific_journal-591	198	5	publishers	publisher	NOUN
american_scientific_journal-591	198	6	,	,	PUNCT
american_scientific_journal-591	198	7	inc	inc	PROPN
american_scientific_journal-591	198	8	.	.	PROPN
american_scientific_journal-591	198	9	,	,	PUNCT
american_scientific_journal-591	198	10	1975	1975	NUM
american_scientific_journal-591	198	11	.	.	PUNCT
american_scientific_journal-591	199	1	[	[	X
american_scientific_journal-591	199	2	5	5	X
american_scientific_journal-591	199	3	]	]	X
american_scientific_journal-591	199	4	t.p	t.p	PROPN
american_scientific_journal-591	199	5	.	.	PROPN
american_scientific_journal-591	199	6	dick	dick	PROPN
american_scientific_journal-591	199	7	and	and	CCONJ
american_scientific_journal-591	199	8	c.m	c.m	PROPN
american_scientific_journal-591	199	9	.	.	PROPN
american_scientific_journal-591	199	10	patron	patron	PROPN
american_scientific_journal-591	199	11	calculus	calculus	PROPN
american_scientific_journal-591	199	12	.	.	PUNCT
american_scientific_journal-591	200	1	boston	boston	PROPN
american_scientific_journal-591	200	2	:	:	PUNCT
american_scientific_journal-591	200	3	pws	pws	PROPN
american_scientific_journal-591	200	4	-	-	PUNCT
american_scientific_journal-591	200	5	kent	kent	PROPN
american_scientific_journal-591	200	6	publishing	publishing	PROPN
american_scientific_journal-591	200	7	company	company	NOUN
american_scientific_journal-591	200	8	,	,	PUNCT
american_scientific_journal-591	200	9	1992	1992	NUM
american_scientific_journal-591	200	10	.	.	PUNCT
american_scientific_journal-591	201	1	[	[	X
american_scientific_journal-591	201	2	6	6	NUM
american_scientific_journal-591	201	3	]	]	SYM
american_scientific_journal-591	201	4	n.m	n.m	PROPN
american_scientific_journal-591	201	5	.	.	PROPN
american_scientific_journal-591	201	6	mame	mame	PROPN
american_scientific_journal-591	201	7	.	.	PUNCT
american_scientific_journal-591	202	1	development	development	NOUN
american_scientific_journal-591	202	2	of	of	ADP
american_scientific_journal-591	202	3	corollaries	corollary	NOUN
american_scientific_journal-591	202	4	to	to	ADP
american_scientific_journal-591	202	5	basic	basic	ADJ
american_scientific_journal-591	202	6	theorems	theorem	NOUN
american_scientific_journal-591	202	7	on	on	ADP
american_scientific_journal-591	202	8	derivatives	derivative	NOUN
american_scientific_journal-591	202	9	of	of	ADP
american_scientific_journal-591	202	10	algebraic	algebraic	ADJ
american_scientific_journal-591	202	11	functions	function	NOUN
american_scientific_journal-591	202	12	.	.	PUNCT
american_scientific_journal-591	203	1	masters	master	NOUN
american_scientific_journal-591	203	2	thesis	thesis	PROPN
american_scientific_journal-591	203	3	,	,	PUNCT
american_scientific_journal-591	203	4	batangas	batangas	PROPN
american_scientific_journal-591	203	5	state	state	PROPN
american_scientific_journal-591	203	6	university	university	PROPN
american_scientific_journal-591	203	7	,	,	PUNCT
american_scientific_journal-591	203	8	2004	2004	NUM
american_scientific_journal-591	203	9	.	.	PUNCT
american_scientific_journal-591	204	1	[	[	X
american_scientific_journal-591	204	2	7	7	X
american_scientific_journal-591	204	3	]	]	X
american_scientific_journal-591	204	4	e.e	e.e	PROPN
american_scientific_journal-591	204	5	.	.	PROPN
american_scientific_journal-591	204	6	moise	moise	PROPN
american_scientific_journal-591	204	7	and	and	CCONJ
american_scientific_journal-591	204	8	f.l	f.l	PROPN
american_scientific_journal-591	204	9	.	.	PROPN
american_scientific_journal-591	204	10	dawas	dawas	PROPN
american_scientific_journal-591	204	11	jr	jr	PROPN
american_scientific_journal-591	204	12	.	.	PROPN
american_scientific_journal-591	204	13	geometry	geometry	PROPN
american_scientific_journal-591	204	14	.	.	PUNCT
american_scientific_journal-591	205	1	massachussetts	massachussetts	PROPN
american_scientific_journal-591	205	2	:	:	PUNCT
american_scientific_journal-591	205	3	addison	addison	PROPN
american_scientific_journal-591	205	4	-	-	PUNCT
american_scientific_journal-591	205	5	wesley	wesley	PROPN
american_scientific_journal-591	205	6	publishing	publishing	PROPN
american_scientific_journal-591	205	7	company	company	PROPN
american_scientific_journal-591	205	8	,	,	PUNCT
american_scientific_journal-591	205	9	inc	inc	PROPN
american_scientific_journal-591	205	10	.	.	PROPN
american_scientific_journal-591	205	11	,	,	PUNCT
american_scientific_journal-591	205	12	1975	1975	NUM
american_scientific_journal-591	205	13	.	.	PUNCT
american_scientific_journal-591	206	1	[	[	X
american_scientific_journal-591	206	2	8	8	NUM
american_scientific_journal-591	206	3	]	]	PUNCT
american_scientific_journal-591	206	4	a.	a.	NOUN
american_scientific_journal-591	206	5	schwartz	schwartz	PROPN
american_scientific_journal-591	206	6	.	.	PUNCT
american_scientific_journal-591	207	1	analytic	analytic	ADJ
american_scientific_journal-591	207	2	geometry	geometry	NOUN
american_scientific_journal-591	207	3	and	and	CCONJ
american_scientific_journal-591	207	4	calculus	calculus	NOUN
american_scientific_journal-591	207	5	.	.	PUNCT
american_scientific_journal-591	208	1	new	new	PROPN
american_scientific_journal-591	208	2	york	york	PROPN
american_scientific_journal-591	208	3	:	:	PUNCT
american_scientific_journal-591	208	4	holt	holt	PROPN
american_scientific_journal-591	208	5	,	,	PUNCT
american_scientific_journal-591	208	6	rinehart	rinehart	PROPN
american_scientific_journal-591	208	7	and	and	CCONJ
american_scientific_journal-591	208	8	winston	winston	PROPN
american_scientific_journal-591	208	9	,	,	PUNCT
american_scientific_journal-591	208	10	1960	1960	NUM
american_scientific_journal-591	208	11	.	.	PUNCT
american_scientific_journal-591	209	1	[	[	X
american_scientific_journal-591	209	2	9	9	NUM
american_scientific_journal-591	209	3	]	]	PUNCT
american_scientific_journal-591	209	4	l.	l.	PROPN
american_scientific_journal-591	209	5	leithold	leithold	PROPN
american_scientific_journal-591	209	6	.	.	PUNCT
american_scientific_journal-591	210	1	the	the	DET
american_scientific_journal-591	210	2	calculus	calculus	NOUN
american_scientific_journal-591	210	3	7	7	NUM
american_scientific_journal-591	210	4	.	.	PUNCT
american_scientific_journal-591	210	5	massachussetts	massachussetts	PROPN
american_scientific_journal-591	210	6	:	:	PUNCT
american_scientific_journal-591	210	7	addison	addison	PROPN
american_scientific_journal-591	210	8	-	-	PUNCT
american_scientific_journal-591	210	9	wesley	wesley	PROPN
american_scientific_journal-591	210	10	publishing	publishing	PROPN
american_scientific_journal-591	210	11	company	company	PROPN
american_scientific_journal-591	210	12	,	,	PUNCT
american_scientific_journal-591	210	13	inc	inc	PROPN
american_scientific_journal-591	210	14	.	.	PROPN
american_scientific_journal-591	210	15	,	,	PUNCT
american_scientific_journal-591	210	16	1996	1996	NUM
american_scientific_journal-591	210	17	.	.	PUNCT
american_scientific_journal-591	211	1	[	[	X
american_scientific_journal-591	211	2	10	10	NUM
american_scientific_journal-591	211	3	]	]	X
american_scientific_journal-591	211	4	h.	h.	PROPN
american_scientific_journal-591	211	5	anton	anton	PROPN
american_scientific_journal-591	211	6	.	.	PUNCT
american_scientific_journal-591	212	1	calculus	calculus	NOUN
american_scientific_journal-591	212	2	with	with	ADP
american_scientific_journal-591	212	3	analytic	analytic	ADJ
american_scientific_journal-591	212	4	geometry	geometry	NOUN
american_scientific_journal-591	212	5	.	.	PUNCT
american_scientific_journal-591	213	1	new	new	PROPN
american_scientific_journal-591	213	2	york	york	PROPN
american_scientific_journal-591	213	3	:	:	PUNCT
american_scientific_journal-591	213	4	john	john	PROPN
american_scientific_journal-591	213	5	wiley	wiley	PROPN
american_scientific_journal-591	213	6	&	&	CCONJ
american_scientific_journal-591	213	7	sons	sons	PROPN
american_scientific_journal-591	213	8	,	,	PUNCT
american_scientific_journal-591	213	9	inc	inc	PROPN
american_scientific_journal-591	213	10	.	.	PROPN
american_scientific_journal-591	213	11	,	,	PUNCT
american_scientific_journal-591	213	12	1995	1995	NUM
american_scientific_journal-591	213	13	.	.	PUNCT
american_scientific_journal-591	214	1	95	95	NUM