id	sid	tid	token	lemma	pos
american_scientific_journal-757	1	1	american	american	PROPN
american_scientific_journal-757	1	2	scientific	scientific	ADJ
american_scientific_journal-757	1	3	research	research	NOUN
american_scientific_journal-757	1	4	journal	journal	NOUN
american_scientific_journal-757	1	5	for	for	ADP
american_scientific_journal-757	1	6	engineering	engineering	NOUN
american_scientific_journal-757	1	7	,	,	PUNCT
american_scientific_journal-757	1	8	technology	technology	NOUN
american_scientific_journal-757	1	9	,	,	PUNCT
american_scientific_journal-757	1	10	and	and	CCONJ
american_scientific_journal-757	1	11	sciences	science	NOUN
american_scientific_journal-757	1	12	(	(	PUNCT
american_scientific_journal-757	1	13	asrjets	asrjet	NOUN
american_scientific_journal-757	1	14	)	)	PUNCT
american_scientific_journal-757	1	15	issn	issn	PROPN
american_scientific_journal-757	1	16	(	(	PUNCT
american_scientific_journal-757	1	17	print	print	NOUN
american_scientific_journal-757	1	18	)	)	PUNCT
american_scientific_journal-757	1	19	2313	2313	NUM
american_scientific_journal-757	1	20	-	-	SYM
american_scientific_journal-757	1	21	4410	4410	NUM
american_scientific_journal-757	1	22	,	,	PUNCT
american_scientific_journal-757	1	23	issn	issn	PROPN
american_scientific_journal-757	1	24	(	(	PUNCT
american_scientific_journal-757	1	25	online	online	ADJ
american_scientific_journal-757	1	26	)	)	PUNCT
american_scientific_journal-757	1	27	2313	2313	NUM
american_scientific_journal-757	1	28	-	-	SYM
american_scientific_journal-757	1	29	4402	4402	NUM
american_scientific_journal-757	1	30	©	©	PROPN
american_scientific_journal-757	1	31	global	global	ADJ
american_scientific_journal-757	1	32	society	society	NOUN
american_scientific_journal-757	1	33	of	of	ADP
american_scientific_journal-757	1	34	scientific	scientific	ADJ
american_scientific_journal-757	1	35	research	research	NOUN
american_scientific_journal-757	1	36	and	and	CCONJ
american_scientific_journal-757	1	37	researchers	researcher	NOUN
american_scientific_journal-757	1	38	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-757	1	39	an	an	DET
american_scientific_journal-757	1	40	alternate	alternate	ADJ
american_scientific_journal-757	1	41	method	method	NOUN
american_scientific_journal-757	1	42	to	to	PART
american_scientific_journal-757	1	43	find	find	VERB
american_scientific_journal-757	1	44	area	area	NOUN
american_scientific_journal-757	1	45	of	of	ADP
american_scientific_journal-757	1	46	triangle	triangle	NOUN
american_scientific_journal-757	1	47	from	from	ADP
american_scientific_journal-757	1	48	its	its	PRON
american_scientific_journal-757	1	49	vertices	vertex	NOUN
american_scientific_journal-757	1	50	alone	alone	ADV
american_scientific_journal-757	1	51	in	in	ADP
american_scientific_journal-757	1	52	a	a	DET
american_scientific_journal-757	1	53	plane	plane	NOUN
american_scientific_journal-757	1	54	jemal	jemal	PROPN
american_scientific_journal-757	1	55	kemal	kemal	PROPN
american_scientific_journal-757	1	56	nigo	nigo	PROPN
american_scientific_journal-757	1	57	*	*	PROPN
american_scientific_journal-757	1	58	adama	adama	PROPN
american_scientific_journal-757	1	59	science	science	PROPN
american_scientific_journal-757	1	60	&	&	CCONJ
american_scientific_journal-757	1	61	technology	technology	PROPN
american_scientific_journal-757	1	62	university	university	PROPN
american_scientific_journal-757	1	63	,	,	PUNCT
american_scientific_journal-757	1	64	school	school	NOUN
american_scientific_journal-757	1	65	of	of	ADP
american_scientific_journal-757	1	66	applied	apply	VERB
american_scientific_journal-757	1	67	natural	natural	ADJ
american_scientific_journal-757	1	68	sciences	science	NOUN
american_scientific_journal-757	1	69	,	,	PUNCT
american_scientific_journal-757	1	70	program	program	NOUN
american_scientific_journal-757	1	71	of	of	ADP
american_scientific_journal-757	1	72	applied	apply	VERB
american_scientific_journal-757	1	73	mathematics	mathematic	NOUN
american_scientific_journal-757	1	74	,	,	PUNCT
american_scientific_journal-757	1	75	adama	adama	PROPN
american_scientific_journal-757	1	76	,	,	PUNCT
american_scientific_journal-757	1	77	oromia	oromia	ADJ
american_scientific_journal-757	1	78	regional	regional	ADJ
american_scientific_journal-757	1	79	state	state	NOUN
american_scientific_journal-757	1	80	,	,	PUNCT
american_scientific_journal-757	1	81	ethiopia	ethiopia	PROPN
american_scientific_journal-757	1	82	email	email	NOUN
american_scientific_journal-757	1	83	:	:	PUNCT
american_scientific_journal-757	2	1	odaadureti@yahoo.com	odaadureti@yahoo.com	X
american_scientific_journal-757	3	1	abstract	abstract	ADV
american_scientific_journal-757	3	2	since	since	SCONJ
american_scientific_journal-757	3	3	the	the	DET
american_scientific_journal-757	3	4	time	time	NOUN
american_scientific_journal-757	3	5	of	of	ADP
american_scientific_journal-757	3	6	ancient	ancient	ADJ
american_scientific_journal-757	3	7	greeks	greek	NOUN
american_scientific_journal-757	3	8	,	,	PUNCT
american_scientific_journal-757	3	9	mathematicians	mathematician	NOUN
american_scientific_journal-757	3	10	have	have	AUX
american_scientific_journal-757	3	11	been	be	AUX
american_scientific_journal-757	3	12	interested	interested	ADJ
american_scientific_journal-757	3	13	in	in	ADP
american_scientific_journal-757	3	14	finding	find	VERB
american_scientific_journal-757	3	15	the	the	DET
american_scientific_journal-757	3	16	areas	area	NOUN
american_scientific_journal-757	3	17	of	of	ADP
american_scientific_journal-757	3	18	basic	basic	ADJ
american_scientific_journal-757	3	19	plane	plane	NOUN
american_scientific_journal-757	3	20	regions	region	NOUN
american_scientific_journal-757	3	21	.	.	PUNCT
american_scientific_journal-757	4	1	from	from	ADP
american_scientific_journal-757	4	2	among	among	ADP
american_scientific_journal-757	4	3	the	the	DET
american_scientific_journal-757	4	4	most	most	ADV
american_scientific_journal-757	4	5	basic	basic	ADJ
american_scientific_journal-757	4	6	plane	plane	NOUN
american_scientific_journal-757	4	7	regions	region	NOUN
american_scientific_journal-757	4	8	are	be	AUX
american_scientific_journal-757	4	9	triangles	triangle	NOUN
american_scientific_journal-757	4	10	.	.	PUNCT
american_scientific_journal-757	5	1	triangular	triangular	NOUN
american_scientific_journal-757	5	2	shapes	shape	NOUN
american_scientific_journal-757	5	3	are	be	AUX
american_scientific_journal-757	5	4	used	use	VERB
american_scientific_journal-757	5	5	in	in	ADP
american_scientific_journal-757	5	6	different	different	ADJ
american_scientific_journal-757	5	7	areas	area	NOUN
american_scientific_journal-757	5	8	of	of	ADP
american_scientific_journal-757	5	9	engineering	engineering	NOUN
american_scientific_journal-757	5	10	,	,	PUNCT
american_scientific_journal-757	5	11	especially	especially	ADV
american_scientific_journal-757	5	12	in	in	ADP
american_scientific_journal-757	5	13	the	the	DET
american_scientific_journal-757	5	14	design	design	NOUN
american_scientific_journal-757	5	15	and	and	CCONJ
american_scientific_journal-757	5	16	analysis	analysis	NOUN
american_scientific_journal-757	5	17	of	of	ADP
american_scientific_journal-757	5	18	trusses	truss	NOUN
american_scientific_journal-757	5	19	and	and	CCONJ
american_scientific_journal-757	5	20	in	in	ADP
american_scientific_journal-757	5	21	finding	find	VERB
american_scientific_journal-757	5	22	moments	moment	NOUN
american_scientific_journal-757	5	23	of	of	ADP
american_scientific_journal-757	5	24	inertia	inertia	NOUN
american_scientific_journal-757	5	25	in	in	ADP
american_scientific_journal-757	5	26	mechanics	mechanic	NOUN
american_scientific_journal-757	5	27	and	and	CCONJ
american_scientific_journal-757	5	28	to	to	PART
american_scientific_journal-757	5	29	find	find	VERB
american_scientific_journal-757	5	30	triangulation	triangulation	NOUN
american_scientific_journal-757	5	31	and	and	CCONJ
american_scientific_journal-757	5	32	trilateration	trilateration	NOUN
american_scientific_journal-757	5	33	in	in	ADP
american_scientific_journal-757	5	34	surveying	surveying	NOUN
american_scientific_journal-757	5	35	.	.	PUNCT
american_scientific_journal-757	6	1	the	the	DET
american_scientific_journal-757	6	2	centroid	centroid	NOUN
american_scientific_journal-757	6	3	of	of	ADP
american_scientific_journal-757	6	4	a	a	DET
american_scientific_journal-757	6	5	triangular	triangular	NOUN
american_scientific_journal-757	6	6	region	region	NOUN
american_scientific_journal-757	6	7	can	can	AUX
american_scientific_journal-757	6	8	be	be	AUX
american_scientific_journal-757	6	9	also	also	ADV
american_scientific_journal-757	6	10	expressed	express	VERB
american_scientific_journal-757	6	11	in	in	ADP
american_scientific_journal-757	6	12	terms	term	NOUN
american_scientific_journal-757	6	13	of	of	ADP
american_scientific_journal-757	6	14	the	the	DET
american_scientific_journal-757	6	15	coordinates	coordinate	NOUN
american_scientific_journal-757	6	16	of	of	ADP
american_scientific_journal-757	6	17	vertices	vertex	NOUN
american_scientific_journal-757	6	18	of	of	ADP
american_scientific_journal-757	6	19	triangles	triangle	NOUN
american_scientific_journal-757	6	20	.	.	PUNCT
american_scientific_journal-757	7	1	literatures	literature	NOUN
american_scientific_journal-757	7	2	have	have	AUX
american_scientific_journal-757	7	3	shown	show	VERB
american_scientific_journal-757	7	4	that	that	SCONJ
american_scientific_journal-757	7	5	there	there	PRON
american_scientific_journal-757	7	6	are	be	VERB
american_scientific_journal-757	7	7	various	various	ADJ
american_scientific_journal-757	7	8	methods	method	NOUN
american_scientific_journal-757	7	9	of	of	ADP
american_scientific_journal-757	7	10	finding	find	VERB
american_scientific_journal-757	7	11	an	an	DET
american_scientific_journal-757	7	12	area	area	NOUN
american_scientific_journal-757	7	13	of	of	ADP
american_scientific_journal-757	7	14	a	a	DET
american_scientific_journal-757	7	15	triangle	triangle	NOUN
american_scientific_journal-757	7	16	.	.	PUNCT
american_scientific_journal-757	8	1	from	from	ADP
american_scientific_journal-757	8	2	among	among	ADP
american_scientific_journal-757	8	3	these	these	PRON
american_scientific_journal-757	8	4	are	be	AUX
american_scientific_journal-757	8	5	using	use	VERB
american_scientific_journal-757	8	6	the	the	DET
american_scientific_journal-757	8	7	length	length	NOUN
american_scientific_journal-757	8	8	of	of	ADP
american_scientific_journal-757	8	9	the	the	DET
american_scientific_journal-757	8	10	base	base	NOUN
american_scientific_journal-757	8	11	and	and	CCONJ
american_scientific_journal-757	8	12	height	height	NOUN
american_scientific_journal-757	8	13	of	of	ADP
american_scientific_journal-757	8	14	a	a	DET
american_scientific_journal-757	8	15	triangle	triangle	NOUN
american_scientific_journal-757	8	16	,	,	PUNCT
american_scientific_journal-757	8	17	using	use	VERB
american_scientific_journal-757	8	18	the	the	DET
american_scientific_journal-757	8	19	length	length	NOUN
american_scientific_journal-757	8	20	of	of	ADP
american_scientific_journal-757	8	21	two	two	NUM
american_scientific_journal-757	8	22	sides	side	NOUN
american_scientific_journal-757	8	23	and	and	CCONJ
american_scientific_journal-757	8	24	the	the	DET
american_scientific_journal-757	8	25	sine	sine	NOUN
american_scientific_journal-757	8	26	of	of	ADP
american_scientific_journal-757	8	27	included	include	VERB
american_scientific_journal-757	8	28	angle	angle	NOUN
american_scientific_journal-757	8	29	or	or	CCONJ
american_scientific_journal-757	8	30	using	use	VERB
american_scientific_journal-757	8	31	heron`s	heron`s	ADJ
american_scientific_journal-757	8	32	formula	formula	NOUN
american_scientific_journal-757	8	33	which	which	PRON
american_scientific_journal-757	8	34	uses	use	VERB
american_scientific_journal-757	8	35	the	the	DET
american_scientific_journal-757	8	36	length	length	NOUN
american_scientific_journal-757	8	37	of	of	ADP
american_scientific_journal-757	8	38	all	all	DET
american_scientific_journal-757	8	39	sides	side	NOUN
american_scientific_journal-757	8	40	of	of	ADP
american_scientific_journal-757	8	41	the	the	DET
american_scientific_journal-757	8	42	triangle	triangle	NOUN
american_scientific_journal-757	8	43	.	.	PUNCT
american_scientific_journal-757	9	1	we	we	PRON
american_scientific_journal-757	9	2	can	can	AUX
american_scientific_journal-757	9	3	also	also	ADV
american_scientific_journal-757	9	4	find	find	VERB
american_scientific_journal-757	9	5	the	the	DET
american_scientific_journal-757	9	6	area	area	NOUN
american_scientific_journal-757	9	7	of	of	ADP
american_scientific_journal-757	9	8	a	a	DET
american_scientific_journal-757	9	9	triangle	triangle	NOUN
american_scientific_journal-757	9	10	if	if	SCONJ
american_scientific_journal-757	9	11	the	the	DET
american_scientific_journal-757	9	12	coordinates	coordinate	NOUN
american_scientific_journal-757	9	13	of	of	ADP
american_scientific_journal-757	9	14	the	the	DET
american_scientific_journal-757	9	15	vertices	vertex	NOUN
american_scientific_journal-757	9	16	are	be	AUX
american_scientific_journal-757	9	17	given	give	VERB
american_scientific_journal-757	9	18	using	use	VERB
american_scientific_journal-757	9	19	either	either	CCONJ
american_scientific_journal-757	9	20	vectors	vector	NOUN
american_scientific_journal-757	9	21	or	or	CCONJ
american_scientific_journal-757	9	22	determinants	determinant	NOUN
american_scientific_journal-757	9	23	.	.	PUNCT
american_scientific_journal-757	10	1	however	however	ADV
american_scientific_journal-757	10	2	,	,	PUNCT
american_scientific_journal-757	10	3	vectors	vector	NOUN
american_scientific_journal-757	10	4	and	and	CCONJ
american_scientific_journal-757	10	5	determinants	determinant	NOUN
american_scientific_journal-757	10	6	are	be	AUX
american_scientific_journal-757	10	7	concepts	concept	NOUN
american_scientific_journal-757	10	8	of	of	ADP
american_scientific_journal-757	10	9	higher	high	ADJ
american_scientific_journal-757	10	10	mathematics	mathematic	NOUN
american_scientific_journal-757	10	11	.	.	PUNCT
american_scientific_journal-757	11	1	in	in	ADP
american_scientific_journal-757	11	2	this	this	DET
american_scientific_journal-757	11	3	article	article	NOUN
american_scientific_journal-757	11	4	,	,	PUNCT
american_scientific_journal-757	11	5	we	we	PRON
american_scientific_journal-757	11	6	present	present	VERB
american_scientific_journal-757	11	7	a	a	DET
american_scientific_journal-757	11	8	method	method	NOUN
american_scientific_journal-757	11	9	that	that	PRON
american_scientific_journal-757	11	10	enables	enable	VERB
american_scientific_journal-757	11	11	us	we	PRON
american_scientific_journal-757	11	12	to	to	PART
american_scientific_journal-757	11	13	find	find	VERB
american_scientific_journal-757	11	14	the	the	DET
american_scientific_journal-757	11	15	area	area	NOUN
american_scientific_journal-757	11	16	of	of	ADP
american_scientific_journal-757	11	17	a	a	DET
american_scientific_journal-757	11	18	triangle	triangle	NOUN
american_scientific_journal-757	11	19	without	without	ADP
american_scientific_journal-757	11	20	the	the	DET
american_scientific_journal-757	11	21	knowledge	knowledge	NOUN
american_scientific_journal-757	11	22	of	of	ADP
american_scientific_journal-757	11	23	vectors	vector	NOUN
american_scientific_journal-757	11	24	or	or	CCONJ
american_scientific_journal-757	11	25	determinants	determinant	NOUN
american_scientific_journal-757	11	26	,	,	PUNCT
american_scientific_journal-757	11	27	provided	provide	VERB
american_scientific_journal-757	11	28	that	that	SCONJ
american_scientific_journal-757	11	29	the	the	DET
american_scientific_journal-757	11	30	coordinates	coordinate	NOUN
american_scientific_journal-757	11	31	of	of	ADP
american_scientific_journal-757	11	32	the	the	DET
american_scientific_journal-757	11	33	vertices	vertex	NOUN
american_scientific_journal-757	11	34	of	of	ADP
american_scientific_journal-757	11	35	a	a	DET
american_scientific_journal-757	11	36	triangle	triangle	NOUN
american_scientific_journal-757	11	37	were	be	AUX
american_scientific_journal-757	11	38	given	give	VERB
american_scientific_journal-757	11	39	.	.	PUNCT
american_scientific_journal-757	12	1	we	we	PRON
american_scientific_journal-757	12	2	use	use	VERB
american_scientific_journal-757	12	3	analytic	analytic	ADJ
american_scientific_journal-757	12	4	approach	approach	NOUN
american_scientific_journal-757	12	5	to	to	PART
american_scientific_journal-757	12	6	derive	derive	VERB
american_scientific_journal-757	12	7	the	the	DET
american_scientific_journal-757	12	8	formula	formula	NOUN
american_scientific_journal-757	12	9	.	.	PUNCT
american_scientific_journal-757	13	1	the	the	DET
american_scientific_journal-757	13	2	method	method	NOUN
american_scientific_journal-757	13	3	use	use	VERB
american_scientific_journal-757	13	4	only	only	ADV
american_scientific_journal-757	13	5	elementary	elementary	ADJ
american_scientific_journal-757	13	6	arithmetic	arithmetic	NOUN
american_scientific_journal-757	13	7	.	.	PUNCT
american_scientific_journal-757	14	1	to	to	ADP
american_scientific_journal-757	14	2	this	this	DET
american_scientific_journal-757	14	3	end	end	NOUN
american_scientific_journal-757	14	4	a	a	DET
american_scientific_journal-757	14	5	procedure	procedure	NOUN
american_scientific_journal-757	14	6	were	be	AUX
american_scientific_journal-757	14	7	designed	design	VERB
american_scientific_journal-757	14	8	and	and	CCONJ
american_scientific_journal-757	14	9	the	the	DET
american_scientific_journal-757	14	10	method	method	NOUN
american_scientific_journal-757	14	11	were	be	AUX
american_scientific_journal-757	14	12	checked	check	VERB
american_scientific_journal-757	14	13	for	for	ADP
american_scientific_journal-757	14	14	accuracy	accuracy	NOUN
american_scientific_journal-757	14	15	using	use	VERB
american_scientific_journal-757	14	16	different	different	ADJ
american_scientific_journal-757	14	17	examples	example	NOUN
american_scientific_journal-757	14	18	.	.	PUNCT
american_scientific_journal-757	15	1	finally	finally	ADV
american_scientific_journal-757	15	2	,	,	PUNCT
american_scientific_journal-757	15	3	a	a	DET
american_scientific_journal-757	15	4	theorem	theorem	NOUN
american_scientific_journal-757	15	5	was	be	AUX
american_scientific_journal-757	15	6	formulated	formulate	VERB
american_scientific_journal-757	15	7	and	and	CCONJ
american_scientific_journal-757	15	8	proved	prove	VERB
american_scientific_journal-757	15	9	.	.	PUNCT
american_scientific_journal-757	16	1	keywords	keyword	NOUN
american_scientific_journal-757	16	2	:	:	PUNCT
american_scientific_journal-757	16	3	area	area	NOUN
american_scientific_journal-757	16	4	of	of	ADP
american_scientific_journal-757	16	5	triangle	triangle	NOUN
american_scientific_journal-757	16	6	;	;	PUNCT
american_scientific_journal-757	16	7	centroid	centroid	NOUN
american_scientific_journal-757	16	8	;	;	PUNCT
american_scientific_journal-757	16	9	vectors	vector	NOUN
american_scientific_journal-757	16	10	&	&	CCONJ
american_scientific_journal-757	16	11	determinants	determinant	NOUN
american_scientific_journal-757	16	12	;	;	PUNCT
american_scientific_journal-757	16	13	procedure	procedure	NOUN
american_scientific_journal-757	16	14	of	of	ADP
american_scientific_journal-757	16	15	evaluation	evaluation	NOUN
american_scientific_journal-757	16	16	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-757	17	1	*	*	PUNCT
american_scientific_journal-757	17	2	corresponding	correspond	VERB
american_scientific_journal-757	17	3	author	author	NOUN
american_scientific_journal-757	17	4	.	.	PUNCT
american_scientific_journal-757	18	1	e	e	X
american_scientific_journal-757	18	2	-	-	NOUN
american_scientific_journal-757	18	3	mail	mail	NOUN
american_scientific_journal-757	18	4	address	address	NOUN
american_scientific_journal-757	18	5	:	:	PUNCT
american_scientific_journal-757	18	6	kejeodaadureti@yahoo.com	kejeodaadureti@yahoo.com	X
american_scientific_journal-757	18	7	,	,	PUNCT
american_scientific_journal-757	18	8	jemal.kemal@astu.edu.et	jemal.kemal@astu.edu.et	PROPN
american_scientific_journal-757	18	9	.	.	PUNCT
american_scientific_journal-757	19	1	49	49	NUM
american_scientific_journal-757	19	2	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-757	19	3	mailto:dureti@yahoo.com	mailto:dureti@yahoo.com	X
american_scientific_journal-757	19	4	mailto:kejeodaadureti@yahoo.com	mailto:kejeodaadureti@yahoo.com	PROPN
american_scientific_journal-757	19	5	american	american	PROPN
american_scientific_journal-757	19	6	scientific	scientific	ADJ
american_scientific_journal-757	19	7	research	research	PROPN
american_scientific_journal-757	19	8	journal	journal	NOUN
american_scientific_journal-757	19	9	for	for	ADP
american_scientific_journal-757	19	10	engineering	engineering	NOUN
american_scientific_journal-757	19	11	,	,	PUNCT
american_scientific_journal-757	19	12	technology	technology	NOUN
american_scientific_journal-757	19	13	,	,	PUNCT
american_scientific_journal-757	19	14	and	and	CCONJ
american_scientific_journal-757	19	15	sciences	science	NOUN
american_scientific_journal-757	19	16	(	(	PUNCT
american_scientific_journal-757	19	17	asrjets	asrjet	NOUN
american_scientific_journal-757	19	18	)	)	PUNCT
american_scientific_journal-757	19	19	(	(	PUNCT
american_scientific_journal-757	19	20	2015	2015	NUM
american_scientific_journal-757	19	21	)	)	PUNCT
american_scientific_journal-757	19	22	volume	volume	NOUN
american_scientific_journal-757	19	23	13	13	NUM
american_scientific_journal-757	19	24	,	,	PUNCT
american_scientific_journal-757	19	25	no	no	DET
american_scientific_journal-757	19	26	1	1	NUM
american_scientific_journal-757	19	27	,	,	PUNCT
american_scientific_journal-757	19	28	pp	pp	ADV
american_scientific_journal-757	19	29	49	49	NUM
american_scientific_journal-757	19	30	-	-	SYM
american_scientific_journal-757	19	31	60	60	NUM
american_scientific_journal-757	19	32	1	1	NUM
american_scientific_journal-757	19	33	.	.	PUNCT
american_scientific_journal-757	20	1	introduction	introduction	NOUN
american_scientific_journal-757	20	2	it	it	PRON
american_scientific_journal-757	20	3	has	have	AUX
american_scientific_journal-757	20	4	been	be	AUX
american_scientific_journal-757	20	5	stated	state	VERB
american_scientific_journal-757	20	6	in	in	ADP
american_scientific_journal-757	20	7	[	[	X
american_scientific_journal-757	20	8	1,2,3,4,7,9,12,13,14	1,2,3,4,7,9,12,13,14	NUM
american_scientific_journal-757	20	9	]	]	X
american_scientific_journal-757	20	10	(	(	PUNCT
american_scientific_journal-757	20	11	elementary	elementary	ADJ
american_scientific_journal-757	20	12	text	text	NOUN
american_scientific_journal-757	20	13	books	book	NOUN
american_scientific_journal-757	20	14	of	of	ADP
american_scientific_journal-757	20	15	mathematics	mathematic	NOUN
american_scientific_journal-757	20	16	)	)	PUNCT
american_scientific_journal-757	20	17	that	that	SCONJ
american_scientific_journal-757	20	18	the	the	DET
american_scientific_journal-757	20	19	area	area	NOUN
american_scientific_journal-757	20	20	of	of	ADP
american_scientific_journal-757	20	21	a	a	DET
american_scientific_journal-757	20	22	triangle	triangle	NOUN
american_scientific_journal-757	20	23	having	have	VERB
american_scientific_journal-757	20	24	base	base	NOUN
american_scientific_journal-757	20	25	b	b	NOUN
american_scientific_journal-757	20	26	and	and	CCONJ
american_scientific_journal-757	20	27	height	height	NOUN
american_scientific_journal-757	20	28	h	h	NOUN
american_scientific_journal-757	20	29	is	be	AUX
american_scientific_journal-757	20	30	given	give	VERB
american_scientific_journal-757	20	31	by	by	ADP
american_scientific_journal-757	20	32	(	(	PUNCT
american_scientific_journal-757	20	33	)	)	SYM
american_scientific_journal-757	20	34	1	1	NUM
american_scientific_journal-757	20	35	2	2	NUM
american_scientific_journal-757	20	36	1	1	NUM
american_scientific_journal-757	20	37	bha	bha	NOUN
american_scientific_journal-757	20	38	=	=	PUNCT
american_scientific_journal-757	20	39	yet	yet	ADV
american_scientific_journal-757	20	40	another	another	DET
american_scientific_journal-757	20	41	expression	expression	NOUN
american_scientific_journal-757	20	42	for	for	ADP
american_scientific_journal-757	20	43	the	the	DET
american_scientific_journal-757	20	44	area	area	NOUN
american_scientific_journal-757	20	45	of	of	ADP
american_scientific_journal-757	20	46	a	a	DET
american_scientific_journal-757	20	47	triangle	triangle	NOUN
american_scientific_journal-757	20	48	is	be	AUX
american_scientific_journal-757	20	49	in	in	ADP
american_scientific_journal-757	20	50	terms	term	NOUN
american_scientific_journal-757	20	51	of	of	ADP
american_scientific_journal-757	20	52	the	the	DET
american_scientific_journal-757	20	53	length	length	NOUN
american_scientific_journal-757	20	54	of	of	ADP
american_scientific_journal-757	20	55	its	its	PRON
american_scientific_journal-757	20	56	sides	side	NOUN
american_scientific_journal-757	20	57	is	be	AUX
american_scientific_journal-757	20	58	credited	credit	VERB
american_scientific_journal-757	20	59	to	to	ADP
american_scientific_journal-757	20	60	a	a	DET
american_scientific_journal-757	20	61	greek	greek	ADJ
american_scientific_journal-757	20	62	mathematician	mathematician	NOUN
american_scientific_journal-757	20	63	,	,	PUNCT
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american_scientific_journal-757	20	65	lived	live	VERB
american_scientific_journal-757	20	66	during	during	ADP
american_scientific_journal-757	20	67	the	the	DET
american_scientific_journal-757	20	68	first	first	ADJ
american_scientific_journal-757	20	69	century	century	NOUN
american_scientific_journal-757	20	70	,	,	PUNCT
american_scientific_journal-757	20	71	heron	heron	NOUN
american_scientific_journal-757	21	1	[	[	X
american_scientific_journal-757	21	2	7,8,10,14,15	7,8,10,14,15	NUM
american_scientific_journal-757	21	3	]	]	PUNCT
american_scientific_journal-757	21	4	.	.	PUNCT
american_scientific_journal-757	22	1	if	if	SCONJ
american_scientific_journal-757	22	2	we	we	PRON
american_scientific_journal-757	22	3	use	use	VERB
american_scientific_journal-757	22	4	the	the	DET
american_scientific_journal-757	22	5	standard	standard	ADJ
american_scientific_journal-757	22	6	notion	notion	NOUN
american_scientific_journal-757	22	7	a	a	DET
american_scientific_journal-757	22	8	,	,	PUNCT
american_scientific_journal-757	22	9	b	b	NOUN
american_scientific_journal-757	22	10	,	,	PUNCT
american_scientific_journal-757	22	11	c	c	NOUN
american_scientific_journal-757	22	12	for	for	ADP
american_scientific_journal-757	22	13	the	the	DET
american_scientific_journal-757	22	14	sides	side	NOUN
american_scientific_journal-757	22	15	of	of	ADP
american_scientific_journal-757	22	16	triangle	triangle	PROPN
american_scientific_journal-757	22	17	pqr	pqr	PROPN
american_scientific_journal-757	22	18	,	,	PUNCT
american_scientific_journal-757	22	19	then	then	ADV
american_scientific_journal-757	22	20	by	by	ADP
american_scientific_journal-757	22	21	herons	heron	NOUN
american_scientific_journal-757	22	22	formula	formula	VERB
american_scientific_journal-757	22	23	the	the	DET
american_scientific_journal-757	22	24	area	area	NOUN
american_scientific_journal-757	22	25	of	of	ADP
american_scientific_journal-757	22	26	the	the	DET
american_scientific_journal-757	22	27	triangle	triangle	NOUN
american_scientific_journal-757	22	28	is	be	AUX
american_scientific_journal-757	22	29	(	(	PUNCT
american_scientific_journal-757	22	30	)	)	PUNCT
american_scientific_journal-757	22	31	(	(	PUNCT
american_scientific_journal-757	22	32	)	)	PUNCT
american_scientific_journal-757	22	33	(	(	PUNCT
american_scientific_journal-757	22	34	)	)	PUNCT
american_scientific_journal-757	22	35	(	(	PUNCT
american_scientific_journal-757	22	36	)	)	PUNCT
american_scientific_journal-757	22	37	2csbsassa	2csbsassa	NUM
american_scientific_journal-757	22	38	−−−=	−−−=	NUM
american_scientific_journal-757	22	39	where	where	SCONJ
american_scientific_journal-757	22	40	(	(	PUNCT
american_scientific_journal-757	22	41	)	)	PUNCT
american_scientific_journal-757	22	42	cbas	cbas	PROPN
american_scientific_journal-757	23	1	+	+	PROPN
american_scientific_journal-757	23	2	+	+	NOUN
american_scientific_journal-757	23	3	=	=	SYM
american_scientific_journal-757	23	4	2	2	NUM
american_scientific_journal-757	23	5	1	1	NUM
american_scientific_journal-757	23	6	.	.	PUNCT
american_scientific_journal-757	23	7	’	'	PUNCT
american_scientific_journal-757	24	1	the	the	DET
american_scientific_journal-757	24	2	area	area	NOUN
american_scientific_journal-757	24	3	of	of	ADP
american_scientific_journal-757	24	4	a	a	DET
american_scientific_journal-757	24	5	triangle	triangle	NOUN
american_scientific_journal-757	24	6	can	can	AUX
american_scientific_journal-757	24	7	also	also	ADV
american_scientific_journal-757	24	8	be	be	AUX
american_scientific_journal-757	24	9	found	find	VERB
american_scientific_journal-757	24	10	from	from	ADP
american_scientific_journal-757	24	11	the	the	DET
american_scientific_journal-757	24	12	product	product	NOUN
american_scientific_journal-757	24	13	of	of	ADP
american_scientific_journal-757	24	14	the	the	DET
american_scientific_journal-757	24	15	length	length	NOUN
american_scientific_journal-757	24	16	of	of	ADP
american_scientific_journal-757	24	17	two	two	NUM
american_scientific_journal-757	24	18	sides	side	NOUN
american_scientific_journal-757	24	19	and	and	CCONJ
american_scientific_journal-757	24	20	the	the	DET
american_scientific_journal-757	24	21	sine	sine	NOUN
american_scientific_journal-757	24	22	of	of	ADP
american_scientific_journal-757	24	23	included	include	VERB
american_scientific_journal-757	24	24	angle	angle	NOUN
american_scientific_journal-757	24	25	[	[	X
american_scientific_journal-757	24	26	1	1	NUM
american_scientific_journal-757	24	27	]	]	PUNCT
american_scientific_journal-757	24	28	,	,	PUNCT
american_scientific_journal-757	24	29	[	[	X
american_scientific_journal-757	24	30	8	8	NUM
american_scientific_journal-757	24	31	]	]	PUNCT
american_scientific_journal-757	24	32	,	,	PUNCT
american_scientific_journal-757	25	1	[	[	X
american_scientific_journal-757	25	2	9	9	NUM
american_scientific_journal-757	25	3	]	]	PUNCT
american_scientific_journal-757	25	4	,	,	PUNCT
american_scientific_journal-757	25	5	[	[	X
american_scientific_journal-757	25	6	10	10	NUM
american_scientific_journal-757	25	7	]	]	PUNCT
american_scientific_journal-757	25	8	,	,	PUNCT
american_scientific_journal-757	26	1	[	[	X
american_scientific_journal-757	26	2	11	11	NUM
american_scientific_journal-757	26	3	]	]	PUNCT
american_scientific_journal-757	26	4	,	,	PUNCT
american_scientific_journal-757	26	5	[	[	X
american_scientific_journal-757	26	6	17	17	NUM
american_scientific_journal-757	26	7	]	]	X
american_scientific_journal-757	26	8	(	(	PUNCT
american_scientific_journal-757	26	9	)	)	PUNCT
american_scientific_journal-757	26	10	3sin	3sin	NUM
american_scientific_journal-757	26	11	2	2	NUM
american_scientific_journal-757	26	12	1	1	NUM
american_scientific_journal-757	26	13	θaba	θaba	NOUN
american_scientific_journal-757	26	14	=	=	SYM
american_scientific_journal-757	26	15	whereθ	whereθ	NOUN
american_scientific_journal-757	26	16	is	be	AUX
american_scientific_journal-757	26	17	the	the	DET
american_scientific_journal-757	26	18	included	include	VERB
american_scientific_journal-757	26	19	angle	angle	NOUN
american_scientific_journal-757	26	20	.	.	PUNCT
american_scientific_journal-757	27	1	the	the	DET
american_scientific_journal-757	27	2	area	area	NOUN
american_scientific_journal-757	27	3	of	of	ADP
american_scientific_journal-757	27	4	a	a	DET
american_scientific_journal-757	27	5	triangle	triangle	NOUN
american_scientific_journal-757	27	6	with	with	ADP
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american_scientific_journal-757	27	12	also	also	ADV
american_scientific_journal-757	27	13	be	be	AUX
american_scientific_journal-757	27	14	found	find	VERB
american_scientific_journal-757	27	15	by	by	ADP
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american_scientific_journal-757	27	23	.	.	PUNCT
american_scientific_journal-757	28	1	the	the	DET
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american_scientific_journal-757	28	3	a	a	PRON
american_scientific_journal-757	28	4	of	of	ADP
american_scientific_journal-757	28	5	a	a	DET
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american_scientific_journal-757	28	14	(	(	PUNCT
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american_scientific_journal-757	28	18	2211	2211	NUM
american_scientific_journal-757	28	19	,	,	PUNCT
american_scientific_journal-757	28	20	,	,	PUNCT
american_scientific_journal-757	28	21	,	,	PUNCT
american_scientific_journal-757	28	22	yxqyxp	yxqyxp	PROPN
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american_scientific_journal-757	28	24	(	(	PUNCT
american_scientific_journal-757	28	25	)	)	PUNCT
american_scientific_journal-757	28	26	,	,	PUNCT
american_scientific_journal-757	28	27	,	,	PUNCT
american_scientific_journal-757	28	28	33	33	NUM
american_scientific_journal-757	28	29	yxr	yxr	NOUN
american_scientific_journal-757	28	30	is	be	AUX
american_scientific_journal-757	28	31	given	give	VERB
american_scientific_journal-757	28	32	by	by	ADP
american_scientific_journal-757	28	33	where	where	SCONJ
american_scientific_journal-757	28	34	,	,	PUNCT
american_scientific_journal-757	28	35	pq	pq	INTJ
american_scientific_journal-757	28	36	and	and	CCONJ
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american_scientific_journal-757	28	47	a	a	DET
american_scientific_journal-757	28	48	plane	plane	NOUN
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american_scientific_journal-757	29	2	16	16	NUM
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american_scientific_journal-757	29	4	.	.	PUNCT
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american_scientific_journal-757	30	4	in	in	ADP
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american_scientific_journal-757	30	7	]	]	PUNCT
american_scientific_journal-757	30	8	,	,	PUNCT
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american_scientific_journal-757	30	11	,	,	PUNCT
american_scientific_journal-757	30	12	we	we	PRON
american_scientific_journal-757	30	13	have	have	VERB
american_scientific_journal-757	30	14	the	the	DET
american_scientific_journal-757	30	15	formula	formula	NOUN
american_scientific_journal-757	30	16	(	(	PUNCT
american_scientific_journal-757	30	17	)	)	PUNCT
american_scientific_journal-757	30	18	5	5	NUM
american_scientific_journal-757	30	19	1	1	NUM
american_scientific_journal-757	30	20	1	1	NUM
american_scientific_journal-757	30	21	1	1	NUM
american_scientific_journal-757	30	22	2	2	NUM
american_scientific_journal-757	30	23	1	1	NUM
american_scientific_journal-757	30	24	33	33	NUM
american_scientific_journal-757	30	25	22	22	NUM
american_scientific_journal-757	30	26	11	11	NUM
american_scientific_journal-757	30	27	yx	yx	NOUN
american_scientific_journal-757	30	28	yx	yx	PROPN
american_scientific_journal-757	30	29	yx	yx	PROPN
american_scientific_journal-757	30	30	a	a	DET
american_scientific_journal-757	30	31	±=	±=	NOUN
american_scientific_journal-757	30	32	(	(	PUNCT
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american_scientific_journal-757	30	34	4	4	NUM
american_scientific_journal-757	30	35	2	2	NUM
american_scientific_journal-757	30	36	1	1	NUM
american_scientific_journal-757	30	37	prpqa	prpqa	NOUN
american_scientific_journal-757	30	38	×±=	×±=	NOUN
american_scientific_journal-757	30	39	50	50	NUM
american_scientific_journal-757	30	40	american	american	ADJ
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american_scientific_journal-757	30	46	,	,	PUNCT
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american_scientific_journal-757	30	48	,	,	PUNCT
american_scientific_journal-757	30	49	and	and	CCONJ
american_scientific_journal-757	30	50	sciences	science	NOUN
american_scientific_journal-757	30	51	(	(	PUNCT
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american_scientific_journal-757	30	54	(	(	PUNCT
american_scientific_journal-757	30	55	2015	2015	NUM
american_scientific_journal-757	30	56	)	)	PUNCT
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american_scientific_journal-757	30	59	,	,	PUNCT
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american_scientific_journal-757	30	61	1	1	NUM
american_scientific_journal-757	30	62	,	,	PUNCT
american_scientific_journal-757	30	63	pp	pp	ADV
american_scientific_journal-757	30	64	49	49	NUM
american_scientific_journal-757	30	65	-	-	SYM
american_scientific_journal-757	30	66	60	60	NUM
american_scientific_journal-757	30	67	note	note	NOUN
american_scientific_journal-757	30	68	that	that	SCONJ
american_scientific_journal-757	30	69	the	the	DET
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american_scientific_journal-757	30	71	(	(	PUNCT
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american_scientific_journal-757	30	73	±	±	PROPN
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american_scientific_journal-757	30	80	.	.	PUNCT
american_scientific_journal-757	31	1	as	as	SCONJ
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american_scientific_journal-757	31	3	in	in	ADP
american_scientific_journal-757	31	4	[	[	X
american_scientific_journal-757	31	5	6	6	NUM
american_scientific_journal-757	31	6	]	]	PUNCT
american_scientific_journal-757	31	7	,	,	PUNCT
american_scientific_journal-757	31	8	the	the	DET
american_scientific_journal-757	31	9	centriod	centriod	NOUN
american_scientific_journal-757	31	10	of	of	ADP
american_scientific_journal-757	31	11	a	a	DET
american_scientific_journal-757	31	12	triangle	triangle	NOUN
american_scientific_journal-757	31	13	having	have	VERB
american_scientific_journal-757	31	14	base	base	NOUN
american_scientific_journal-757	31	15	b	b	NOUN
american_scientific_journal-757	31	16	and	and	CCONJ
american_scientific_journal-757	31	17	height	height	NOUN
american_scientific_journal-757	31	18	h	h	NOUN
american_scientific_journal-757	31	19	is	be	AUX
american_scientific_journal-757	31	20	located	locate	VERB
american_scientific_journal-757	31	21	at	at	ADP
american_scientific_journal-757	31	22	one	one	NUM
american_scientific_journal-757	31	23	-	-	PUNCT
american_scientific_journal-757	31	24	third	third	NOUN
american_scientific_journal-757	31	25	of	of	ADP
american_scientific_journal-757	31	26	the	the	DET
american_scientific_journal-757	31	27	height	height	NOUN
american_scientific_journal-757	31	28	from	from	ADP
american_scientific_journal-757	31	29	the	the	DET
american_scientific_journal-757	31	30	base	base	NOUN
american_scientific_journal-757	31	31	of	of	ADP
american_scientific_journal-757	31	32	the	the	DET
american_scientific_journal-757	31	33	triangle	triangle	NOUN
american_scientific_journal-757	31	34	and	and	CCONJ
american_scientific_journal-757	31	35	this	this	PRON
american_scientific_journal-757	31	36	is	be	AUX
american_scientific_journal-757	31	37	valid	valid	ADJ
american_scientific_journal-757	31	38	for	for	ADP
american_scientific_journal-757	31	39	any	any	DET
american_scientific_journal-757	31	40	type	type	NOUN
american_scientific_journal-757	31	41	of	of	ADP
american_scientific_journal-757	31	42	triangles	triangle	NOUN
american_scientific_journal-757	31	43	.	.	PUNCT
american_scientific_journal-757	32	1	in	in	ADP
american_scientific_journal-757	32	2	[	[	X
american_scientific_journal-757	32	3	5	5	NUM
american_scientific_journal-757	32	4	]	]	PUNCT
american_scientific_journal-757	32	5	,	,	PUNCT
american_scientific_journal-757	32	6	it	it	PRON
american_scientific_journal-757	32	7	have	have	AUX
american_scientific_journal-757	32	8	been	be	AUX
american_scientific_journal-757	32	9	stated	state	VERB
american_scientific_journal-757	32	10	that	that	SCONJ
american_scientific_journal-757	32	11	the	the	DET
american_scientific_journal-757	32	12	coordinates	coordinate	NOUN
american_scientific_journal-757	32	13	of	of	ADP
american_scientific_journal-757	32	14	the	the	DET
american_scientific_journal-757	32	15	location	location	NOUN
american_scientific_journal-757	32	16	of	of	ADP
american_scientific_journal-757	32	17	the	the	DET
american_scientific_journal-757	32	18	centriod	centriod	NOUN
american_scientific_journal-757	32	19	of	of	ADP
american_scientific_journal-757	32	20	an	an	DET
american_scientific_journal-757	32	21	arbitrary	arbitrary	ADJ
american_scientific_journal-757	32	22	triangle	triangle	NOUN
american_scientific_journal-757	32	23	having	have	VERB
american_scientific_journal-757	32	24	vertices	vertex	NOUN
american_scientific_journal-757	32	25	(	(	PUNCT
american_scientific_journal-757	32	26	)	)	PUNCT
american_scientific_journal-757	32	27	(	(	PUNCT
american_scientific_journal-757	32	28	)	)	PUNCT
american_scientific_journal-757	32	29	2211	2211	NUM
american_scientific_journal-757	32	30	,	,	PUNCT
american_scientific_journal-757	32	31	,	,	PUNCT
american_scientific_journal-757	32	32	,	,	PUNCT
american_scientific_journal-757	32	33	yxqyxp	yxqyxp	PROPN
american_scientific_journal-757	32	34	and	and	CCONJ
american_scientific_journal-757	32	35	(	(	PUNCT
american_scientific_journal-757	32	36	)	)	PUNCT
american_scientific_journal-757	32	37	,	,	PUNCT
american_scientific_journal-757	32	38	,	,	PUNCT
american_scientific_journal-757	32	39	33	33	NUM
american_scientific_journal-757	32	40	yxr	yxr	NOUN
american_scientific_journal-757	32	41	is	be	AUX
american_scientific_journal-757	32	42	3	3	NUM
american_scientific_journal-757	32	43	321	321	NUM
american_scientific_journal-757	32	44	xxx	xxx	NOUN
american_scientific_journal-757	32	45	xc	xc	NOUN
american_scientific_journal-757	33	1	+	+	PROPN
american_scientific_journal-757	33	2	+	+	CCONJ
american_scientific_journal-757	33	3	=	=	SYM
american_scientific_journal-757	33	4	and	and	CCONJ
american_scientific_journal-757	33	5	(	(	PUNCT
american_scientific_journal-757	33	6	)	)	SYM
american_scientific_journal-757	33	7	6	6	NUM
american_scientific_journal-757	33	8	3	3	NUM
american_scientific_journal-757	33	9	321	321	NUM
american_scientific_journal-757	33	10	yyy	yyy	NOUN
american_scientific_journal-757	33	11	yc	yc	PROPN
american_scientific_journal-757	34	1	+	+	PROPN
american_scientific_journal-757	34	2	+	+	CCONJ
american_scientific_journal-757	34	3	=	=	SYM
american_scientific_journal-757	34	4	although	although	SCONJ
american_scientific_journal-757	34	5	it	it	PRON
american_scientific_journal-757	34	6	is	be	AUX
american_scientific_journal-757	34	7	possible	possible	ADJ
american_scientific_journal-757	34	8	to	to	PART
american_scientific_journal-757	34	9	find	find	VERB
american_scientific_journal-757	34	10	the	the	DET
american_scientific_journal-757	34	11	area	area	NOUN
american_scientific_journal-757	34	12	of	of	ADP
american_scientific_journal-757	34	13	a	a	DET
american_scientific_journal-757	34	14	triangle	triangle	NOUN
american_scientific_journal-757	34	15	from	from	ADP
american_scientific_journal-757	34	16	its	its	PRON
american_scientific_journal-757	34	17	vertices	vertex	NOUN
american_scientific_journal-757	34	18	by	by	ADP
american_scientific_journal-757	34	19	using	use	VERB
american_scientific_journal-757	34	20	the	the	DET
american_scientific_journal-757	34	21	concept	concept	NOUN
american_scientific_journal-757	34	22	of	of	ADP
american_scientific_journal-757	34	23	vectors	vector	NOUN
american_scientific_journal-757	34	24	&	&	CCONJ
american_scientific_journal-757	34	25	determinants	determinant	NOUN
american_scientific_journal-757	34	26	,	,	PUNCT
american_scientific_journal-757	34	27	we	we	PRON
american_scientific_journal-757	34	28	come	come	VERB
american_scientific_journal-757	34	29	up	up	ADP
american_scientific_journal-757	34	30	with	with	ADP
american_scientific_journal-757	34	31	another	another	DET
american_scientific_journal-757	34	32	way	way	NOUN
american_scientific_journal-757	34	33	of	of	ADP
american_scientific_journal-757	34	34	finding	find	VERB
american_scientific_journal-757	34	35	the	the	DET
american_scientific_journal-757	34	36	area	area	NOUN
american_scientific_journal-757	34	37	of	of	ADP
american_scientific_journal-757	34	38	a	a	DET
american_scientific_journal-757	34	39	triangle	triangle	NOUN
american_scientific_journal-757	34	40	which	which	PRON
american_scientific_journal-757	34	41	uses	use	VERB
american_scientific_journal-757	34	42	vertical	vertical	ADJ
american_scientific_journal-757	34	43	alignment	alignment	NOUN
american_scientific_journal-757	34	44	of	of	ADP
american_scientific_journal-757	34	45	vertices	vertex	NOUN
american_scientific_journal-757	34	46	and	and	CCONJ
american_scientific_journal-757	34	47	is	be	AUX
american_scientific_journal-757	34	48	more	more	ADV
american_scientific_journal-757	34	49	convenient	convenient	ADJ
american_scientific_journal-757	34	50	for	for	ADP
american_scientific_journal-757	34	51	computing	compute	VERB
american_scientific_journal-757	34	52	.	.	PUNCT
american_scientific_journal-757	35	1	2	2	X
american_scientific_journal-757	35	2	.	.	X
american_scientific_journal-757	35	3	methodology	methodology	NOUN
american_scientific_journal-757	35	4	this	this	DET
american_scientific_journal-757	35	5	study	study	NOUN
american_scientific_journal-757	35	6	is	be	AUX
american_scientific_journal-757	35	7	a	a	DET
american_scientific_journal-757	35	8	basic	basic	ADJ
american_scientific_journal-757	35	9	research	research	NOUN
american_scientific_journal-757	35	10	that	that	PRON
american_scientific_journal-757	35	11	employs	employ	VERB
american_scientific_journal-757	35	12	mathematical	mathematical	ADJ
american_scientific_journal-757	35	13	exploration	exploration	NOUN
american_scientific_journal-757	35	14	and	and	CCONJ
american_scientific_journal-757	35	15	experimentation	experimentation	NOUN
american_scientific_journal-757	35	16	.	.	PUNCT
american_scientific_journal-757	36	1	the	the	DET
american_scientific_journal-757	36	2	researcher	researcher	NOUN
american_scientific_journal-757	36	3	explored	explore	VERB
american_scientific_journal-757	36	4	the	the	DET
american_scientific_journal-757	36	5	concepts	concept	NOUN
american_scientific_journal-757	36	6	regarding	regard	VERB
american_scientific_journal-757	36	7	the	the	DET
american_scientific_journal-757	36	8	subject	subject	NOUN
american_scientific_journal-757	36	9	of	of	ADP
american_scientific_journal-757	36	10	study	study	NOUN
american_scientific_journal-757	36	11	presented	present	VERB
american_scientific_journal-757	36	12	in	in	ADP
american_scientific_journal-757	36	13	different	different	ADJ
american_scientific_journal-757	36	14	areas	area	NOUN
american_scientific_journal-757	36	15	of	of	ADP
american_scientific_journal-757	36	16	mathematics	mathematic	NOUN
american_scientific_journal-757	36	17	and	and	CCONJ
american_scientific_journal-757	36	18	engineering	engineering	NOUN
american_scientific_journal-757	36	19	namely	namely	ADV
american_scientific_journal-757	36	20	geometry	geometry	NOUN
american_scientific_journal-757	36	21	,	,	PUNCT
american_scientific_journal-757	36	22	analytic	analytic	ADJ
american_scientific_journal-757	36	23	geometry	geometry	NOUN
american_scientific_journal-757	36	24	,	,	PUNCT
american_scientific_journal-757	36	25	algebra	algebra	NOUN
american_scientific_journal-757	36	26	,	,	PUNCT
american_scientific_journal-757	36	27	mechanics	mechanic	NOUN
american_scientific_journal-757	36	28	and	and	CCONJ
american_scientific_journal-757	36	29	surveying	surveying	NOUN
american_scientific_journal-757	36	30	.	.	PUNCT
american_scientific_journal-757	37	1	in	in	ADP
american_scientific_journal-757	37	2	this	this	DET
american_scientific_journal-757	37	3	study	study	NOUN
american_scientific_journal-757	37	4	,	,	PUNCT
american_scientific_journal-757	37	5	the	the	DET
american_scientific_journal-757	37	6	derivation	derivation	NOUN
american_scientific_journal-757	37	7	of	of	ADP
american_scientific_journal-757	37	8	the	the	DET
american_scientific_journal-757	37	9	formula	formula	NOUN
american_scientific_journal-757	37	10	for	for	ADP
american_scientific_journal-757	37	11	calculating	calculate	VERB
american_scientific_journal-757	37	12	the	the	DET
american_scientific_journal-757	37	13	area	area	NOUN
american_scientific_journal-757	37	14	of	of	ADP
american_scientific_journal-757	37	15	a	a	DET
american_scientific_journal-757	37	16	triangle	triangle	NOUN
american_scientific_journal-757	37	17	in	in	ADP
american_scientific_journal-757	37	18	a	a	DET
american_scientific_journal-757	37	19	plane	plane	NOUN
american_scientific_journal-757	37	20	was	be	AUX
american_scientific_journal-757	37	21	done	do	VERB
american_scientific_journal-757	37	22	in	in	ADP
american_scientific_journal-757	37	23	analytic	analytic	ADJ
american_scientific_journal-757	37	24	approach	approach	NOUN
american_scientific_journal-757	37	25	.	.	PUNCT
american_scientific_journal-757	38	1	the	the	DET
american_scientific_journal-757	38	2	procedure	procedure	NOUN
american_scientific_journal-757	38	3	was	be	AUX
american_scientific_journal-757	38	4	devised	devise	VERB
american_scientific_journal-757	38	5	following	follow	VERB
american_scientific_journal-757	38	6	the	the	DET
american_scientific_journal-757	38	7	principle	principle	NOUN
american_scientific_journal-757	38	8	of	of	ADP
american_scientific_journal-757	38	9	problem	problem	NOUN
american_scientific_journal-757	38	10	solving	solve	VERB
american_scientific_journal-757	38	11	and	and	CCONJ
american_scientific_journal-757	38	12	inductive	inductive	ADJ
american_scientific_journal-757	38	13	approach	approach	NOUN
american_scientific_journal-757	38	14	.	.	PUNCT
american_scientific_journal-757	39	1	a	a	DET
american_scientific_journal-757	39	2	series	series	NOUN
american_scientific_journal-757	39	3	of	of	ADP
american_scientific_journal-757	39	4	mathematical	mathematical	ADJ
american_scientific_journal-757	39	5	experiments	experiment	NOUN
american_scientific_journal-757	39	6	and	and	CCONJ
american_scientific_journal-757	39	7	computations	computation	NOUN
american_scientific_journal-757	39	8	were	be	AUX
american_scientific_journal-757	39	9	done	do	VERB
american_scientific_journal-757	39	10	in	in	ADP
american_scientific_journal-757	39	11	order	order	NOUN
american_scientific_journal-757	39	12	to	to	PART
american_scientific_journal-757	39	13	establish	establish	VERB
american_scientific_journal-757	39	14	the	the	DET
american_scientific_journal-757	39	15	procedure	procedure	NOUN
american_scientific_journal-757	39	16	of	of	ADP
american_scientific_journal-757	39	17	computation	computation	NOUN
american_scientific_journal-757	39	18	and	and	CCONJ
american_scientific_journal-757	39	19	the	the	DET
american_scientific_journal-757	39	20	use	use	NOUN
american_scientific_journal-757	39	21	of	of	ADP
american_scientific_journal-757	39	22	derived	derive	VERB
american_scientific_journal-757	39	23	formula	formula	NOUN
american_scientific_journal-757	39	24	for	for	ADP
american_scientific_journal-757	39	25	different	different	ADJ
american_scientific_journal-757	39	26	types	type	NOUN
american_scientific_journal-757	39	27	of	of	ADP
american_scientific_journal-757	39	28	triangles	triangle	NOUN
american_scientific_journal-757	39	29	.	.	PUNCT
american_scientific_journal-757	40	1	the	the	DET
american_scientific_journal-757	40	2	results	result	NOUN
american_scientific_journal-757	40	3	of	of	ADP
american_scientific_journal-757	40	4	the	the	DET
american_scientific_journal-757	40	5	study	study	NOUN
american_scientific_journal-757	40	6	were	be	AUX
american_scientific_journal-757	40	7	also	also	ADV
american_scientific_journal-757	40	8	compared	compare	VERB
american_scientific_journal-757	40	9	with	with	ADP
american_scientific_journal-757	40	10	previously	previously	ADV
american_scientific_journal-757	40	11	established	establish	VERB
american_scientific_journal-757	40	12	rules	rule	NOUN
american_scientific_journal-757	40	13	and	and	CCONJ
american_scientific_journal-757	40	14	formulas	formula	NOUN
american_scientific_journal-757	40	15	.	.	PUNCT
american_scientific_journal-757	41	1	in	in	ADP
american_scientific_journal-757	41	2	the	the	DET
american_scientific_journal-757	41	3	following	following	ADJ
american_scientific_journal-757	41	4	section	section	NOUN
american_scientific_journal-757	41	5	,	,	PUNCT
american_scientific_journal-757	41	6	we	we	PRON
american_scientific_journal-757	41	7	shall	shall	AUX
american_scientific_journal-757	41	8	present	present	VERB
american_scientific_journal-757	41	9	the	the	DET
american_scientific_journal-757	41	10	main	main	ADJ
american_scientific_journal-757	41	11	steps	step	NOUN
american_scientific_journal-757	41	12	which	which	PRON
american_scientific_journal-757	41	13	are	be	AUX
american_scientific_journal-757	41	14	used	use	VERB
american_scientific_journal-757	41	15	in	in	ADP
american_scientific_journal-757	41	16	the	the	DET
american_scientific_journal-757	41	17	new	new	ADJ
american_scientific_journal-757	41	18	approach	approach	NOUN
american_scientific_journal-757	41	19	as	as	ADP
american_scientific_journal-757	41	20	a	a	DET
american_scientific_journal-757	41	21	procedure	procedure	NOUN
american_scientific_journal-757	41	22	.	.	PUNCT
american_scientific_journal-757	42	1	3	3	X
american_scientific_journal-757	42	2	.	.	NOUN
american_scientific_journal-757	42	3	results	result	NOUN
american_scientific_journal-757	42	4	and	and	CCONJ
american_scientific_journal-757	42	5	discussion	discussion	NOUN
american_scientific_journal-757	42	6	3.1	3.1	NUM
american_scientific_journal-757	42	7	.	.	PUNCT
american_scientific_journal-757	42	8	procedure	procedure	NOUN
american_scientific_journal-757	42	9	of	of	ADP
american_scientific_journal-757	42	10	evaluation	evaluation	NOUN
american_scientific_journal-757	42	11	below	below	ADP
american_scientific_journal-757	42	12	we	we	PRON
american_scientific_journal-757	42	13	list	list	VERB
american_scientific_journal-757	42	14	the	the	DET
american_scientific_journal-757	42	15	major	major	ADJ
american_scientific_journal-757	42	16	steps	step	NOUN
american_scientific_journal-757	42	17	of	of	ADP
american_scientific_journal-757	42	18	the	the	DET
american_scientific_journal-757	42	19	method	method	NOUN
american_scientific_journal-757	42	20	as	as	ADP
american_scientific_journal-757	42	21	a	a	DET
american_scientific_journal-757	42	22	procedure	procedure	NOUN
american_scientific_journal-757	42	23	that	that	PRON
american_scientific_journal-757	42	24	guide	guide	VERB
american_scientific_journal-757	42	25	us	we	PRON
american_scientific_journal-757	42	26	in	in	ADP
american_scientific_journal-757	42	27	finding	find	VERB
american_scientific_journal-757	42	28	the	the	DET
american_scientific_journal-757	42	29	area	area	NOUN
american_scientific_journal-757	42	30	of	of	ADP
american_scientific_journal-757	42	31	a	a	DET
american_scientific_journal-757	42	32	triangle	triangle	NOUN
american_scientific_journal-757	42	33	.	.	PUNCT
american_scientific_journal-757	43	1	step	step	NOUN
american_scientific_journal-757	43	2	1	1	NUM
american_scientific_journal-757	43	3	rewrite	rewrite	VERB
american_scientific_journal-757	43	4	the	the	DET
american_scientific_journal-757	43	5	points	point	NOUN
american_scientific_journal-757	43	6	of	of	ADP
american_scientific_journal-757	43	7	vertices	vertex	NOUN
american_scientific_journal-757	43	8	vertically	vertically	ADV
american_scientific_journal-757	43	9	down	down	ADV
american_scientific_journal-757	43	10	in	in	ADP
american_scientific_journal-757	43	11	column	column	NOUN
american_scientific_journal-757	43	12	form	form	NOUN
american_scientific_journal-757	43	13	.	.	PUNCT
american_scientific_journal-757	44	1	step	step	NOUN
american_scientific_journal-757	44	2	2	2	NUM
american_scientific_journal-757	44	3	add	add	VERB
american_scientific_journal-757	44	4	the	the	DET
american_scientific_journal-757	44	5	first	first	ADJ
american_scientific_journal-757	44	6	components	component	NOUN
american_scientific_journal-757	44	7	together	together	ADV
american_scientific_journal-757	44	8	and	and	CCONJ
american_scientific_journal-757	44	9	put	put	VERB
american_scientific_journal-757	44	10	the	the	DET
american_scientific_journal-757	44	11	sum	sum	NOUN
american_scientific_journal-757	44	12	exactly	exactly	ADV
american_scientific_journal-757	44	13	under	under	ADP
american_scientific_journal-757	44	14	the	the	DET
american_scientific_journal-757	44	15	first	first	ADJ
american_scientific_journal-757	44	16	coordinate	coordinate	NOUN
american_scientific_journal-757	44	17	of	of	ADP
american_scientific_journal-757	44	18	the	the	DET
american_scientific_journal-757	44	19	last	last	ADJ
american_scientific_journal-757	44	20	vertex	vertex	NOUN
american_scientific_journal-757	44	21	.	.	PUNCT
american_scientific_journal-757	45	1	step	step	NOUN
american_scientific_journal-757	45	2	3	3	NUM
american_scientific_journal-757	45	3	repeat	repeat	NOUN
american_scientific_journal-757	45	4	step	step	NOUN
american_scientific_journal-757	45	5	2	2	NUM
american_scientific_journal-757	45	6	for	for	ADP
american_scientific_journal-757	45	7	second	second	ADJ
american_scientific_journal-757	45	8	component	component	NOUN
american_scientific_journal-757	45	9	.	.	PUNCT
american_scientific_journal-757	46	1	step	step	NOUN
american_scientific_journal-757	46	2	4	4	NUM
american_scientific_journal-757	46	3	find	find	VERB
american_scientific_journal-757	46	4	the	the	DET
american_scientific_journal-757	46	5	product	product	NOUN
american_scientific_journal-757	46	6	of	of	ADP
american_scientific_journal-757	46	7	the	the	DET
american_scientific_journal-757	46	8	results	result	NOUN
american_scientific_journal-757	46	9	that	that	PRON
american_scientific_journal-757	46	10	are	be	AUX
american_scientific_journal-757	46	11	obtained	obtain	VERB
american_scientific_journal-757	46	12	in	in	ADP
american_scientific_journal-757	46	13	step	step	NOUN
american_scientific_journal-757	46	14	2	2	NUM
american_scientific_journal-757	46	15	and	and	CCONJ
american_scientific_journal-757	46	16	3	3	NUM
american_scientific_journal-757	46	17	51	51	NUM
american_scientific_journal-757	46	18	american	american	ADJ
american_scientific_journal-757	46	19	scientific	scientific	ADJ
american_scientific_journal-757	46	20	research	research	NOUN
american_scientific_journal-757	46	21	journal	journal	NOUN
american_scientific_journal-757	46	22	for	for	ADP
american_scientific_journal-757	46	23	engineering	engineering	NOUN
american_scientific_journal-757	46	24	,	,	PUNCT
american_scientific_journal-757	46	25	technology	technology	NOUN
american_scientific_journal-757	46	26	,	,	PUNCT
american_scientific_journal-757	46	27	and	and	CCONJ
american_scientific_journal-757	46	28	sciences	science	NOUN
american_scientific_journal-757	46	29	(	(	PUNCT
american_scientific_journal-757	46	30	asrjets	asrjet	NOUN
american_scientific_journal-757	46	31	)	)	PUNCT
american_scientific_journal-757	46	32	(	(	PUNCT
american_scientific_journal-757	46	33	2015	2015	NUM
american_scientific_journal-757	46	34	)	)	PUNCT
american_scientific_journal-757	46	35	volume	volume	NOUN
american_scientific_journal-757	46	36	13	13	NUM
american_scientific_journal-757	46	37	,	,	PUNCT
american_scientific_journal-757	46	38	no	no	DET
american_scientific_journal-757	46	39	1	1	NUM
american_scientific_journal-757	46	40	,	,	PUNCT
american_scientific_journal-757	46	41	pp	pp	ADV
american_scientific_journal-757	46	42	49	49	NUM
american_scientific_journal-757	46	43	-	-	SYM
american_scientific_journal-757	46	44	60	60	NUM
american_scientific_journal-757	46	45	step	step	NOUN
american_scientific_journal-757	46	46	5	5	NUM
american_scientific_journal-757	46	47	multiply	multiply	NOUN
american_scientific_journal-757	46	48	the	the	DET
american_scientific_journal-757	46	49	coordinates	coordinate	NOUN
american_scientific_journal-757	46	50	of	of	ADP
american_scientific_journal-757	46	51	each	each	DET
american_scientific_journal-757	46	52	vertex	vertex	NOUN
american_scientific_journal-757	46	53	with	with	ADP
american_scientific_journal-757	46	54	each	each	DET
american_scientific_journal-757	46	55	other	other	ADJ
american_scientific_journal-757	46	56	and	and	CCONJ
american_scientific_journal-757	46	57	put	put	VERB
american_scientific_journal-757	46	58	the	the	DET
american_scientific_journal-757	46	59	product	product	NOUN
american_scientific_journal-757	46	60	in	in	ADP
american_scientific_journal-757	46	61	front	front	NOUN
american_scientific_journal-757	46	62	of	of	ADP
american_scientific_journal-757	46	63	each	each	DET
american_scientific_journal-757	46	64	vertex	vertex	NOUN
american_scientific_journal-757	46	65	in	in	ADP
american_scientific_journal-757	46	66	the	the	DET
american_scientific_journal-757	46	67	third	third	ADJ
american_scientific_journal-757	46	68	column	column	NOUN
american_scientific_journal-757	46	69	.	.	PUNCT
american_scientific_journal-757	47	1	step	step	NOUN
american_scientific_journal-757	47	2	6	6	NUM
american_scientific_journal-757	47	3	find	find	VERB
american_scientific_journal-757	47	4	the	the	DET
american_scientific_journal-757	47	5	sum	sum	NOUN
american_scientific_journal-757	47	6	of	of	ADP
american_scientific_journal-757	47	7	the	the	DET
american_scientific_journal-757	47	8	products	product	NOUN
american_scientific_journal-757	47	9	obtained	obtain	VERB
american_scientific_journal-757	47	10	in	in	ADP
american_scientific_journal-757	47	11	step	step	NOUN
american_scientific_journal-757	47	12	5	5	NUM
american_scientific_journal-757	47	13	and	and	CCONJ
american_scientific_journal-757	47	14	change	change	VERB
american_scientific_journal-757	47	15	its	its	PRON
american_scientific_journal-757	47	16	sign	sign	NOUN
american_scientific_journal-757	47	17	&	&	CCONJ
american_scientific_journal-757	47	18	put	put	VERB
american_scientific_journal-757	47	19	the	the	DET
american_scientific_journal-757	47	20	result	result	NOUN
american_scientific_journal-757	47	21	under	under	ADP
american_scientific_journal-757	47	22	the	the	DET
american_scientific_journal-757	47	23	last	last	ADJ
american_scientific_journal-757	47	24	component	component	NOUN
american_scientific_journal-757	47	25	under	under	ADP
american_scientific_journal-757	47	26	the	the	DET
american_scientific_journal-757	47	27	third	third	ADJ
american_scientific_journal-757	47	28	column	column	NOUN
american_scientific_journal-757	47	29	.	.	PUNCT
american_scientific_journal-757	48	1	step	step	NOUN
american_scientific_journal-757	48	2	7	7	NUM
american_scientific_journal-757	48	3	draw	draw	VERB
american_scientific_journal-757	48	4	a	a	DET
american_scientific_journal-757	48	5	line	line	NOUN
american_scientific_journal-757	48	6	from	from	ADP
american_scientific_journal-757	48	7	the	the	DET
american_scientific_journal-757	48	8	1st	1st	ADJ
american_scientific_journal-757	48	9	coordinate	coordinate	NOUN
american_scientific_journal-757	48	10	of	of	ADP
american_scientific_journal-757	48	11	the	the	DET
american_scientific_journal-757	48	12	first	first	ADJ
american_scientific_journal-757	48	13	vertex	vertex	NOUN
american_scientific_journal-757	48	14	to	to	ADP
american_scientific_journal-757	48	15	the	the	DET
american_scientific_journal-757	48	16	2nd	2nd	ADJ
american_scientific_journal-757	48	17	coordinate	coordinate	NOUN
american_scientific_journal-757	48	18	of	of	ADP
american_scientific_journal-757	48	19	the	the	DET
american_scientific_journal-757	48	20	last	last	ADJ
american_scientific_journal-757	48	21	vertex	vertex	NOUN
american_scientific_journal-757	48	22	.	.	PUNCT
american_scientific_journal-757	49	1	draw	draw	VERB
american_scientific_journal-757	49	2	a	a	DET
american_scientific_journal-757	49	3	line	line	NOUN
american_scientific_journal-757	49	4	from	from	ADP
american_scientific_journal-757	49	5	the	the	DET
american_scientific_journal-757	49	6	1st	1st	ADJ
american_scientific_journal-757	49	7	coordinate	coordinate	NOUN
american_scientific_journal-757	49	8	of	of	ADP
american_scientific_journal-757	49	9	the	the	DET
american_scientific_journal-757	49	10	second	second	ADJ
american_scientific_journal-757	49	11	vertex	vertex	NOUN
american_scientific_journal-757	49	12	to	to	ADP
american_scientific_journal-757	49	13	the	the	DET
american_scientific_journal-757	49	14	2nd	2nd	ADJ
american_scientific_journal-757	49	15	coordinate	coordinate	NOUN
american_scientific_journal-757	49	16	of	of	ADP
american_scientific_journal-757	49	17	the	the	DET
american_scientific_journal-757	49	18	first	first	ADJ
american_scientific_journal-757	49	19	vertex	vertex	NOUN
american_scientific_journal-757	49	20	.	.	PUNCT
american_scientific_journal-757	50	1	next	next	ADV
american_scientific_journal-757	50	2	,	,	PUNCT
american_scientific_journal-757	50	3	draw	draw	VERB
american_scientific_journal-757	50	4	a	a	DET
american_scientific_journal-757	50	5	line	line	NOUN
american_scientific_journal-757	50	6	from	from	ADP
american_scientific_journal-757	50	7	the	the	DET
american_scientific_journal-757	50	8	1st	1st	ADJ
american_scientific_journal-757	50	9	coordinate	coordinate	NOUN
american_scientific_journal-757	50	10	of	of	ADP
american_scientific_journal-757	50	11	the	the	DET
american_scientific_journal-757	50	12	third	third	ADJ
american_scientific_journal-757	50	13	vertex	vertex	NOUN
american_scientific_journal-757	50	14	to	to	ADP
american_scientific_journal-757	50	15	the	the	DET
american_scientific_journal-757	50	16	2nd	2nd	ADJ
american_scientific_journal-757	50	17	coordinate	coordinate	NOUN
american_scientific_journal-757	50	18	of	of	ADP
american_scientific_journal-757	50	19	the	the	DET
american_scientific_journal-757	50	20	second	second	ADJ
american_scientific_journal-757	50	21	vertex	vertex	NOUN
american_scientific_journal-757	50	22	.	.	PUNCT
american_scientific_journal-757	51	1	multiply	multiply	VERB
american_scientific_journal-757	51	2	the	the	DET
american_scientific_journal-757	51	3	corresponding	corresponding	ADJ
american_scientific_journal-757	51	4	numbers	number	NOUN
american_scientific_journal-757	51	5	joined	join	VERB
american_scientific_journal-757	51	6	by	by	ADP
american_scientific_journal-757	51	7	the	the	DET
american_scientific_journal-757	51	8	end	end	NOUN
american_scientific_journal-757	51	9	points	point	NOUN
american_scientific_journal-757	51	10	of	of	ADP
american_scientific_journal-757	51	11	the	the	DET
american_scientific_journal-757	51	12	lines	line	NOUN
american_scientific_journal-757	51	13	.	.	PUNCT
american_scientific_journal-757	52	1	put	put	VERB
american_scientific_journal-757	52	2	their	their	PRON
american_scientific_journal-757	52	3	results	result	NOUN
american_scientific_journal-757	52	4	under	under	ADP
american_scientific_journal-757	52	5	the	the	DET
american_scientific_journal-757	52	6	fourth	fourth	ADJ
american_scientific_journal-757	52	7	column	column	NOUN
american_scientific_journal-757	52	8	in	in	ADP
american_scientific_journal-757	52	9	the	the	DET
american_scientific_journal-757	52	10	3rd	3rd	ADJ
american_scientific_journal-757	52	11	,	,	PUNCT
american_scientific_journal-757	52	12	1st	1st	ADJ
american_scientific_journal-757	52	13	and	and	CCONJ
american_scientific_journal-757	52	14	2nd	2nd	ADJ
american_scientific_journal-757	52	15	rows	row	NOUN
american_scientific_journal-757	52	16	respectively	respectively	ADV
american_scientific_journal-757	52	17	.	.	PUNCT
american_scientific_journal-757	53	1	find	find	VERB
american_scientific_journal-757	53	2	the	the	DET
american_scientific_journal-757	53	3	sum	sum	NOUN
american_scientific_journal-757	53	4	of	of	ADP
american_scientific_journal-757	53	5	the	the	DET
american_scientific_journal-757	53	6	products	product	NOUN
american_scientific_journal-757	53	7	obtained	obtain	VERB
american_scientific_journal-757	53	8	in	in	ADP
american_scientific_journal-757	53	9	this	this	DET
american_scientific_journal-757	53	10	step	step	NOUN
american_scientific_journal-757	53	11	and	and	CCONJ
american_scientific_journal-757	53	12	multiply	multiply	VERB
american_scientific_journal-757	53	13	the	the	DET
american_scientific_journal-757	53	14	result	result	NOUN
american_scientific_journal-757	53	15	by	by	ADP
american_scientific_journal-757	53	16	-2	-2	INTJ
american_scientific_journal-757	53	17	.	.	PUNCT
american_scientific_journal-757	54	1	step	step	NOUN
american_scientific_journal-757	54	2	8	8	NUM
american_scientific_journal-757	54	3	finally	finally	ADV
american_scientific_journal-757	54	4	,	,	PUNCT
american_scientific_journal-757	54	5	the	the	DET
american_scientific_journal-757	54	6	area	area	NOUN
american_scientific_journal-757	54	7	of	of	ADP
american_scientific_journal-757	54	8	the	the	DET
american_scientific_journal-757	54	9	triangle	triangle	NOUN
american_scientific_journal-757	54	10	is	be	AUX
american_scientific_journal-757	54	11	half	half	DET
american_scientific_journal-757	54	12	the	the	DET
american_scientific_journal-757	54	13	algebraic	algebraic	ADJ
american_scientific_journal-757	54	14	sum	sum	NOUN
american_scientific_journal-757	54	15	of	of	ADP
american_scientific_journal-757	54	16	the	the	DET
american_scientific_journal-757	54	17	numbers	number	NOUN
american_scientific_journal-757	54	18	obtained	obtain	VERB
american_scientific_journal-757	54	19	in	in	ADP
american_scientific_journal-757	54	20	steps	step	NOUN
american_scientific_journal-757	54	21	4	4	NUM
american_scientific_journal-757	54	22	,	,	PUNCT
american_scientific_journal-757	54	23	step	step	NOUN
american_scientific_journal-757	54	24	6	6	NUM
american_scientific_journal-757	54	25	and	and	CCONJ
american_scientific_journal-757	54	26	step	step	NOUN
american_scientific_journal-757	54	27	7	7	NUM
american_scientific_journal-757	54	28	.	.	PUNCT
american_scientific_journal-757	55	1	remark1	remark1	NOUN
american_scientific_journal-757	55	2	:	:	PUNCT
american_scientific_journal-757	55	3	if	if	SCONJ
american_scientific_journal-757	55	4	the	the	DET
american_scientific_journal-757	55	5	calculated	calculate	VERB
american_scientific_journal-757	55	6	value	value	NOUN
american_scientific_journal-757	55	7	is	be	AUX
american_scientific_journal-757	55	8	positive	positive	ADJ
american_scientific_journal-757	55	9	,	,	PUNCT
american_scientific_journal-757	55	10	this	this	PRON
american_scientific_journal-757	55	11	indicates	indicate	VERB
american_scientific_journal-757	55	12	that	that	SCONJ
american_scientific_journal-757	55	13	the	the	DET
american_scientific_journal-757	55	14	orientation	orientation	NOUN
american_scientific_journal-757	55	15	of	of	ADP
american_scientific_journal-757	55	16	the	the	DET
american_scientific_journal-757	55	17	vertices	vertex	NOUN
american_scientific_journal-757	55	18	is	be	AUX
american_scientific_journal-757	55	19	anti	anti	ADJ
american_scientific_journal-757	55	20	-	-	ADJ
american_scientific_journal-757	55	21	clockwise	clockwise	NOUN
american_scientific_journal-757	55	22	.	.	PUNCT
american_scientific_journal-757	56	1	if	if	SCONJ
american_scientific_journal-757	56	2	the	the	DET
american_scientific_journal-757	56	3	result	result	NOUN
american_scientific_journal-757	56	4	of	of	ADP
american_scientific_journal-757	56	5	the	the	DET
american_scientific_journal-757	56	6	calculation	calculation	NOUN
american_scientific_journal-757	56	7	is	be	AUX
american_scientific_journal-757	56	8	negative	negative	ADJ
american_scientific_journal-757	56	9	,	,	PUNCT
american_scientific_journal-757	56	10	this	this	PRON
american_scientific_journal-757	56	11	indicates	indicate	VERB
american_scientific_journal-757	56	12	that	that	SCONJ
american_scientific_journal-757	56	13	the	the	DET
american_scientific_journal-757	56	14	orientations	orientation	NOUN
american_scientific_journal-757	56	15	of	of	ADP
american_scientific_journal-757	56	16	the	the	DET
american_scientific_journal-757	56	17	vertices	vertex	NOUN
american_scientific_journal-757	56	18	are	be	AUX
american_scientific_journal-757	56	19	in	in	ADP
american_scientific_journal-757	56	20	clockwise	clockwise	NOUN
american_scientific_journal-757	56	21	.	.	PUNCT
american_scientific_journal-757	57	1	in	in	ADP
american_scientific_journal-757	57	2	the	the	DET
american_scientific_journal-757	57	3	latter	latter	ADJ
american_scientific_journal-757	57	4	case	case	NOUN
american_scientific_journal-757	57	5	we	we	PRON
american_scientific_journal-757	57	6	drop	drop	VERB
american_scientific_journal-757	57	7	the	the	DET
american_scientific_journal-757	57	8	negative	negative	ADJ
american_scientific_journal-757	57	9	sign	sign	NOUN
american_scientific_journal-757	57	10	and	and	CCONJ
american_scientific_journal-757	57	11	take	take	VERB
american_scientific_journal-757	57	12	the	the	DET
american_scientific_journal-757	57	13	positive	positive	ADJ
american_scientific_journal-757	57	14	numerical	numerical	ADJ
american_scientific_journal-757	57	15	value	value	NOUN
american_scientific_journal-757	57	16	alone	alone	ADV
american_scientific_journal-757	57	17	for	for	ADP
american_scientific_journal-757	57	18	the	the	DET
american_scientific_journal-757	57	19	area	area	NOUN
american_scientific_journal-757	57	20	.	.	PUNCT
american_scientific_journal-757	58	1	remark2	remark2	NOUN
american_scientific_journal-757	58	2	:	:	PUNCT
american_scientific_journal-757	58	3	the	the	DET
american_scientific_journal-757	58	4	method	method	NOUN
american_scientific_journal-757	58	5	is	be	AUX
american_scientific_journal-757	58	6	independent	independent	ADJ
american_scientific_journal-757	58	7	of	of	ADP
american_scientific_journal-757	58	8	the	the	DET
american_scientific_journal-757	58	9	order	order	NOUN
american_scientific_journal-757	58	10	of	of	ADP
american_scientific_journal-757	58	11	arrangements	arrangement	NOUN
american_scientific_journal-757	58	12	of	of	ADP
american_scientific_journal-757	58	13	the	the	DET
american_scientific_journal-757	58	14	vertices	vertex	NOUN
american_scientific_journal-757	58	15	of	of	ADP
american_scientific_journal-757	58	16	a	a	DET
american_scientific_journal-757	58	17	triangle	triangle	NOUN
american_scientific_journal-757	58	18	.	.	PUNCT
american_scientific_journal-757	59	1	the	the	DET
american_scientific_journal-757	59	2	formula	formula	NOUN
american_scientific_journal-757	59	3	for	for	ADP
american_scientific_journal-757	59	4	finding	find	VERB
american_scientific_journal-757	59	5	the	the	DET
american_scientific_journal-757	59	6	area	area	NOUN
american_scientific_journal-757	59	7	of	of	ADP
american_scientific_journal-757	59	8	a	a	DET
american_scientific_journal-757	59	9	triangle	triangle	NOUN
american_scientific_journal-757	59	10	from	from	ADP
american_scientific_journal-757	59	11	its	its	PRON
american_scientific_journal-757	59	12	vertices	vertex	NOUN
american_scientific_journal-757	59	13	alone	alone	ADV
american_scientific_journal-757	59	14	is	be	AUX
american_scientific_journal-757	59	15	given	give	VERB
american_scientific_journal-757	59	16	below	below	ADV
american_scientific_journal-757	59	17	.	.	PUNCT
american_scientific_journal-757	60	1	let	let	VERB
american_scientific_journal-757	60	2	(	(	PUNCT
american_scientific_journal-757	60	3	)	)	PUNCT
american_scientific_journal-757	60	4	(	(	PUNCT
american_scientific_journal-757	60	5	)	)	PUNCT
american_scientific_journal-757	60	6	2211	2211	NUM
american_scientific_journal-757	60	7	,	,	PUNCT
american_scientific_journal-757	60	8	,	,	PUNCT
american_scientific_journal-757	60	9	,	,	PUNCT
american_scientific_journal-757	60	10	yxqyxp	yxqyxp	PROPN
american_scientific_journal-757	60	11	and	and	CCONJ
american_scientific_journal-757	60	12	(	(	PUNCT
american_scientific_journal-757	60	13	)	)	PUNCT
american_scientific_journal-757	60	14	,	,	PUNCT
american_scientific_journal-757	60	15	,	,	PUNCT
american_scientific_journal-757	60	16	33	33	NUM
american_scientific_journal-757	60	17	yxr	yxr	NOUN
american_scientific_journal-757	60	18	be	be	VERB
american_scientific_journal-757	60	19	the	the	DET
american_scientific_journal-757	60	20	cartesian	cartesian	ADJ
american_scientific_journal-757	60	21	coordinates	coordinate	NOUN
american_scientific_journal-757	60	22	of	of	ADP
american_scientific_journal-757	60	23	triangle	triangle	PROPN
american_scientific_journal-757	60	24	pqr	pqr	PROPN
american_scientific_journal-757	60	25	.	.	PUNCT
american_scientific_journal-757	61	1	then	then	ADV
american_scientific_journal-757	61	2	the	the	DET
american_scientific_journal-757	61	3	above	above	ADJ
american_scientific_journal-757	61	4	steps	step	NOUN
american_scientific_journal-757	61	5	can	can	AUX
american_scientific_journal-757	61	6	be	be	AUX
american_scientific_journal-757	61	7	generalized	generalize	VERB
american_scientific_journal-757	61	8	and	and	CCONJ
american_scientific_journal-757	61	9	put	put	VERB
american_scientific_journal-757	61	10	in	in	ADP
american_scientific_journal-757	61	11	a	a	DET
american_scientific_journal-757	61	12	compact	compact	ADJ
american_scientific_journal-757	61	13	form	form	NOUN
american_scientific_journal-757	61	14	as	as	SCONJ
american_scientific_journal-757	61	15	shown	show	VERB
american_scientific_journal-757	61	16	below	below	ADV
american_scientific_journal-757	61	17	.	.	PUNCT
american_scientific_journal-757	62	1	(	(	PUNCT
american_scientific_journal-757	62	2	)	)	PUNCT
american_scientific_journal-757	62	3	7	7	NUM
american_scientific_journal-757	62	4	in	in	ADP
american_scientific_journal-757	62	5	addition	addition	NOUN
american_scientific_journal-757	62	6	,	,	PUNCT
american_scientific_journal-757	62	7	the	the	DET
american_scientific_journal-757	62	8	formula	formula	NOUN
american_scientific_journal-757	62	9	showing	show	VERB
american_scientific_journal-757	62	10	the	the	DET
american_scientific_journal-757	62	11	relationship	relationship	NOUN
american_scientific_journal-757	62	12	between	between	ADP
american_scientific_journal-757	62	13	i	i	PROPN
american_scientific_journal-757	62	14	and	and	CCONJ
american_scientific_journal-757	62	15	j	j	PROPN
american_scientific_journal-757	62	16	is	be	AUX
american_scientific_journal-757	62	17			NOUN
american_scientific_journal-757	62	18			PUNCT
american_scientific_journal-757	63	1			PROPN
american_scientific_journal-757	63	2			NOUN
american_scientific_journal-757	63	3			PROPN
american_scientific_journal-757	63	4	−=	−=	ADJ
american_scientific_journal-757	63	5	3	3	NUM
american_scientific_journal-757	63	6	2cos2	2cos2	NUM
american_scientific_journal-757	63	7	πjji	πjji	NOUN
american_scientific_journal-757	63	8	for	for	ADP
american_scientific_journal-757	63	9	31	31	NUM
american_scientific_journal-757	63	10	≤≤	≤≤	NUM
american_scientific_journal-757	63	11	j	j	PROPN
american_scientific_journal-757	63	12	(	(	PUNCT
american_scientific_journal-757	63	13	)	)	PUNCT
american_scientific_journal-757	63	14	8	8	NUM
american_scientific_journal-757	63	15	or	or	CCONJ
american_scientific_journal-757	63	16	using	use	VERB
american_scientific_journal-757	63	17	the	the	DET
american_scientific_journal-757	63	18	concept	concept	NOUN
american_scientific_journal-757	63	19	of	of	ADP
american_scientific_journal-757	63	20	permutation	permutation	NOUN
american_scientific_journal-757	63	21	(	(	PUNCT
american_scientific_journal-757	63	22	)	)	PUNCT
american_scientific_journal-757	63	23	123	123	NUM
american_scientific_journal-757	63	24	132	132	NUM
american_scientific_journal-757	63	25	321	321	NUM
american_scientific_journal-757	63	26	=	=	NOUN
american_scientific_journal-757	63	27			NOUN
american_scientific_journal-757	63	28			PUNCT
american_scientific_journal-757	64	1			PROPN
american_scientific_journal-757	65	1			INTJ
american_scientific_journal-757	65	2			NOUN
american_scientific_journal-757	65	3			VERB
american_scientific_journal-757	65	4	52	52	NUM
american_scientific_journal-757	65	5	american	american	ADJ
american_scientific_journal-757	65	6	scientific	scientific	ADJ
american_scientific_journal-757	65	7	research	research	NOUN
american_scientific_journal-757	65	8	journal	journal	NOUN
american_scientific_journal-757	65	9	for	for	ADP
american_scientific_journal-757	65	10	engineering	engineering	NOUN
american_scientific_journal-757	65	11	,	,	PUNCT
american_scientific_journal-757	65	12	technology	technology	NOUN
american_scientific_journal-757	65	13	,	,	PUNCT
american_scientific_journal-757	65	14	and	and	CCONJ
american_scientific_journal-757	65	15	sciences	science	NOUN
american_scientific_journal-757	65	16	(	(	PUNCT
american_scientific_journal-757	65	17	asrjets	asrjet	NOUN
american_scientific_journal-757	65	18	)	)	PUNCT
american_scientific_journal-757	65	19	(	(	PUNCT
american_scientific_journal-757	65	20	2015	2015	NUM
american_scientific_journal-757	65	21	)	)	PUNCT
american_scientific_journal-757	65	22	volume	volume	NOUN
american_scientific_journal-757	65	23	13	13	NUM
american_scientific_journal-757	65	24	,	,	PUNCT
american_scientific_journal-757	65	25	no	no	DET
american_scientific_journal-757	65	26	1	1	NUM
american_scientific_journal-757	65	27	,	,	PUNCT
american_scientific_journal-757	65	28	pp	pp	ADV
american_scientific_journal-757	65	29	49	49	NUM
american_scientific_journal-757	65	30	-	-	SYM
american_scientific_journal-757	65	31	60	60	NUM
american_scientific_journal-757	65	32	thus	thus	ADV
american_scientific_journal-757	65	33	122331	122331	NUM
american_scientific_journal-757	65	34	3	3	NUM
american_scientific_journal-757	65	35	2cos2	2cos2	NUM
american_scientific_journal-757	65	36	31	31	NUM
american_scientific_journal-757	65	37	3	3	NUM
american_scientific_journal-757	65	38	2cos2	2cos2	NUM
american_scientific_journal-757	65	39	31	31	NUM
american_scientific_journal-757	65	40	yxyxyxxyyx	yxyxyxxyyx	NOUN
american_scientific_journal-757	65	41	jji	jji	NOUN
american_scientific_journal-757	65	42	j	j	PROPN
american_scientific_journal-757	66	1	ij	ij	INTJ
american_scientific_journal-757	67	1	jji	jji	PROPN
american_scientific_journal-757	67	2	j	j	PROPN
american_scientific_journal-757	67	3	ji	ji	PROPN
american_scientific_journal-757	68	1	+	+	PROPN
american_scientific_journal-757	68	2	+	+	PROPN
american_scientific_journal-757	68	3	=	=	NOUN
american_scientific_journal-757	68	4	=	=	SYM
american_scientific_journal-757	68	5	∑∑	∑∑	NOUN
american_scientific_journal-757	68	6			VERB
american_scientific_journal-757	68	7			PUNCT
american_scientific_journal-757	69	1			PROPN
american_scientific_journal-757	69	2			NOUN
american_scientific_journal-757	69	3			PROPN
american_scientific_journal-757	69	4	−=	−=	ADJ
american_scientific_journal-757	69	5	≤≤	≤≤	PROPN
american_scientific_journal-757	69	6			NOUN
american_scientific_journal-757	69	7			PUNCT
american_scientific_journal-757	70	1			PROPN
american_scientific_journal-757	70	2			NOUN
american_scientific_journal-757	70	3			PROPN
american_scientific_journal-757	70	4	−=	−=	ADJ
american_scientific_journal-757	70	5	≤≤	≤≤	NOUN
american_scientific_journal-757	70	6	ππ	ππ	ADP
american_scientific_journal-757	70	7	3.2	3.2	NUM
american_scientific_journal-757	70	8	.	.	PUNCT
american_scientific_journal-757	71	1	problems	problem	NOUN
american_scientific_journal-757	71	2	and	and	CCONJ
american_scientific_journal-757	71	3	solutions	solution	NOUN
american_scientific_journal-757	71	4	sample	sample	NOUN
american_scientific_journal-757	71	5	problems	problem	NOUN
american_scientific_journal-757	71	6	and	and	CCONJ
american_scientific_journal-757	71	7	solution	solution	NOUN
american_scientific_journal-757	71	8	to	to	PART
american_scientific_journal-757	71	9	illustrate	illustrate	VERB
american_scientific_journal-757	71	10	the	the	DET
american_scientific_journal-757	71	11	use	use	NOUN
american_scientific_journal-757	71	12	of	of	ADP
american_scientific_journal-757	71	13	procedure	procedure	NOUN
american_scientific_journal-757	71	14	and	and	CCONJ
american_scientific_journal-757	71	15	the	the	DET
american_scientific_journal-757	71	16	derived	derived	ADJ
american_scientific_journal-757	71	17	formula	formula	NOUN
american_scientific_journal-757	71	18	are	be	AUX
american_scientific_journal-757	71	19	presented	present	VERB
american_scientific_journal-757	71	20	here	here	ADV
american_scientific_journal-757	71	21	.	.	PUNCT
american_scientific_journal-757	72	1	example	example	NOUN
american_scientific_journal-757	72	2	1	1	NUM
american_scientific_journal-757	72	3	:	:	PUNCT
american_scientific_journal-757	72	4	(	(	PUNCT
american_scientific_journal-757	72	5	right	right	ADV
american_scientific_journal-757	72	6	angled	angled	ADJ
american_scientific_journal-757	72	7	triangle	triangle	NOUN
american_scientific_journal-757	72	8	)	)	PUNCT
american_scientific_journal-757	72	9	consider	consider	VERB
american_scientific_journal-757	72	10	a	a	DET
american_scientific_journal-757	72	11	triangle	triangle	NOUN
american_scientific_journal-757	72	12	having	have	VERB
american_scientific_journal-757	72	13	vertices	vertex	NOUN
american_scientific_journal-757	72	14	(	(	PUNCT
american_scientific_journal-757	72	15	)	)	PUNCT
american_scientific_journal-757	72	16	(	(	PUNCT
american_scientific_journal-757	72	17	)	)	PUNCT
american_scientific_journal-757	72	18	0,3,0,0	0,3,0,0	NUM
american_scientific_journal-757	72	19	qp	qp	ADP
american_scientific_journal-757	72	20	and	and	CCONJ
american_scientific_journal-757	72	21	(	(	PUNCT
american_scientific_journal-757	72	22	)	)	PUNCT
american_scientific_journal-757	72	23	4,3r	4,3r	NUM
american_scientific_journal-757	72	24	.find	.find	ADP
american_scientific_journal-757	72	25	the	the	DET
american_scientific_journal-757	72	26	area	area	NOUN
american_scientific_journal-757	72	27	a	a	PRON
american_scientific_journal-757	72	28	of	of	ADP
american_scientific_journal-757	72	29	triangle	triangle	NOUN
american_scientific_journal-757	72	30	pqr	pqr	PROPN
american_scientific_journal-757	72	31	solution	solution	NOUN
american_scientific_journal-757	72	32	:	:	PUNCT
american_scientific_journal-757	72	33	rewrite	rewrite	VERB
american_scientific_journal-757	72	34	the	the	DET
american_scientific_journal-757	72	35	vertices	vertex	NOUN
american_scientific_journal-757	72	36	as	as	ADP
american_scientific_journal-757	72	37	(	(	PUNCT
american_scientific_journal-757	72	38	)	)	PUNCT
american_scientific_journal-757	72	39	(	(	PUNCT
american_scientific_journal-757	72	40	)	)	PUNCT
american_scientific_journal-757	72	41	(	(	PUNCT
american_scientific_journal-757	72	42	)	)	PUNCT
american_scientific_journal-757	72	43	(	(	PUNCT
american_scientific_journal-757	72	44	)	)	PUNCT
american_scientific_journal-757	72	45	(	(	PUNCT
american_scientific_journal-757	72	46	)	)	PUNCT
american_scientific_journal-757	72	47	(	(	PUNCT
american_scientific_journal-757	72	48	)	)	PUNCT
american_scientific_journal-757	72	49	(	(	PUNCT
american_scientific_journal-757	72	50	)	)	PUNCT
american_scientific_journal-757	72	51	(	(	PUNCT
american_scientific_journal-757	72	52	)	)	PUNCT
american_scientific_journal-757	72	53	(	(	PUNCT
american_scientific_journal-757	72	54	)	)	PUNCT
american_scientific_journal-757	72	55	(	(	PUNCT
american_scientific_journal-757	72	56	)	)	PUNCT
american_scientific_journal-757	72	57	003034022	003034022	NUM
american_scientific_journal-757	72	58	12430300	12430300	NUM
american_scientific_journal-757	72	59	400330	400330	NUM
american_scientific_journal-757	72	60	=	=	NOUN
american_scientific_journal-757	72	61	×+×+×−=−	×+×+×−=−	NOUN
american_scientific_journal-757	72	62	−=×+×+×−=−	−=×+×+×−=−	VERB
american_scientific_journal-757	72	63	+	+	PROPN
american_scientific_journal-757	73	1	+	+	ADJ
american_scientific_journal-757	73	2	+	+	ADJ
american_scientific_journal-757	73	3	+	+	NOUN
american_scientific_journal-757	73	4	=	=	SYM
american_scientific_journal-757	73	5	∑	∑	PUNCT
american_scientific_journal-757	73	6	∑	∑	PUNCT
american_scientific_journal-757	73	7	∑∑	∑∑	PROPN
american_scientific_journal-757	73	8	ji	ji	PROPN
american_scientific_journal-757	73	9	ii	ii	PROPN
american_scientific_journal-757	73	10	ii	ii	PROPN
american_scientific_journal-757	73	11	yx	yx	PROPN
american_scientific_journal-757	73	12	yx	yx	PROPN
american_scientific_journal-757	73	13	yx	yx	PROPN
american_scientific_journal-757	73	14	therefore	therefore	ADV
american_scientific_journal-757	73	15	,	,	PUNCT
american_scientific_journal-757	73	16	[	[	PUNCT
american_scientific_journal-757	73	17	]	]	X
american_scientific_journal-757	73	18	[	[	PUNCT
american_scientific_journal-757	73	19	]	]	X
american_scientific_journal-757	73	20	601224	601224	NUM
american_scientific_journal-757	73	21	2	2	NUM
american_scientific_journal-757	73	22	1	1	NUM
american_scientific_journal-757	73	23	2	2	NUM
american_scientific_journal-757	73	24	2	2	NUM
american_scientific_journal-757	73	25	1	1	NUM
american_scientific_journal-757	73	26	=	=	NUM
american_scientific_journal-757	73	27	−−=	−−=	NOUN
american_scientific_journal-757	73	28	−−=	−−=	NOUN
american_scientific_journal-757	73	29	∑∑∑∑	∑∑∑∑	NOUN
american_scientific_journal-757	73	30	a	a	DET
american_scientific_journal-757	73	31	yxyxyxa	yxyxyxa	PROPN
american_scientific_journal-757	73	32	jiiiii	jiiiii	NOUN
american_scientific_journal-757	73	33	the	the	DET
american_scientific_journal-757	73	34	above	above	ADJ
american_scientific_journal-757	73	35	triangle	triangle	NOUN
american_scientific_journal-757	73	36	is	be	AUX
american_scientific_journal-757	73	37	a	a	DET
american_scientific_journal-757	73	38	right	right	ADV
american_scientific_journal-757	73	39	angled	angled	ADJ
american_scientific_journal-757	73	40	triangle	triangle	NOUN
american_scientific_journal-757	73	41	having	have	VERB
american_scientific_journal-757	73	42	legs	leg	NOUN
american_scientific_journal-757	73	43	of	of	ADP
american_scientific_journal-757	73	44	length	length	NOUN
american_scientific_journal-757	73	45	3	3	NUM
american_scientific_journal-757	73	46	and	and	CCONJ
american_scientific_journal-757	73	47	4	4	NUM
american_scientific_journal-757	73	48	.	.	X
american_scientific_journal-757	74	1	hence	hence	ADV
american_scientific_journal-757	74	2	the	the	DET
american_scientific_journal-757	74	3	area	area	NOUN
american_scientific_journal-757	74	4	is	be	AUX
american_scientific_journal-757	74	5	half	half	DET
american_scientific_journal-757	74	6	the	the	DET
american_scientific_journal-757	74	7	product	product	NOUN
american_scientific_journal-757	74	8	of	of	ADP
american_scientific_journal-757	74	9	the	the	DET
american_scientific_journal-757	74	10	length	length	NOUN
american_scientific_journal-757	74	11	of	of	ADP
american_scientific_journal-757	74	12	the	the	DET
american_scientific_journal-757	74	13	legs	leg	NOUN
american_scientific_journal-757	74	14	which	which	PRON
american_scientific_journal-757	74	15	is	be	AUX
american_scientific_journal-757	74	16	6	6	NUM
american_scientific_journal-757	74	17	units	unit	NOUN
american_scientific_journal-757	74	18	square	square	ADJ
american_scientific_journal-757	74	19	.	.	PUNCT
american_scientific_journal-757	75	1	example	example	NOUN
american_scientific_journal-757	76	1	2	2	NUM
american_scientific_journal-757	76	2	:	:	PUNCT
american_scientific_journal-757	76	3	(	(	PUNCT
american_scientific_journal-757	76	4	30	30	NUM
american_scientific_journal-757	76	5	-	-	SYM
american_scientific_journal-757	76	6	60	60	NUM
american_scientific_journal-757	76	7	degree	degree	NOUN
american_scientific_journal-757	76	8	)	)	PUNCT
american_scientific_journal-757	76	9	consider	consider	VERB
american_scientific_journal-757	76	10	a	a	DET
american_scientific_journal-757	76	11	triangle	triangle	NOUN
american_scientific_journal-757	76	12	having	have	VERB
american_scientific_journal-757	76	13	vertices	vertex	NOUN
american_scientific_journal-757	76	14	(	(	PUNCT
american_scientific_journal-757	76	15	)	)	PUNCT
american_scientific_journal-757	76	16	(	(	PUNCT
american_scientific_journal-757	76	17	)	)	PUNCT
american_scientific_journal-757	76	18	0,34,0,0	0,34,0,0	NOUN
american_scientific_journal-757	76	19	ba	ba	NOUN
american_scientific_journal-757	76	20	and	and	CCONJ
american_scientific_journal-757	76	21	(	(	PUNCT
american_scientific_journal-757	76	22	)	)	PUNCT
american_scientific_journal-757	77	1	4,34c	4,34c	ADV
american_scientific_journal-757	77	2	.then	.then	PUNCT
american_scientific_journal-757	77	3	the	the	DET
american_scientific_journal-757	77	4	area	area	NOUN
american_scientific_journal-757	77	5	a	a	PRON
american_scientific_journal-757	77	6	is	be	AUX
american_scientific_journal-757	77	7	53	53	NUM
american_scientific_journal-757	77	8	american	american	ADJ
american_scientific_journal-757	77	9	scientific	scientific	ADJ
american_scientific_journal-757	77	10	research	research	NOUN
american_scientific_journal-757	77	11	journal	journal	NOUN
american_scientific_journal-757	77	12	for	for	ADP
american_scientific_journal-757	77	13	engineering	engineering	NOUN
american_scientific_journal-757	77	14	,	,	PUNCT
american_scientific_journal-757	77	15	technology	technology	NOUN
american_scientific_journal-757	77	16	,	,	PUNCT
american_scientific_journal-757	77	17	and	and	CCONJ
american_scientific_journal-757	77	18	sciences	science	NOUN
american_scientific_journal-757	77	19	(	(	PUNCT
american_scientific_journal-757	77	20	asrjets	asrjet	NOUN
american_scientific_journal-757	77	21	)	)	PUNCT
american_scientific_journal-757	77	22	(	(	PUNCT
american_scientific_journal-757	77	23	2015	2015	NUM
american_scientific_journal-757	77	24	)	)	PUNCT
american_scientific_journal-757	77	25	volume	volume	NOUN
american_scientific_journal-757	77	26	13	13	NUM
american_scientific_journal-757	77	27	,	,	PUNCT
american_scientific_journal-757	77	28	no	no	DET
american_scientific_journal-757	77	29	1	1	NUM
american_scientific_journal-757	77	30	,	,	PUNCT
american_scientific_journal-757	77	31	pp	pp	ADV
american_scientific_journal-757	77	32	49	49	NUM
american_scientific_journal-757	77	33	-	-	SYM
american_scientific_journal-757	77	34	60	60	NUM
american_scientific_journal-757	77	35	solution	solution	NOUN
american_scientific_journal-757	77	36	rewrite	rewrite	VERB
american_scientific_journal-757	77	37	the	the	DET
american_scientific_journal-757	77	38	vertices	vertex	NOUN
american_scientific_journal-757	77	39	as	as	ADP
american_scientific_journal-757	77	40	(	(	PUNCT
american_scientific_journal-757	77	41	)	)	PUNCT
american_scientific_journal-757	77	42	(	(	PUNCT
american_scientific_journal-757	77	43	)	)	PUNCT
american_scientific_journal-757	77	44	(	(	PUNCT
american_scientific_journal-757	77	45	)	)	PUNCT
american_scientific_journal-757	77	46	(	(	PUNCT
american_scientific_journal-757	77	47	)	)	PUNCT
american_scientific_journal-757	77	48	(	(	PUNCT
american_scientific_journal-757	77	49	)	)	PUNCT
american_scientific_journal-757	77	50	[	[	PUNCT
american_scientific_journal-757	77	51	]	]	X
american_scientific_journal-757	77	52	(	(	PUNCT
american_scientific_journal-757	77	53	)	)	PUNCT
american_scientific_journal-757	77	54	(	(	PUNCT
american_scientific_journal-757	77	55	)	)	PUNCT
american_scientific_journal-757	77	56	(	(	PUNCT
american_scientific_journal-757	77	57	)	)	PUNCT
american_scientific_journal-757	77	58	38316	38316	NUM
american_scientific_journal-757	77	59	2	2	NUM
american_scientific_journal-757	77	60	112316	112316	NUM
american_scientific_journal-757	77	61	2	2	NUM
american_scientific_journal-757	77	62	1	1	NUM
american_scientific_journal-757	77	63	02316438	02316438	NUM
american_scientific_journal-757	77	64	2	2	NUM
american_scientific_journal-757	77	65	1	1	NUM
american_scientific_journal-757	77	66	03164,34	03164,34	NOUN
american_scientific_journal-757	77	67	000,34	000,34	NOUN
american_scientific_journal-757	77	68	00,0,0	00,0,0	NOUN
american_scientific_journal-757	78	1	=	=	SYM
american_scientific_journal-757	78	2	=	=	NOUN
american_scientific_journal-757	78	3	−=	−=	X
american_scientific_journal-757	78	4	×−−=	×−−=	NOUN
american_scientific_journal-757	78	5	=	=	SYM
american_scientific_journal-757	79	1	=	=	SYM
american_scientific_journal-757	79	2	=	=	PUNCT
american_scientific_journal-757	79	3	a	a	DET
american_scientific_journal-757	79	4	a	a	DET
american_scientific_journal-757	79	5	c	c	NOUN
american_scientific_journal-757	79	6	b	b	PROPN
american_scientific_journal-757	79	7	a	a	DET
american_scientific_journal-757	79	8	figure1	figure1	PROPN
american_scientific_journal-757	79	9	:	:	PUNCT
american_scientific_journal-757	79	10			VERB
american_scientific_journal-757	79	11	6030	6030	NUM
american_scientific_journal-757	79	12	−	−	NOUN
american_scientific_journal-757	79	13	degree	degree	NOUN
american_scientific_journal-757	79	14	triangle	triangle	NOUN
american_scientific_journal-757	79	15	the	the	DET
american_scientific_journal-757	79	16	above	above	ADJ
american_scientific_journal-757	79	17	triangle	triangle	NOUN
american_scientific_journal-757	79	18	is	be	AUX
american_scientific_journal-757	79	19	a	a	DET
american_scientific_journal-757	79	20	30	30	NUM
american_scientific_journal-757	79	21	-	-	SYM
american_scientific_journal-757	79	22	60	60	NUM
american_scientific_journal-757	79	23	degree	degree	NOUN
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american_scientific_journal-757	79	25	angled	angled	ADJ
american_scientific_journal-757	79	26	triangle	triangle	NOUN
american_scientific_journal-757	79	27	having	have	VERB
american_scientific_journal-757	79	28	hypotenuse	hypotenuse	NOUN
american_scientific_journal-757	79	29	of	of	ADP
american_scientific_journal-757	79	30	length	length	NOUN
american_scientific_journal-757	79	31	8	8	NUM
american_scientific_journal-757	79	32	units	unit	NOUN
american_scientific_journal-757	79	33	,	,	PUNCT
american_scientific_journal-757	79	34	legs	leg	NOUN
american_scientific_journal-757	79	35	of	of	ADP
american_scientific_journal-757	79	36	length	length	NOUN
american_scientific_journal-757	79	37	34	34	NUM
american_scientific_journal-757	79	38	and	and	CCONJ
american_scientific_journal-757	79	39	4	4	NUM
american_scientific_journal-757	79	40	units	unit	NOUN
american_scientific_journal-757	79	41	.	.	PUNCT
american_scientific_journal-757	80	1	hence	hence	ADV
american_scientific_journal-757	80	2	the	the	DET
american_scientific_journal-757	80	3	area	area	NOUN
american_scientific_journal-757	80	4	is	be	AUX
american_scientific_journal-757	80	5	half	half	DET
american_scientific_journal-757	80	6	the	the	DET
american_scientific_journal-757	80	7	product	product	NOUN
american_scientific_journal-757	80	8	of	of	ADP
american_scientific_journal-757	80	9	the	the	DET
american_scientific_journal-757	80	10	length	length	NOUN
american_scientific_journal-757	80	11	of	of	ADP
american_scientific_journal-757	80	12	the	the	DET
american_scientific_journal-757	80	13	adjacent	adjacent	ADJ
american_scientific_journal-757	80	14	leg	leg	NOUN
american_scientific_journal-757	80	15	34	34	NUM
american_scientific_journal-757	80	16	and	and	CCONJ
american_scientific_journal-757	80	17	the	the	DET
american_scientific_journal-757	80	18	hypotenuse	hypotenuse	NOUN
american_scientific_journal-757	80	19	8	8	NUM
american_scientific_journal-757	80	20	and	and	CCONJ
american_scientific_journal-757	80	21	30sin	30sin	NOUN
american_scientific_journal-757	80	22	which	which	PRON
american_scientific_journal-757	80	23	is	be	AUX
american_scientific_journal-757	80	24	38	38	NUM
american_scientific_journal-757	80	25	units	unit	NOUN
american_scientific_journal-757	80	26	square	square	ADJ
american_scientific_journal-757	80	27	.	.	PUNCT
american_scientific_journal-757	81	1	example	example	NOUN
american_scientific_journal-757	82	1	3	3	NUM
american_scientific_journal-757	82	2	:	:	PUNCT
american_scientific_journal-757	82	3	(	(	PUNCT
american_scientific_journal-757	82	4	isosceles	isoscele	NOUN
american_scientific_journal-757	82	5	triangle	triangle	NOUN
american_scientific_journal-757	82	6	)	)	PUNCT
american_scientific_journal-757	82	7	consider	consider	VERB
american_scientific_journal-757	82	8	a	a	DET
american_scientific_journal-757	82	9	triangle	triangle	NOUN
american_scientific_journal-757	82	10	having	have	VERB
american_scientific_journal-757	82	11	vertices	vertex	NOUN
american_scientific_journal-757	82	12	(	(	PUNCT
american_scientific_journal-757	82	13	)	)	PUNCT
american_scientific_journal-757	82	14	(	(	PUNCT
american_scientific_journal-757	82	15	)	)	PUNCT
american_scientific_journal-757	82	16	2,4,4,1	2,4,4,1	NUM
american_scientific_journal-757	82	17	−−	−−	NOUN
american_scientific_journal-757	82	18	qp	qp	PROPN
american_scientific_journal-757	82	19	and	and	CCONJ
american_scientific_journal-757	82	20	(	(	PUNCT
american_scientific_journal-757	82	21	)	)	PUNCT
american_scientific_journal-757	82	22	2,2q	2,2q	NOUN
american_scientific_journal-757	82	23	.then	.then	VERB
american_scientific_journal-757	83	1	the	the	DET
american_scientific_journal-757	83	2	area	area	NOUN
american_scientific_journal-757	83	3	a	a	PRON
american_scientific_journal-757	83	4	is	be	AUX
american_scientific_journal-757	83	5	solution	solution	NOUN
american_scientific_journal-757	83	6	rewrite	rewrite	VERB
american_scientific_journal-757	83	7	the	the	DET
american_scientific_journal-757	83	8	vertices	vertex	NOUN
american_scientific_journal-757	83	9	as	as	ADP
american_scientific_journal-757	83	10	10	10	NUM
american_scientific_journal-757	83	11	8	8	NUM
american_scientific_journal-757	83	12	6	6	NUM
american_scientific_journal-757	83	13	4	4	NUM
american_scientific_journal-757	83	14	2	2	NUM
american_scientific_journal-757	83	15	2	2	NUM
american_scientific_journal-757	83	16	4	4	NUM
american_scientific_journal-757	83	17	15	15	NUM
american_scientific_journal-757	83	18	10	10	NUM
american_scientific_journal-757	83	19	5	5	NUM
american_scientific_journal-757	83	20	5	5	NUM
american_scientific_journal-757	83	21	10	10	NUM
american_scientific_journal-757	83	22	15	15	NUM
american_scientific_journal-757	83	23	k	k	PROPN
american_scientific_journal-757	83	24	j	j	PROPN
american_scientific_journal-757	83	25	sin	sin	NOUN
american_scientific_journal-757	83	26	30	30	NUM
american_scientific_journal-757	83	27	(	(	PUNCT
american_scientific_journal-757	83	28	)	)	PUNCT
american_scientific_journal-757	83	29	∙ab∙ac∙0.5	∙ab∙ac∙0.5	NOUN
american_scientific_journal-757	83	30	=	=	SYM
american_scientific_journal-757	83	31	13.77	13.77	NUM
american_scientific_journal-757	83	32	slope	slope	NOUN
american_scientific_journal-757	83	33	k	k	NOUN
american_scientific_journal-757	83	34	=	=	PUNCT
american_scientific_journal-757	83	35	0.58	0.58	NUM
american_scientific_journal-757	83	36	slope	slope	NOUN
american_scientific_journal-757	83	37	j	j	PROPN
american_scientific_journal-757	84	1	=	=	PROPN
american_scientific_journal-757	84	2	undefined	undefined	ADJ
american_scientific_journal-757	84	3	slope	slope	NOUN
american_scientific_journal-757	84	4	ab	ab	PROPN
american_scientific_journal-757	85	1	=	=	PUNCT
american_scientific_journal-757	85	2	0.00	0.00	NUM
american_scientific_journal-757	85	3	bc	bc	NOUN
american_scientific_journal-757	85	4	=	=	SYM
american_scientific_journal-757	85	5	4.00	4.00	NUM
american_scientific_journal-757	85	6	ab	ab	NOUN
american_scientific_journal-757	86	1	=	=	PUNCT
american_scientific_journal-757	86	2	6.91	6.91	NUM
american_scientific_journal-757	86	3	ac	ac	NOUN
american_scientific_journal-757	86	4	=	=	PROPN
american_scientific_journal-757	86	5	7.98	7.98	NUM
american_scientific_journal-757	86	6	xc	xc	NOUN
american_scientific_journal-757	87	1	=	=	NOUN
american_scientific_journal-757	87	2	6.91	6.91	NUM
american_scientific_journal-757	87	3	xb	xb	X
american_scientific_journal-757	88	1	=	=	PUNCT
american_scientific_journal-757	89	1	6.91	6.91	NUM
american_scientific_journal-757	89	2	xa	xa	NOUN
american_scientific_journal-757	89	3	=	=	NUM
american_scientific_journal-757	89	4	0.00	0.00	NUM
american_scientific_journal-757	89	5	c	c	NOUN
american_scientific_journal-757	89	6	:	:	PUNCT
american_scientific_journal-757	89	7	(	(	PUNCT
american_scientific_journal-757	89	8	6.91	6.91	NUM
american_scientific_journal-757	89	9	,	,	PUNCT
american_scientific_journal-757	89	10	4.00	4.00	NUM
american_scientific_journal-757	89	11	)	)	PUNCT
american_scientific_journal-757	89	12	b	b	NOUN
american_scientific_journal-757	89	13	:	:	PUNCT
american_scientific_journal-757	89	14	(	(	PUNCT
american_scientific_journal-757	89	15	6.91	6.91	NUM
american_scientific_journal-757	89	16	,	,	PUNCT
american_scientific_journal-757	89	17	0.00	0.00	NUM
american_scientific_journal-757	89	18	)	)	PUNCT
american_scientific_journal-757	89	19	a	a	X
american_scientific_journal-757	89	20	:	:	PUNCT
american_scientific_journal-757	89	21	(	(	PUNCT
american_scientific_journal-757	89	22	0.00	0.00	NUM
american_scientific_journal-757	89	23	,	,	PUNCT
american_scientific_journal-757	89	24	0.00	0.00	NUM
american_scientific_journal-757	89	25	)	)	PUNCT
american_scientific_journal-757	89	26	m∠cab	m∠cab	NOUN
american_scientific_journal-757	89	27	=	=	PUNCT
american_scientific_journal-757	89	28	30.05	30.05	NUM
american_scientific_journal-757	89	29	°	°	PRON
american_scientific_journal-757	90	1	m∠bca	m∠bca	NOUN
american_scientific_journal-757	90	2	=	=	NOUN
american_scientific_journal-757	91	1	59.95	59.95	NUM
american_scientific_journal-757	91	2	°	°	PRON
american_scientific_journal-757	91	3	m∠abc	m∠abc	NOUN
american_scientific_journal-757	91	4	=	=	PUNCT
american_scientific_journal-757	91	5	90.00	90.00	NUM
american_scientific_journal-757	91	6	°	°	X
american_scientific_journal-757	92	1	k	k	X
american_scientific_journal-757	92	2	=	=	PUNCT
american_scientific_journal-757	92	3	7.98	7.98	NUM
american_scientific_journal-757	92	4	cm	cm	NUM
american_scientific_journal-757	92	5	j	j	PROPN
american_scientific_journal-757	93	1	=	=	NOUN
american_scientific_journal-757	93	2	4.00	4.00	NUM
american_scientific_journal-757	93	3	cm	cm	NOUN
american_scientific_journal-757	93	4	m	m	VERB
american_scientific_journal-757	93	5	ab	ab	NOUN
american_scientific_journal-757	93	6	=	=	PUNCT
american_scientific_journal-757	93	7	6.91	6.91	NUM
american_scientific_journal-757	93	8	cm	cm	NOUN
american_scientific_journal-757	93	9	a	a	DET
american_scientific_journal-757	93	10	c	c	PROPN
american_scientific_journal-757	93	11	b	b	SYM
american_scientific_journal-757	93	12	54	54	NUM
american_scientific_journal-757	93	13	american	american	ADJ
american_scientific_journal-757	93	14	scientific	scientific	ADJ
american_scientific_journal-757	93	15	research	research	NOUN
american_scientific_journal-757	93	16	journal	journal	NOUN
american_scientific_journal-757	93	17	for	for	ADP
american_scientific_journal-757	93	18	engineering	engineering	NOUN
american_scientific_journal-757	93	19	,	,	PUNCT
american_scientific_journal-757	93	20	technology	technology	NOUN
american_scientific_journal-757	93	21	,	,	PUNCT
american_scientific_journal-757	93	22	and	and	CCONJ
american_scientific_journal-757	93	23	sciences	science	NOUN
american_scientific_journal-757	93	24	(	(	PUNCT
american_scientific_journal-757	93	25	asrjets	asrjet	NOUN
american_scientific_journal-757	93	26	)	)	PUNCT
american_scientific_journal-757	93	27	(	(	PUNCT
american_scientific_journal-757	93	28	2015	2015	NUM
american_scientific_journal-757	93	29	)	)	PUNCT
american_scientific_journal-757	93	30	volume	volume	NOUN
american_scientific_journal-757	93	31	13	13	NUM
american_scientific_journal-757	93	32	,	,	PUNCT
american_scientific_journal-757	93	33	no	no	DET
american_scientific_journal-757	93	34	1	1	NUM
american_scientific_journal-757	93	35	,	,	PUNCT
american_scientific_journal-757	93	36	pp	pp	ADV
american_scientific_journal-757	93	37	49	49	NUM
american_scientific_journal-757	93	38	-	-	SYM
american_scientific_journal-757	93	39	60	60	NUM
american_scientific_journal-757	93	40	(	(	PUNCT
american_scientific_journal-757	93	41	)	)	PUNCT
american_scientific_journal-757	93	42	(	(	PUNCT
american_scientific_journal-757	93	43	)	)	PUNCT
american_scientific_journal-757	93	44	(	(	PUNCT
american_scientific_journal-757	93	45	)	)	PUNCT
american_scientific_journal-757	93	46	(	(	PUNCT
american_scientific_journal-757	93	47	)	)	PUNCT
american_scientific_journal-757	93	48	(	(	PUNCT
american_scientific_journal-757	93	49	)	)	PUNCT
american_scientific_journal-757	93	50	(	(	PUNCT
american_scientific_journal-757	93	51	)	)	PUNCT
american_scientific_journal-757	93	52	(	(	PUNCT
american_scientific_journal-757	93	53	)	)	PUNCT
american_scientific_journal-757	93	54	[	[	PUNCT
american_scientific_journal-757	93	55	]	]	X
american_scientific_journal-757	93	56	(	(	PUNCT
american_scientific_journal-757	93	57	)	)	PUNCT
american_scientific_journal-757	93	58	(	(	PUNCT
american_scientific_journal-757	93	59	)	)	PUNCT
american_scientific_journal-757	93	60	612	612	NUM
american_scientific_journal-757	93	61	2	2	NUM
american_scientific_journal-757	93	62	1]3624	1]3624	NUM
american_scientific_journal-757	93	63	[	[	PUNCT
american_scientific_journal-757	93	64	2	2	NUM
american_scientific_journal-757	93	65	1	1	NUM
american_scientific_journal-757	93	66	142883	142883	NUM
american_scientific_journal-757	93	67	2	2	NUM
american_scientific_journal-757	93	68	1	1	NUM
american_scientific_journal-757	93	69	242,2	242,2	NUM
american_scientific_journal-757	93	70	482,4	482,4	NOUN
american_scientific_journal-757	93	71	164,4,1	164,4,1	NUM
american_scientific_journal-757	93	72	=	=	SYM
american_scientific_journal-757	93	73	=	=	SYM
american_scientific_journal-757	93	74	+	+	ADJ
american_scientific_journal-757	93	75	−=	−=	ADJ
american_scientific_journal-757	93	76	−×−−−−=	−×−−−−=	PROPN
american_scientific_journal-757	93	77	−=	−=	PART
american_scientific_journal-757	93	78	−=−	−=−	NUM
american_scientific_journal-757	93	79	−−=−	−−=−	ADP
american_scientific_journal-757	93	80	a	a	DET
american_scientific_journal-757	93	81	a	a	DET
american_scientific_journal-757	93	82	r	r	NOUN
american_scientific_journal-757	93	83	q	q	NOUN
american_scientific_journal-757	93	84	p	p	NOUN
american_scientific_journal-757	93	85	the	the	DET
american_scientific_journal-757	93	86	above	above	ADJ
american_scientific_journal-757	93	87	triangle	triangle	NOUN
american_scientific_journal-757	93	88	is	be	AUX
american_scientific_journal-757	93	89	an	an	DET
american_scientific_journal-757	93	90	isosceles	isoscele	NOUN
american_scientific_journal-757	93	91	triangle	triangle	NOUN
american_scientific_journal-757	93	92	having	have	VERB
american_scientific_journal-757	93	93	height	height	NOUN
american_scientific_journal-757	93	94	2	2	NUM
american_scientific_journal-757	93	95	units	unit	NOUN
american_scientific_journal-757	93	96	and	and	CCONJ
american_scientific_journal-757	93	97	base	base	VERB
american_scientific_journal-757	93	98	6	6	NUM
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american_scientific_journal-757	93	100	.	.	PUNCT
american_scientific_journal-757	93	101	example	example	NOUN
american_scientific_journal-757	94	1	4	4	NUM
american_scientific_journal-757	94	2	:	:	PUNCT
american_scientific_journal-757	94	3	(	(	PUNCT
american_scientific_journal-757	94	4	obtuse	obtuse	ADJ
american_scientific_journal-757	94	5	triangle	triangle	NOUN
american_scientific_journal-757	94	6	)	)	PUNCT
american_scientific_journal-757	94	7	consider	consider	VERB
american_scientific_journal-757	94	8	a	a	DET
american_scientific_journal-757	94	9	triangle	triangle	NOUN
american_scientific_journal-757	94	10	having	have	VERB
american_scientific_journal-757	94	11	vertices	vertex	NOUN
american_scientific_journal-757	94	12	(	(	PUNCT
american_scientific_journal-757	94	13	)	)	PUNCT
american_scientific_journal-757	94	14	(	(	PUNCT
american_scientific_journal-757	94	15	)	)	PUNCT
american_scientific_journal-757	94	16	2,11,4,7	2,11,4,7	NOUN
american_scientific_journal-757	94	17	−qp	−qp	NUM
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american_scientific_journal-757	94	19	(	(	PUNCT
american_scientific_journal-757	94	20	)	)	PUNCT
american_scientific_journal-757	94	21	2,15	2,15	NUM
american_scientific_journal-757	94	22	−q	−q	NOUN
american_scientific_journal-757	94	23	.then	.then	VERB
american_scientific_journal-757	95	1	the	the	DET
american_scientific_journal-757	95	2	area	area	NOUN
american_scientific_journal-757	95	3	a	a	PRON
american_scientific_journal-757	95	4	is	be	AUX
american_scientific_journal-757	95	5	solution	solution	NOUN
american_scientific_journal-757	95	6	rewrite	rewrite	VERB
american_scientific_journal-757	95	7	the	the	DET
american_scientific_journal-757	95	8	vertices	vertex	NOUN
american_scientific_journal-757	95	9	as	as	ADP
american_scientific_journal-757	95	10	(	(	PUNCT
american_scientific_journal-757	95	11	)	)	PUNCT
american_scientific_journal-757	95	12	(	(	PUNCT
american_scientific_journal-757	95	13	)	)	PUNCT
american_scientific_journal-757	95	14	(	(	PUNCT
american_scientific_journal-757	95	15	)	)	PUNCT
american_scientific_journal-757	95	16	(	(	PUNCT
american_scientific_journal-757	95	17	)	)	PUNCT
american_scientific_journal-757	95	18	(	(	PUNCT
american_scientific_journal-757	95	19	)	)	PUNCT
american_scientific_journal-757	95	20	(	(	PUNCT
american_scientific_journal-757	95	21	)	)	PUNCT
american_scientific_journal-757	95	22	[	[	PUNCT
american_scientific_journal-757	95	23	]	]	X
american_scientific_journal-757	95	24	(	(	PUNCT
american_scientific_journal-757	95	25	)	)	PUNCT
american_scientific_journal-757	95	26	(	(	PUNCT
american_scientific_journal-757	95	27	)	)	PUNCT
american_scientific_journal-757	95	28	1224	1224	NUM
american_scientific_journal-757	95	29	2	2	NUM
american_scientific_journal-757	95	30	1]0240	1]0240	NUM
american_scientific_journal-757	95	31	[	[	PUNCT
american_scientific_journal-757	95	32	2	2	NUM
american_scientific_journal-757	95	33	1	1	NUM
american_scientific_journal-757	95	34	0224033	0224033	NUM
american_scientific_journal-757	95	35	2	2	NUM
american_scientific_journal-757	95	36	1	1	NUM
american_scientific_journal-757	95	37	14302,15	14302,15	NUM
american_scientific_journal-757	95	38	30222,11	30222,11	NUM
american_scientific_journal-757	95	39	44284,7	44284,7	NOUN
american_scientific_journal-757	95	40	=	=	NOUN
american_scientific_journal-757	95	41	=	=	NOUN
american_scientific_journal-757	95	42	−+=	−+=	X
american_scientific_journal-757	95	43	×−−−=	×−−−=	PRON
american_scientific_journal-757	95	44	−−=−	−−=−	X
american_scientific_journal-757	95	45	−−=−	−−=−	NOUN
american_scientific_journal-757	95	46	=	=	PUNCT
american_scientific_journal-757	95	47	a	a	DET
american_scientific_journal-757	95	48	a	a	DET
american_scientific_journal-757	95	49	r	r	NOUN
american_scientific_journal-757	95	50	q	q	NOUN
american_scientific_journal-757	95	51	p	p	NOUN
american_scientific_journal-757	95	52	the	the	DET
american_scientific_journal-757	95	53	above	above	ADJ
american_scientific_journal-757	95	54	triangle	triangle	NOUN
american_scientific_journal-757	95	55	is	be	AUX
american_scientific_journal-757	95	56	an	an	DET
american_scientific_journal-757	95	57	obtuse	obtuse	ADJ
american_scientific_journal-757	95	58	triangle	triangle	NOUN
american_scientific_journal-757	95	59	with	with	ADP
american_scientific_journal-757	95	60	base	base	NOUN
american_scientific_journal-757	95	61	and	and	CCONJ
american_scientific_journal-757	95	62	height	height	NOUN
american_scientific_journal-757	95	63	4	4	NUM
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american_scientific_journal-757	95	65	6	6	NUM
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american_scientific_journal-757	95	69	.	.	PUNCT
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american_scientific_journal-757	95	71	5	5	NUM
american_scientific_journal-757	95	72	:	:	PUNCT
american_scientific_journal-757	95	73	(	(	PUNCT
american_scientific_journal-757	95	74	acute	acute	NOUN
american_scientific_journal-757	95	75	triangle	triangle	NOUN
american_scientific_journal-757	95	76	)	)	PUNCT
american_scientific_journal-757	95	77	consider	consider	VERB
american_scientific_journal-757	95	78	a	a	DET
american_scientific_journal-757	95	79	triangle	triangle	NOUN
american_scientific_journal-757	95	80	having	have	VERB
american_scientific_journal-757	95	81	vertices	vertex	NOUN
american_scientific_journal-757	95	82	(	(	PUNCT
american_scientific_journal-757	95	83	)	)	PUNCT
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american_scientific_journal-757	95	85	)	)	PUNCT
american_scientific_journal-757	95	86	0,34,0,0	0,34,0,0	NOUN
american_scientific_journal-757	95	87	qp	qp	NOUN
american_scientific_journal-757	95	88	and	and	CCONJ
american_scientific_journal-757	95	89	(	(	PUNCT
american_scientific_journal-757	95	90	)	)	PUNCT
american_scientific_journal-757	95	91	4,34q	4,34q	NUM
american_scientific_journal-757	95	92	.then	.then	X
american_scientific_journal-757	96	1	the	the	DET
american_scientific_journal-757	96	2	area	area	NOUN
american_scientific_journal-757	96	3	a	a	PRON
american_scientific_journal-757	96	4	is	be	AUX
american_scientific_journal-757	96	5	solution	solution	NOUN
american_scientific_journal-757	96	6	rewrite	rewrite	VERB
american_scientific_journal-757	96	7	the	the	DET
american_scientific_journal-757	96	8	vertices	vertex	NOUN
american_scientific_journal-757	96	9	as	as	ADP
american_scientific_journal-757	96	10	55	55	NUM
american_scientific_journal-757	96	11	american	american	ADJ
american_scientific_journal-757	96	12	scientific	scientific	ADJ
american_scientific_journal-757	96	13	research	research	NOUN
american_scientific_journal-757	96	14	journal	journal	NOUN
american_scientific_journal-757	96	15	for	for	ADP
american_scientific_journal-757	96	16	engineering	engineering	NOUN
american_scientific_journal-757	96	17	,	,	PUNCT
american_scientific_journal-757	96	18	technology	technology	NOUN
american_scientific_journal-757	96	19	,	,	PUNCT
american_scientific_journal-757	96	20	and	and	CCONJ
american_scientific_journal-757	96	21	sciences	science	NOUN
american_scientific_journal-757	96	22	(	(	PUNCT
american_scientific_journal-757	96	23	asrjets	asrjet	NOUN
american_scientific_journal-757	96	24	)	)	PUNCT
american_scientific_journal-757	96	25	(	(	PUNCT
american_scientific_journal-757	96	26	2015	2015	NUM
american_scientific_journal-757	96	27	)	)	PUNCT
american_scientific_journal-757	96	28	volume	volume	NOUN
american_scientific_journal-757	96	29	13	13	NUM
american_scientific_journal-757	96	30	,	,	PUNCT
american_scientific_journal-757	96	31	no	no	DET
american_scientific_journal-757	96	32	1	1	NUM
american_scientific_journal-757	96	33	,	,	PUNCT
american_scientific_journal-757	96	34	pp	pp	ADV
american_scientific_journal-757	96	35	49	49	NUM
american_scientific_journal-757	96	36	-	-	SYM
american_scientific_journal-757	96	37	60	60	NUM
american_scientific_journal-757	96	38	(	(	PUNCT
american_scientific_journal-757	96	39	)	)	PUNCT
american_scientific_journal-757	96	40	(	(	PUNCT
american_scientific_journal-757	96	41	)	)	PUNCT
american_scientific_journal-757	96	42	(	(	PUNCT
american_scientific_journal-757	96	43	)	)	PUNCT
american_scientific_journal-757	96	44	(	(	PUNCT
american_scientific_journal-757	96	45	)	)	PUNCT
american_scientific_journal-757	96	46	7	7	NUM
american_scientific_journal-757	96	47	244	244	NUM
american_scientific_journal-757	96	48	7	7	NUM
american_scientific_journal-757	96	49	12	12	NUM
american_scientific_journal-757	96	50	2	2	NUM
american_scientific_journal-757	96	51	184	184	NUM
american_scientific_journal-757	96	52	7	7	NUM
american_scientific_journal-757	96	53	12	12	NUM
american_scientific_journal-757	96	54	2	2	NUM
american_scientific_journal-757	96	55	1	1	NUM
american_scientific_journal-757	96	56	7	7	NUM
american_scientific_journal-757	96	57	282	282	NUM
american_scientific_journal-757	96	58	49	49	NUM
american_scientific_journal-757	96	59	144	144	NUM
american_scientific_journal-757	96	60	7	7	NUM
american_scientific_journal-757	96	61	40	40	NUM
american_scientific_journal-757	96	62	7	7	NUM
american_scientific_journal-757	96	63	12	12	NUM
american_scientific_journal-757	96	64	2	2	NUM
american_scientific_journal-757	96	65	1	1	NUM
american_scientific_journal-757	96	66	0	0	NUM
american_scientific_journal-757	96	67	49	49	NUM
american_scientific_journal-757	96	68	144	144	NUM
american_scientific_journal-757	96	69	7	7	NUM
american_scientific_journal-757	96	70	12	12	NUM
american_scientific_journal-757	96	71	,	,	PUNCT
american_scientific_journal-757	96	72	7	7	NUM
american_scientific_journal-757	96	73	12	12	NUM
american_scientific_journal-757	96	74	7	7	NUM
american_scientific_journal-757	96	75	2804,0	2804,0	NUM
american_scientific_journal-757	96	76	000,0	000,0	NOUN
american_scientific_journal-757	96	77	−=−	−=−	PUNCT
american_scientific_journal-757	96	78			PUNCT
american_scientific_journal-757	97	1			PROPN
american_scientific_journal-757	97	2			PROPN
american_scientific_journal-757	97	3			NOUN
american_scientific_journal-757	97	4	=−	=−	ADV
american_scientific_journal-757	97	5			PUNCT
american_scientific_journal-757	98	1			PROPN
american_scientific_journal-757	98	2			NOUN
american_scientific_journal-757	98	3			NOUN
american_scientific_journal-757	98	4	=	=	VERB
american_scientific_journal-757	98	5			PROPN
american_scientific_journal-757	98	6			PROPN
american_scientific_journal-757	98	7			PROPN
american_scientific_journal-757	98	8			ADJ
american_scientific_journal-757	98	9			NUM
american_scientific_journal-757	98	10			NOUN
american_scientific_journal-757	99	1	×−−	×−−	PROPN
american_scientific_journal-757	99	2			PUNCT
american_scientific_journal-757	100	1			PROPN
american_scientific_journal-757	100	2			NOUN
american_scientific_journal-757	100	3			NOUN
american_scientific_journal-757	100	4			NOUN
american_scientific_journal-757	100	5			NOUN
american_scientific_journal-757	100	6			PUNCT
american_scientific_journal-757	101	1			PROPN
american_scientific_journal-757	101	2			NOUN
american_scientific_journal-757	102	1			NOUN
american_scientific_journal-757	102	2	=	=	VERB
american_scientific_journal-757	102	3	=	=	NOUN
american_scientific_journal-757	102	4			NOUN
american_scientific_journal-757	102	5			PUNCT
american_scientific_journal-757	103	1			PROPN
american_scientific_journal-757	103	2			NOUN
american_scientific_journal-757	103	3			NOUN
american_scientific_journal-757	103	4			VERB
american_scientific_journal-757	103	5	=	=	PUNCT
american_scientific_journal-757	103	6	=	=	PUNCT
american_scientific_journal-757	103	7	a	a	DET
american_scientific_journal-757	103	8	a	a	DET
american_scientific_journal-757	103	9	r	r	NOUN
american_scientific_journal-757	103	10	q	q	NOUN
american_scientific_journal-757	103	11	p	p	NOUN
american_scientific_journal-757	103	12	the	the	DET
american_scientific_journal-757	103	13	above	above	ADJ
american_scientific_journal-757	103	14	triangle	triangle	NOUN
american_scientific_journal-757	103	15	is	be	AUX
american_scientific_journal-757	103	16	an	an	DET
american_scientific_journal-757	103	17	acute	acute	ADJ
american_scientific_journal-757	103	18	triangle	triangle	NOUN
american_scientific_journal-757	103	19	having	have	VERB
american_scientific_journal-757	103	20	base	base	NOUN
american_scientific_journal-757	103	21	4	4	NUM
american_scientific_journal-757	103	22	units	unit	NOUN
american_scientific_journal-757	103	23	long	long	ADJ
american_scientific_journal-757	103	24	and	and	CCONJ
american_scientific_journal-757	103	25	height	height	NOUN
american_scientific_journal-757	103	26	7	7	NUM
american_scientific_journal-757	103	27	12	12	NUM
american_scientific_journal-757	103	28	units	unit	NOUN
american_scientific_journal-757	103	29	long	long	ADJ
american_scientific_journal-757	103	30	.	.	PUNCT
american_scientific_journal-757	103	31	example	example	NOUN
american_scientific_journal-757	103	32	6	6	NUM
american_scientific_journal-757	103	33	:	:	PUNCT
american_scientific_journal-757	103	34	show	show	VERB
american_scientific_journal-757	103	35	that	that	SCONJ
american_scientific_journal-757	103	36	the	the	DET
american_scientific_journal-757	103	37	area	area	NOUN
american_scientific_journal-757	103	38	of	of	ADP
american_scientific_journal-757	103	39	a	a	DET
american_scientific_journal-757	103	40	right	right	ADV
american_scientific_journal-757	103	41	angled	angle	VERB
american_scientific_journal-757	103	42	triangle	triangle	NOUN
american_scientific_journal-757	103	43	with	with	ADP
american_scientific_journal-757	103	44	base	base	NOUN
american_scientific_journal-757	103	45	b	b	PROPN
american_scientific_journal-757	103	46	and	and	CCONJ
american_scientific_journal-757	103	47	height	height	NOUN
american_scientific_journal-757	103	48	h	h	NOUN
american_scientific_journal-757	103	49	is	be	AUX
american_scientific_journal-757	103	50	bha	bha	X
american_scientific_journal-757	103	51	2	2	NUM
american_scientific_journal-757	103	52	1	1	NUM
american_scientific_journal-757	103	53	=	=	NOUN
american_scientific_journal-757	103	54	solution	solution	NOUN
american_scientific_journal-757	103	55	let	let	VERB
american_scientific_journal-757	103	56	us	we	PRON
american_scientific_journal-757	103	57	construct	construct	VERB
american_scientific_journal-757	103	58	a	a	DET
american_scientific_journal-757	103	59	right	right	ADV
american_scientific_journal-757	103	60	angled	angled	ADJ
american_scientific_journal-757	103	61	triangle	triangle	NOUN
american_scientific_journal-757	103	62	having	have	VERB
american_scientific_journal-757	103	63	base	base	NOUN
american_scientific_journal-757	103	64	b	b	NOUN
american_scientific_journal-757	103	65	and	and	CCONJ
american_scientific_journal-757	103	66	height	height	NOUN
american_scientific_journal-757	103	67	h	h	NOUN
american_scientific_journal-757	103	68	as	as	ADP
american_scientific_journal-757	103	69	in	in	ADP
american_scientific_journal-757	103	70	fig	fig	NOUN
american_scientific_journal-757	103	71	1	1	NUM
american_scientific_journal-757	103	72	below	below	ADP
american_scientific_journal-757	103	73	.	.	PUNCT
american_scientific_journal-757	104	1	without	without	ADP
american_scientific_journal-757	104	2	loss	loss	NOUN
american_scientific_journal-757	104	3	of	of	ADP
american_scientific_journal-757	104	4	generality	generality	NOUN
american_scientific_journal-757	104	5	,	,	PUNCT
american_scientific_journal-757	104	6	let	let	VERB
american_scientific_journal-757	104	7	us	we	PRON
american_scientific_journal-757	104	8	take	take	VERB
american_scientific_journal-757	104	9	the	the	DET
american_scientific_journal-757	104	10	first	first	ADJ
american_scientific_journal-757	104	11	quadrant	quadrant	NOUN
american_scientific_journal-757	104	12	and	and	CCONJ
american_scientific_journal-757	104	13	the	the	DET
american_scientific_journal-757	104	14	vertex	vertex	NOUN
american_scientific_journal-757	104	15	of	of	ADP
american_scientific_journal-757	104	16	the	the	DET
american_scientific_journal-757	104	17	right	right	ADJ
american_scientific_journal-757	104	18	angle	angle	NOUN
american_scientific_journal-757	104	19	be	be	AUX
american_scientific_journal-757	104	20	at	at	ADP
american_scientific_journal-757	104	21	the	the	DET
american_scientific_journal-757	104	22	origin	origin	NOUN
american_scientific_journal-757	104	23	.	.	PUNCT
american_scientific_journal-757	105	1	the	the	DET
american_scientific_journal-757	105	2	vertices	vertex	NOUN
american_scientific_journal-757	105	3	of	of	ADP
american_scientific_journal-757	105	4	the	the	DET
american_scientific_journal-757	105	5	triangle	triangle	NOUN
american_scientific_journal-757	105	6	are	be	AUX
american_scientific_journal-757	105	7	b	b	NUM
american_scientific_journal-757	105	8	h	h	NOUN
american_scientific_journal-757	105	9	figure	figure	NOUN
american_scientific_journal-757	105	10	2	2	NUM
american_scientific_journal-757	105	11	:	:	PUNCT
american_scientific_journal-757	105	12	right	right	ADJ
american_scientific_journal-757	105	13	triangle	triangle	NOUN
american_scientific_journal-757	106	1	g	g	PROPN
american_scientific_journal-757	106	2	h	h	NOUN
american_scientific_journal-757	106	3	i	i	PRON
american_scientific_journal-757	106	4	56	56	NUM
american_scientific_journal-757	106	5	american	american	ADJ
american_scientific_journal-757	106	6	scientific	scientific	ADJ
american_scientific_journal-757	106	7	research	research	NOUN
american_scientific_journal-757	106	8	journal	journal	NOUN
american_scientific_journal-757	106	9	for	for	ADP
american_scientific_journal-757	106	10	engineering	engineering	NOUN
american_scientific_journal-757	106	11	,	,	PUNCT
american_scientific_journal-757	106	12	technology	technology	NOUN
american_scientific_journal-757	106	13	,	,	PUNCT
american_scientific_journal-757	106	14	and	and	CCONJ
american_scientific_journal-757	106	15	sciences	science	NOUN
american_scientific_journal-757	106	16	(	(	PUNCT
american_scientific_journal-757	106	17	asrjets	asrjet	NOUN
american_scientific_journal-757	106	18	)	)	PUNCT
american_scientific_journal-757	106	19	(	(	PUNCT
american_scientific_journal-757	106	20	2015	2015	NUM
american_scientific_journal-757	106	21	)	)	PUNCT
american_scientific_journal-757	106	22	volume	volume	NOUN
american_scientific_journal-757	106	23	13	13	NUM
american_scientific_journal-757	106	24	,	,	PUNCT
american_scientific_journal-757	106	25	no	no	DET
american_scientific_journal-757	106	26	1	1	NUM
american_scientific_journal-757	106	27	,	,	PUNCT
american_scientific_journal-757	106	28	pp	pp	ADV
american_scientific_journal-757	106	29	49	49	NUM
american_scientific_journal-757	106	30	-	-	SYM
american_scientific_journal-757	106	31	60	60	NUM
american_scientific_journal-757	106	32	(	(	PUNCT
american_scientific_journal-757	106	33	)	)	PUNCT
american_scientific_journal-757	106	34	(	(	PUNCT
american_scientific_journal-757	106	35	)	)	PUNCT
american_scientific_journal-757	106	36	(	(	PUNCT
american_scientific_journal-757	106	37	)	)	PUNCT
american_scientific_journal-757	106	38	(	(	PUNCT
american_scientific_journal-757	106	39	)	)	PUNCT
american_scientific_journal-757	106	40	(	(	PUNCT
american_scientific_journal-757	106	41	)	)	PUNCT
american_scientific_journal-757	106	42	[	[	PUNCT
american_scientific_journal-757	106	43	]	]	X
american_scientific_journal-757	106	44	bhhba	bhhba	X
american_scientific_journal-757	106	45	hr	hr	PROPN
american_scientific_journal-757	106	46	bq	bq	PROPN
american_scientific_journal-757	106	47	p	p	PROPN
american_scientific_journal-757	106	48	2	2	NUM
american_scientific_journal-757	106	49	1020	1020	NUM
american_scientific_journal-757	106	50	2	2	NUM
american_scientific_journal-757	106	51	1	1	NUM
american_scientific_journal-757	106	52	00,0	00,0	NOUN
american_scientific_journal-757	106	53	000	000	NUM
american_scientific_journal-757	106	54	,	,	PUNCT
american_scientific_journal-757	106	55	00,0,0	00,0,0	NOUN
american_scientific_journal-757	106	56	=	=	NUM
american_scientific_journal-757	106	57	×−−=	×−−=	X
american_scientific_journal-757	106	58	=	=	SYM
american_scientific_journal-757	107	1	=	=	SYM
american_scientific_journal-757	107	2	=	=	PUNCT
american_scientific_journal-757	107	3	our	our	PRON
american_scientific_journal-757	107	4	next	next	ADJ
american_scientific_journal-757	107	5	goal	goal	NOUN
american_scientific_journal-757	107	6	is	be	AUX
american_scientific_journal-757	107	7	to	to	PART
american_scientific_journal-757	107	8	establish	establish	VERB
american_scientific_journal-757	107	9	some	some	PRON
american_scientific_journal-757	107	10	of	of	ADP
american_scientific_journal-757	107	11	the	the	DET
american_scientific_journal-757	107	12	basic	basic	ADJ
american_scientific_journal-757	107	13	algebraic	algebraic	ADJ
american_scientific_journal-757	107	14	formulas	formula	NOUN
american_scientific_journal-757	107	15	based	base	VERB
american_scientific_journal-757	107	16	on	on	ADP
american_scientific_journal-757	107	17	the	the	DET
american_scientific_journal-757	107	18	procedure	procedure	NOUN
american_scientific_journal-757	107	19	above	above	ADV
american_scientific_journal-757	107	20	.	.	PUNCT
american_scientific_journal-757	108	1	to	to	PART
american_scientific_journal-757	108	2	do	do	VERB
american_scientific_journal-757	108	3	this	this	PRON
american_scientific_journal-757	108	4	,	,	PUNCT
american_scientific_journal-757	108	5	we	we	PRON
american_scientific_journal-757	108	6	use	use	VERB
american_scientific_journal-757	108	7	the	the	DET
american_scientific_journal-757	108	8	concept	concept	NOUN
american_scientific_journal-757	108	9	of	of	ADP
american_scientific_journal-757	108	10	centroid	centroid	NOUN
american_scientific_journal-757	108	11	of	of	ADP
american_scientific_journal-757	108	12	a	a	DET
american_scientific_journal-757	108	13	triangle	triangle	NOUN
american_scientific_journal-757	108	14	and	and	CCONJ
american_scientific_journal-757	108	15	area	area	NOUN
american_scientific_journal-757	108	16	of	of	ADP
american_scientific_journal-757	108	17	a	a	DET
american_scientific_journal-757	108	18	triangle	triangle	NOUN
american_scientific_journal-757	108	19	using	use	VERB
american_scientific_journal-757	108	20	determinant	determinant	ADJ
american_scientific_journal-757	108	21	.	.	PUNCT
american_scientific_journal-757	109	1	theorems	theorem	NOUN
american_scientific_journal-757	109	2	theorem	theorem	VERB
american_scientific_journal-757	109	3	1	1	NUM
american_scientific_journal-757	109	4	:	:	PUNCT
american_scientific_journal-757	109	5	the	the	DET
american_scientific_journal-757	109	6	area	area	NOUN
american_scientific_journal-757	109	7	a	a	PRON
american_scientific_journal-757	109	8	of	of	ADP
american_scientific_journal-757	109	9	a	a	DET
american_scientific_journal-757	109	10	triangle	triangle	NOUN
american_scientific_journal-757	109	11	having	have	VERB
american_scientific_journal-757	109	12	vertices	vertex	NOUN
american_scientific_journal-757	109	13	(	(	PUNCT
american_scientific_journal-757	109	14	)	)	PUNCT
american_scientific_journal-757	109	15	(	(	PUNCT
american_scientific_journal-757	109	16	)	)	PUNCT
american_scientific_journal-757	109	17	2211	2211	NUM
american_scientific_journal-757	109	18	,	,	PUNCT
american_scientific_journal-757	109	19	,	,	PUNCT
american_scientific_journal-757	109	20	,	,	PUNCT
american_scientific_journal-757	109	21	yxqyxp	yxqyxp	PROPN
american_scientific_journal-757	109	22	and	and	CCONJ
american_scientific_journal-757	109	23	(	(	PUNCT
american_scientific_journal-757	109	24	)	)	PUNCT
american_scientific_journal-757	109	25	,	,	PUNCT
american_scientific_journal-757	109	26	,	,	PUNCT
american_scientific_journal-757	109	27	33	33	NUM
american_scientific_journal-757	109	28	yxr	yxr	NOUN
american_scientific_journal-757	109	29	is	be	AUX
american_scientific_journal-757	109	30	given	give	VERB
american_scientific_journal-757	109	31	by	by	ADP
american_scientific_journal-757	109	32			PROPN
american_scientific_journal-757	109	33			PROPN
american_scientific_journal-757	109	34			PROPN
american_scientific_journal-757	109	35			ADJ
american_scientific_journal-757	109	36			NOUN
american_scientific_journal-757	109	37			VERB
american_scientific_journal-757	109	38	−	−	PRON
american_scientific_journal-757	109	39			PUNCT
american_scientific_journal-757	110	1			PROPN
american_scientific_journal-757	110	2			NOUN
american_scientific_journal-757	110	3			NOUN
american_scientific_journal-757	110	4			VERB
american_scientific_journal-757	110	5	−	−	PRON
american_scientific_journal-757	110	6			PUNCT
american_scientific_journal-757	111	1			PROPN
american_scientific_journal-757	111	2			NOUN
american_scientific_journal-757	111	3			NOUN
american_scientific_journal-757	111	4			NOUN
american_scientific_journal-757	111	5			NOUN
american_scientific_journal-757	111	6			PUNCT
american_scientific_journal-757	112	1			PROPN
american_scientific_journal-757	112	2			NOUN
american_scientific_journal-757	112	3			NOUN
american_scientific_journal-757	112	4			NOUN
american_scientific_journal-757	112	5	=	=	PUNCT
american_scientific_journal-757	112	6	∑∑∑∑	∑∑∑∑	PROPN
american_scientific_journal-757	112	7	=	=	SYM
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american_scientific_journal-757	112	10	=	=	SYM
american_scientific_journal-757	112	11	j	j	PROPN
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american_scientific_journal-757	113	2	ii	ii	VERB
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american_scientific_journal-757	114	2	i	i	PRON
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american_scientific_journal-757	115	2	i	i	PRON
american_scientific_journal-757	116	1	i	i	PRON
american_scientific_journal-757	116	2	i	i	PRON
american_scientific_journal-757	116	3	yxyxyxa	yxyxyxa	VERB
american_scientific_journal-757	116	4	3	3	NUM
american_scientific_journal-757	116	5	1	1	NUM
american_scientific_journal-757	116	6	3	3	NUM
american_scientific_journal-757	116	7	1	1	NUM
american_scientific_journal-757	116	8	3	3	NUM
american_scientific_journal-757	116	9	1	1	NUM
american_scientific_journal-757	116	10	3	3	NUM
american_scientific_journal-757	116	11	1	1	NUM
american_scientific_journal-757	116	12	2	2	NUM
american_scientific_journal-757	116	13	2	2	NUM
american_scientific_journal-757	116	14	1	1	NUM
american_scientific_journal-757	116	15	or	or	CCONJ
american_scientific_journal-757	116	16	for	for	ADP
american_scientific_journal-757	116	17	short	short	ADJ
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american_scientific_journal-757	116	21	yxyxyxa	yxyxyxa	PROPN
american_scientific_journal-757	116	22	∑∑∑∑	∑∑∑∑	PROPN
american_scientific_journal-757	116	23	−−=	−−=	PROPN
american_scientific_journal-757	116	24	2	2	NUM
american_scientific_journal-757	116	25	2	2	NUM
american_scientific_journal-757	116	26	1	1	NUM
american_scientific_journal-757	117	1	where	where	SCONJ
american_scientific_journal-757	117	2	(	(	PUNCT
american_scientific_journal-757	117	3	)	)	PUNCT
american_scientific_journal-757	117	4	(	(	PUNCT
american_scientific_journal-757	117	5	)	)	PUNCT
american_scientific_journal-757	117	6	321321	321321	NUM
american_scientific_journal-757	117	7	yyyxxxyx	yyyxxxyx	NOUN
american_scientific_journal-757	117	8	ii	ii	PROPN
american_scientific_journal-757	118	1	+	+	PROPN
american_scientific_journal-757	118	2	+	+	ADJ
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american_scientific_journal-757	118	6	∑∑	∑∑	PROPN
american_scientific_journal-757	118	7	,	,	PUNCT
american_scientific_journal-757	118	8	332211	332211	NUM
american_scientific_journal-757	118	9	yxyxyxyx	yxyxyxyx	NOUN
american_scientific_journal-757	118	10	ii	ii	PROPN
american_scientific_journal-757	118	11	+	+	PROPN
american_scientific_journal-757	118	12	+	+	PROPN
american_scientific_journal-757	118	13	=	=	ADJ
american_scientific_journal-757	118	14	∑	∑	ADJ
american_scientific_journal-757	118	15	and	and	CCONJ
american_scientific_journal-757	118	16	122331	122331	NUM
american_scientific_journal-757	118	17	yxyxyxyx	yxyxyxyx	NOUN
american_scientific_journal-757	119	1	ji	ji	PROPN
american_scientific_journal-757	119	2	+	+	PROPN
american_scientific_journal-757	119	3	+	+	PROPN
american_scientific_journal-757	119	4	=	=	ADJ
american_scientific_journal-757	119	5	∑	∑	ADJ
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american_scientific_journal-757	119	7	:	:	PUNCT
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american_scientific_journal-757	119	28	.	.	PUNCT
american_scientific_journal-757	120	1	the	the	DET
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american_scientific_journal-757	120	9	3	3	NUM
american_scientific_journal-757	120	10	,	,	PUNCT
american_scientific_journal-757	120	11	3	3	NUM
american_scientific_journal-757	120	12	321321	321321	NUM
american_scientific_journal-757	120	13	yyy	yyy	NOUN
american_scientific_journal-757	120	14	y	y	PROPN
american_scientific_journal-757	120	15	xxx	xxx	NOUN
american_scientific_journal-757	120	16	x	x	PUNCT
american_scientific_journal-757	120	17	cc	cc	ADP
american_scientific_journal-757	120	18	+	+	PROPN
american_scientific_journal-757	120	19	+	+	X
american_scientific_journal-757	120	20	=	=	SYM
american_scientific_journal-757	120	21	+	+	PROPN
american_scientific_journal-757	120	22	+	+	NOUN
american_scientific_journal-757	120	23	=	=	SYM
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american_scientific_journal-757	120	25	product	product	NOUN
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american_scientific_journal-757	120	27	the	the	DET
american_scientific_journal-757	120	28	coordinates	coordinate	NOUN
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american_scientific_journal-757	120	33	(	(	PUNCT
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american_scientific_journal-757	120	37			NOUN
american_scientific_journal-757	120	38			PUNCT
american_scientific_journal-757	121	1			PROPN
american_scientific_journal-757	121	2			NOUN
american_scientific_journal-757	121	3			NOUN
american_scientific_journal-757	121	4			VERB
american_scientific_journal-757	121	5	+	+	NOUN
american_scientific_journal-757	121	6	+	+	NUM
american_scientific_journal-757	121	7			NOUN
american_scientific_journal-757	121	8			PUNCT
american_scientific_journal-757	122	1			PROPN
american_scientific_journal-757	122	2			NOUN
american_scientific_journal-757	122	3			NOUN
american_scientific_journal-757	122	4			VERB
american_scientific_journal-757	122	5	+	+	PROPN
american_scientific_journal-757	122	6	+	+	NUM
american_scientific_journal-757	122	7	=	=	SYM
american_scientific_journal-757	122	8	33	33	NUM
american_scientific_journal-757	122	9	321321	321321	NUM
american_scientific_journal-757	122	10	yyyxxx	yyyxxx	NOUN
american_scientific_journal-757	122	11	yx	yx	PROPN
american_scientific_journal-757	122	12	cc	cc	PROPN
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american_scientific_journal-757	122	16	57	57	NUM
american_scientific_journal-757	122	17	american	american	ADJ
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american_scientific_journal-757	122	25	,	,	PUNCT
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american_scientific_journal-757	122	28	(	(	PUNCT
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american_scientific_journal-757	122	32	2015	2015	NUM
american_scientific_journal-757	122	33	)	)	PUNCT
american_scientific_journal-757	122	34	volume	volume	NOUN
american_scientific_journal-757	122	35	13	13	NUM
american_scientific_journal-757	122	36	,	,	PUNCT
american_scientific_journal-757	122	37	no	no	DET
american_scientific_journal-757	122	38	1	1	NUM
american_scientific_journal-757	122	39	,	,	PUNCT
american_scientific_journal-757	122	40	pp	pp	ADV
american_scientific_journal-757	122	41	49	49	NUM
american_scientific_journal-757	122	42	-	-	SYM
american_scientific_journal-757	122	43	60	60	NUM
american_scientific_journal-757	122	44	(	(	PUNCT
american_scientific_journal-757	122	45	)	)	PUNCT
american_scientific_journal-757	122	46	(	(	PUNCT
american_scientific_journal-757	122	47	)	)	PUNCT
american_scientific_journal-757	122	48	(	(	PUNCT
american_scientific_journal-757	122	49	)	)	PUNCT
american_scientific_journal-757	122	50	(	(	PUNCT
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american_scientific_journal-757	122	52	(	(	PUNCT
american_scientific_journal-757	122	53	)	)	PUNCT
american_scientific_journal-757	122	54	9	9	NUM
american_scientific_journal-757	122	55	9	9	NUM
american_scientific_journal-757	122	56	332313322212312111	332313322212312111	NUM
american_scientific_journal-757	122	57	321321	321321	NUM
american_scientific_journal-757	122	58	yxyxyxyxyxyxyxyxyx	yxyxyxyxyxyxyxyxyx	NOUN
american_scientific_journal-757	122	59	yxyyyxxxyx	yxyyyxxxyx	PROPN
american_scientific_journal-757	122	60	iicc	iicc	VERB
american_scientific_journal-757	123	1	+	+	PROPN
american_scientific_journal-757	123	2	+	+	ADJ
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american_scientific_journal-757	123	9	=	=	SYM
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american_scientific_journal-757	123	11	+	+	PROPN
american_scientific_journal-757	123	12	+	+	ADJ
american_scientific_journal-757	123	13	+	+	ADJ
american_scientific_journal-757	123	14	+	+	NOUN
american_scientific_journal-757	123	15	=	=	NOUN
american_scientific_journal-757	123	16	∑∑	∑∑	NOUN
american_scientific_journal-757	123	17	it	it	PRON
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american_scientific_journal-757	123	21	in	in	ADP
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american_scientific_journal-757	123	24	]	]	PUNCT
american_scientific_journal-757	123	25	that	that	SCONJ
american_scientific_journal-757	123	26	the	the	DET
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american_scientific_journal-757	123	36	(	(	PUNCT
american_scientific_journal-757	123	37	)	)	PUNCT
american_scientific_journal-757	123	38	10	10	NUM
american_scientific_journal-757	123	39	2	2	NUM
american_scientific_journal-757	123	40	1	1	NUM
american_scientific_journal-757	123	41	2	2	NUM
american_scientific_journal-757	123	42	1	1	NUM
american_scientific_journal-757	123	43	231231211332	231231211332	NUM
american_scientific_journal-757	123	44	1312	1312	NUM
american_scientific_journal-757	123	45	1312	1312	NUM
american_scientific_journal-757	123	46	yxyxyxyxyxyx	yxyxyxyxyxyx	NOUN
american_scientific_journal-757	123	47	yyyy	yyyy	PROPN
american_scientific_journal-757	123	48	xxxx	xxxx	PROPN
american_scientific_journal-757	123	49	a	a	DET
american_scientific_journal-757	123	50	−−−++=	−−−++=	PROPN
american_scientific_journal-757	123	51	−−	−−	PROPN
american_scientific_journal-757	123	52	−−	−−	NOUN
american_scientific_journal-757	123	53	±=	±=	NOUN
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american_scientific_journal-757	123	75	∑∑∑∑	∑∑∑∑	ADJ
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american_scientific_journal-757	124	1	−−++++++++	−−++++++++	NOUN
american_scientific_journal-757	124	2	=	=	SYM
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american_scientific_journal-757	124	6	2222	2222	NUM
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american_scientific_journal-757	124	9	2211332313322212312111	2211332313322212312111	NUM
american_scientific_journal-757	124	10	where	where	SCONJ
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american_scientific_journal-757	124	15	321321	321321	NUM
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american_scientific_journal-757	124	17	ii	ii	PROPN
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american_scientific_journal-757	125	7	,	,	PUNCT
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american_scientific_journal-757	126	12	31	31	NUM
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american_scientific_journal-757	127	5	∑∑	∑∑	NOUN
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american_scientific_journal-757	128	4	−=	−=	ADJ
american_scientific_journal-757	128	5	≤≤	≤≤	PROPN
american_scientific_journal-757	128	6			NOUN
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american_scientific_journal-757	129	1			PROPN
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american_scientific_journal-757	129	4	−=	−=	ADJ
american_scientific_journal-757	129	5	≤≤	≤≤	NOUN
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american_scientific_journal-757	129	9	:	:	PUNCT
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american_scientific_journal-757	129	14	a	a	DET
american_scientific_journal-757	129	15	parallelogram	parallelogram	NOUN
american_scientific_journal-757	129	16	who	who	PRON
american_scientific_journal-757	129	17	’s	’	VERB
american_scientific_journal-757	129	18	any	any	DET
american_scientific_journal-757	129	19	three	three	NUM
american_scientific_journal-757	129	20	of	of	ADP
american_scientific_journal-757	129	21	its	its	PRON
american_scientific_journal-757	129	22	four	four	NUM
american_scientific_journal-757	129	23	vertices	vertex	NOUN
american_scientific_journal-757	129	24	(	(	PUNCT
american_scientific_journal-757	129	25	)	)	PUNCT
american_scientific_journal-757	129	26	(	(	PUNCT
american_scientific_journal-757	129	27	)	)	PUNCT
american_scientific_journal-757	129	28	2211	2211	NUM
american_scientific_journal-757	129	29	,	,	PUNCT
american_scientific_journal-757	129	30	,	,	PUNCT
american_scientific_journal-757	129	31	,	,	PUNCT
american_scientific_journal-757	129	32	yxqyxp	yxqyxp	PROPN
american_scientific_journal-757	129	33	and	and	CCONJ
american_scientific_journal-757	129	34	(	(	PUNCT
american_scientific_journal-757	129	35	)	)	PUNCT
american_scientific_journal-757	129	36	,	,	PUNCT
american_scientific_journal-757	129	37	,	,	PUNCT
american_scientific_journal-757	129	38	33	33	NUM
american_scientific_journal-757	129	39	yxr	yxr	NOUN
american_scientific_journal-757	129	40	is	be	AUX
american_scientific_journal-757	129	41	given	give	VERB
american_scientific_journal-757	129	42	by	by	ADP
american_scientific_journal-757	129	43			PROPN
american_scientific_journal-757	129	44			PROPN
american_scientific_journal-757	129	45			PROPN
american_scientific_journal-757	129	46			ADJ
american_scientific_journal-757	129	47			NOUN
american_scientific_journal-757	129	48			VERB
american_scientific_journal-757	129	49	−	−	PRON
american_scientific_journal-757	129	50			PUNCT
american_scientific_journal-757	130	1			PROPN
american_scientific_journal-757	130	2			NOUN
american_scientific_journal-757	130	3			NOUN
american_scientific_journal-757	130	4			VERB
american_scientific_journal-757	130	5	−	−	PRON
american_scientific_journal-757	130	6			PUNCT
american_scientific_journal-757	131	1			PROPN
american_scientific_journal-757	131	2			NOUN
american_scientific_journal-757	131	3			NOUN
american_scientific_journal-757	131	4			NOUN
american_scientific_journal-757	131	5			NOUN
american_scientific_journal-757	131	6			PUNCT
american_scientific_journal-757	132	1			PROPN
american_scientific_journal-757	132	2			NOUN
american_scientific_journal-757	132	3			NOUN
american_scientific_journal-757	132	4			NOUN
american_scientific_journal-757	132	5	=	=	PUNCT
american_scientific_journal-757	132	6	∑∑∑∑	∑∑∑∑	PROPN
american_scientific_journal-757	132	7	=	=	SYM
american_scientific_journal-757	132	8	=	=	SYM
american_scientific_journal-757	132	9	=	=	SYM
american_scientific_journal-757	132	10	=	=	SYM
american_scientific_journal-757	132	11	j	j	PROPN
american_scientific_journal-757	133	1	i	i	NOUN
american_scientific_journal-757	133	2	ii	ii	VERB
american_scientific_journal-757	134	1	i	i	PRON
american_scientific_journal-757	134	2	i	i	PRON
american_scientific_journal-757	135	1	i	i	PRON
american_scientific_journal-757	135	2	i	i	PRON
american_scientific_journal-757	136	1	i	i	PRON
american_scientific_journal-757	136	2	i	i	PRON
american_scientific_journal-757	136	3	yxyxyxa	yxyxyxa	VERB
american_scientific_journal-757	136	4	3	3	NUM
american_scientific_journal-757	136	5	1	1	NUM
american_scientific_journal-757	136	6	3	3	NUM
american_scientific_journal-757	136	7	1	1	NUM
american_scientific_journal-757	136	8	3	3	NUM
american_scientific_journal-757	136	9	1	1	NUM
american_scientific_journal-757	136	10	3	3	NUM
american_scientific_journal-757	136	11	1	1	NUM
american_scientific_journal-757	136	12	2	2	NUM
american_scientific_journal-757	136	13	or	or	CCONJ
american_scientific_journal-757	136	14	for	for	ADP
american_scientific_journal-757	136	15	short	short	ADJ
american_scientific_journal-757	136	16	[	[	PUNCT
american_scientific_journal-757	136	17	]	]	X
american_scientific_journal-757	136	18	jiiiii	jiiiii	PROPN
american_scientific_journal-757	136	19	yxyxyxa	yxyxyxa	PROPN
american_scientific_journal-757	136	20	∑∑∑∑	∑∑∑∑	PROPN
american_scientific_journal-757	136	21	−−=	−−=	PROPN
american_scientific_journal-757	136	22	2	2	NUM
american_scientific_journal-757	137	1	where	where	SCONJ
american_scientific_journal-757	137	2	(	(	PUNCT
american_scientific_journal-757	137	3	)	)	PUNCT
american_scientific_journal-757	137	4	(	(	PUNCT
american_scientific_journal-757	137	5	)	)	PUNCT
american_scientific_journal-757	137	6	321321	321321	NUM
american_scientific_journal-757	137	7	yyyxxxyx	yyyxxxyx	NOUN
american_scientific_journal-757	137	8	ii	ii	PROPN
american_scientific_journal-757	138	1	+	+	PROPN
american_scientific_journal-757	138	2	+	+	ADJ
american_scientific_journal-757	138	3	+	+	ADJ
american_scientific_journal-757	138	4	+	+	ADJ
american_scientific_journal-757	138	5	=	=	ADJ
american_scientific_journal-757	138	6	∑∑	∑∑	PROPN
american_scientific_journal-757	138	7	,	,	PUNCT
american_scientific_journal-757	138	8	332211	332211	NUM
american_scientific_journal-757	138	9	yxyxyxyx	yxyxyxyx	NOUN
american_scientific_journal-757	138	10	ii	ii	PROPN
american_scientific_journal-757	138	11	+	+	PROPN
american_scientific_journal-757	138	12	+	+	PROPN
american_scientific_journal-757	138	13	=	=	NOUN
american_scientific_journal-757	138	14	∑	∑	ADJ
american_scientific_journal-757	138	15	and	and	CCONJ
american_scientific_journal-757	138	16	58	58	NUM
american_scientific_journal-757	138	17	american	american	ADJ
american_scientific_journal-757	138	18	scientific	scientific	ADJ
american_scientific_journal-757	138	19	research	research	NOUN
american_scientific_journal-757	138	20	journal	journal	NOUN
american_scientific_journal-757	138	21	for	for	ADP
american_scientific_journal-757	138	22	engineering	engineering	NOUN
american_scientific_journal-757	138	23	,	,	PUNCT
american_scientific_journal-757	138	24	technology	technology	NOUN
american_scientific_journal-757	138	25	,	,	PUNCT
american_scientific_journal-757	138	26	and	and	CCONJ
american_scientific_journal-757	138	27	sciences	science	NOUN
american_scientific_journal-757	138	28	(	(	PUNCT
american_scientific_journal-757	138	29	asrjets	asrjet	NOUN
american_scientific_journal-757	138	30	)	)	PUNCT
american_scientific_journal-757	138	31	(	(	PUNCT
american_scientific_journal-757	138	32	2015	2015	NUM
american_scientific_journal-757	138	33	)	)	PUNCT
american_scientific_journal-757	138	34	volume	volume	NOUN
american_scientific_journal-757	138	35	13	13	NUM
american_scientific_journal-757	138	36	,	,	PUNCT
american_scientific_journal-757	138	37	no	no	DET
american_scientific_journal-757	138	38	1	1	NUM
american_scientific_journal-757	138	39	,	,	PUNCT
american_scientific_journal-757	138	40	pp	pp	ADV
american_scientific_journal-757	138	41	49	49	NUM
american_scientific_journal-757	138	42	-	-	SYM
american_scientific_journal-757	138	43	60	60	NUM
american_scientific_journal-757	138	44	122331	122331	NUM
american_scientific_journal-757	138	45	yxyxyxyx	yxyxyxyx	NOUN
american_scientific_journal-757	139	1	ji	ji	PROPN
american_scientific_journal-757	139	2	+	+	PROPN
american_scientific_journal-757	139	3	+	+	PROPN
american_scientific_journal-757	139	4	=	=	ADJ
american_scientific_journal-757	139	5	∑	∑	ADJ
american_scientific_journal-757	139	6	proof	proof	NOUN
american_scientific_journal-757	139	7	:	:	PUNCT
american_scientific_journal-757	139	8	since	since	SCONJ
american_scientific_journal-757	139	9	the	the	DET
american_scientific_journal-757	139	10	diagonal	diagonal	NOUN
american_scientific_journal-757	139	11	of	of	ADP
american_scientific_journal-757	139	12	a	a	DET
american_scientific_journal-757	139	13	parallelogram	parallelogram	NOUN
american_scientific_journal-757	139	14	divides	divide	VERB
american_scientific_journal-757	139	15	it	it	PRON
american_scientific_journal-757	139	16	in	in	ADV
american_scientific_journal-757	139	17	to	to	ADP
american_scientific_journal-757	139	18	two	two	NUM
american_scientific_journal-757	139	19	triangles	triangle	NOUN
american_scientific_journal-757	139	20	having	have	VERB
american_scientific_journal-757	139	21	the	the	DET
american_scientific_journal-757	139	22	same	same	ADJ
american_scientific_journal-757	139	23	area	area	NOUN
american_scientific_journal-757	139	24	,	,	PUNCT
american_scientific_journal-757	139	25	once	once	SCONJ
american_scientific_journal-757	139	26	we	we	PRON
american_scientific_journal-757	139	27	determine	determine	VERB
american_scientific_journal-757	139	28	the	the	DET
american_scientific_journal-757	139	29	area	area	NOUN
american_scientific_journal-757	139	30	of	of	ADP
american_scientific_journal-757	139	31	one	one	NUM
american_scientific_journal-757	139	32	triangle	triangle	NOUN
american_scientific_journal-757	139	33	,	,	PUNCT
american_scientific_journal-757	139	34	we	we	PRON
american_scientific_journal-757	139	35	can	can	AUX
american_scientific_journal-757	139	36	multiply	multiply	VERB
american_scientific_journal-757	139	37	it	it	PRON
american_scientific_journal-757	139	38	by	by	ADP
american_scientific_journal-757	139	39	two	two	NUM
american_scientific_journal-757	139	40	to	to	PART
american_scientific_journal-757	139	41	obtain	obtain	VERB
american_scientific_journal-757	139	42	the	the	DET
american_scientific_journal-757	139	43	area	area	NOUN
american_scientific_journal-757	139	44	of	of	ADP
american_scientific_journal-757	139	45	the	the	DET
american_scientific_journal-757	139	46	parallelogram	parallelogram	NOUN
american_scientific_journal-757	139	47	.	.	PUNCT
american_scientific_journal-757	140	1	4	4	NUM
american_scientific_journal-757	140	2	.	.	X
american_scientific_journal-757	140	3	conclusion	conclusion	NOUN
american_scientific_journal-757	140	4	and	and	CCONJ
american_scientific_journal-757	140	5	directions	direction	NOUN
american_scientific_journal-757	140	6	finding	find	VERB
american_scientific_journal-757	140	7	the	the	DET
american_scientific_journal-757	140	8	area	area	NOUN
american_scientific_journal-757	140	9	of	of	ADP
american_scientific_journal-757	140	10	a	a	DET
american_scientific_journal-757	140	11	triangle	triangle	NOUN
american_scientific_journal-757	140	12	and	and	CCONJ
american_scientific_journal-757	140	13	rectangles	rectangle	NOUN
american_scientific_journal-757	140	14	is	be	AUX
american_scientific_journal-757	140	15	very	very	ADV
american_scientific_journal-757	140	16	important	important	ADJ
american_scientific_journal-757	140	17	in	in	ADP
american_scientific_journal-757	140	18	mathematics	mathematic	NOUN
american_scientific_journal-757	140	19	,	,	PUNCT
american_scientific_journal-757	140	20	mechanics	mechanic	NOUN
american_scientific_journal-757	140	21	and	and	CCONJ
american_scientific_journal-757	140	22	surveying	surveying	NOUN
american_scientific_journal-757	140	23	.	.	PUNCT
american_scientific_journal-757	141	1	in	in	ADP
american_scientific_journal-757	141	2	engineering	engineering	NOUN
american_scientific_journal-757	141	3	mechanics	mechanic	NOUN
american_scientific_journal-757	141	4	it	it	PRON
american_scientific_journal-757	141	5	is	be	AUX
american_scientific_journal-757	141	6	used	use	VERB
american_scientific_journal-757	141	7	to	to	PART
american_scientific_journal-757	141	8	find	find	VERB
american_scientific_journal-757	141	9	the	the	DET
american_scientific_journal-757	141	10	moment	moment	NOUN
american_scientific_journal-757	141	11	of	of	ADP
american_scientific_journal-757	141	12	inertia	inertia	NOUN
american_scientific_journal-757	141	13	,	,	PUNCT
american_scientific_journal-757	141	14	and	and	CCONJ
american_scientific_journal-757	141	15	in	in	ADP
american_scientific_journal-757	141	16	the	the	DET
american_scientific_journal-757	141	17	design	design	NOUN
american_scientific_journal-757	141	18	and	and	CCONJ
american_scientific_journal-757	141	19	analysis	analysis	NOUN
american_scientific_journal-757	141	20	of	of	ADP
american_scientific_journal-757	141	21	plane	plane	NOUN
american_scientific_journal-757	141	22	trusses	truss	NOUN
american_scientific_journal-757	141	23	.	.	PUNCT
american_scientific_journal-757	142	1	in	in	ADP
american_scientific_journal-757	142	2	surveying	survey	VERB
american_scientific_journal-757	142	3	it	it	PRON
american_scientific_journal-757	142	4	is	be	AUX
american_scientific_journal-757	142	5	used	use	VERB
american_scientific_journal-757	142	6	in	in	ADP
american_scientific_journal-757	142	7	triangulation	triangulation	NOUN
american_scientific_journal-757	142	8	and	and	CCONJ
american_scientific_journal-757	142	9	trilateration	trilateration	NOUN
american_scientific_journal-757	142	10	.	.	PUNCT
american_scientific_journal-757	143	1	the	the	DET
american_scientific_journal-757	143	2	technique	technique	NOUN
american_scientific_journal-757	143	3	and	and	CCONJ
american_scientific_journal-757	143	4	formula	formula	NOUN
american_scientific_journal-757	143	5	found	find	VERB
american_scientific_journal-757	143	6	here	here	ADV
american_scientific_journal-757	143	7	may	may	AUX
american_scientific_journal-757	143	8	be	be	AUX
american_scientific_journal-757	143	9	used	use	VERB
american_scientific_journal-757	143	10	as	as	ADP
american_scientific_journal-757	143	11	an	an	DET
american_scientific_journal-757	143	12	alternative	alternative	ADJ
american_scientific_journal-757	143	13	way	way	NOUN
american_scientific_journal-757	143	14	of	of	ADP
american_scientific_journal-757	143	15	finding	find	VERB
american_scientific_journal-757	143	16	an	an	DET
american_scientific_journal-757	143	17	area	area	NOUN
american_scientific_journal-757	143	18	of	of	ADP
american_scientific_journal-757	143	19	triangles	triangle	NOUN
american_scientific_journal-757	143	20	in	in	ADP
american_scientific_journal-757	143	21	a	a	DET
american_scientific_journal-757	143	22	plane	plane	NOUN
american_scientific_journal-757	143	23	.	.	PUNCT
american_scientific_journal-757	144	1	the	the	DET
american_scientific_journal-757	144	2	method	method	NOUN
american_scientific_journal-757	144	3	is	be	AUX
american_scientific_journal-757	144	4	direct	direct	ADJ
american_scientific_journal-757	144	5	and	and	CCONJ
american_scientific_journal-757	144	6	can	can	AUX
american_scientific_journal-757	144	7	be	be	AUX
american_scientific_journal-757	144	8	done	do	VERB
american_scientific_journal-757	144	9	easily	easily	ADV
american_scientific_journal-757	144	10	with	with	ADP
american_scientific_journal-757	144	11	greater	great	ADJ
american_scientific_journal-757	144	12	accuracy	accuracy	NOUN
american_scientific_journal-757	144	13	and	and	CCONJ
american_scientific_journal-757	144	14	speed	speed	NOUN
american_scientific_journal-757	144	15	.	.	PUNCT
american_scientific_journal-757	145	1	the	the	DET
american_scientific_journal-757	145	2	formula	formula	NOUN
american_scientific_journal-757	145	3	is	be	AUX
american_scientific_journal-757	145	4	derived	derive	VERB
american_scientific_journal-757	145	5	using	use	VERB
american_scientific_journal-757	145	6	analytic	analytic	ADJ
american_scientific_journal-757	145	7	approach	approach	NOUN
american_scientific_journal-757	145	8	.	.	PUNCT
american_scientific_journal-757	146	1	the	the	DET
american_scientific_journal-757	146	2	property	property	NOUN
american_scientific_journal-757	146	3	of	of	ADP
american_scientific_journal-757	146	4	centriod	centriod	NOUN
american_scientific_journal-757	146	5	of	of	ADP
american_scientific_journal-757	146	6	a	a	DET
american_scientific_journal-757	146	7	triangle	triangle	NOUN
american_scientific_journal-757	146	8	together	together	ADV
american_scientific_journal-757	146	9	with	with	ADP
american_scientific_journal-757	146	10	the	the	DET
american_scientific_journal-757	146	11	method	method	NOUN
american_scientific_journal-757	146	12	of	of	ADP
american_scientific_journal-757	146	13	finding	find	VERB
american_scientific_journal-757	146	14	its	its	PRON
american_scientific_journal-757	146	15	area	area	NOUN
american_scientific_journal-757	146	16	using	use	VERB
american_scientific_journal-757	146	17	the	the	DET
american_scientific_journal-757	146	18	method	method	NOUN
american_scientific_journal-757	146	19	of	of	ADP
american_scientific_journal-757	146	20	determinants	determinant	NOUN
american_scientific_journal-757	146	21	provides	provide	VERB
american_scientific_journal-757	146	22	the	the	DET
american_scientific_journal-757	146	23	present	present	ADJ
american_scientific_journal-757	146	24	method	method	NOUN
american_scientific_journal-757	146	25	.	.	PUNCT
american_scientific_journal-757	147	1	despite	despite	SCONJ
american_scientific_journal-757	147	2	the	the	DET
american_scientific_journal-757	147	3	restriction	restriction	NOUN
american_scientific_journal-757	147	4	of	of	ADP
american_scientific_journal-757	147	5	orientation	orientation	NOUN
american_scientific_journal-757	147	6	stated	state	VERB
american_scientific_journal-757	147	7	in	in	ADP
american_scientific_journal-757	147	8	remark1	remark1	NOUN
american_scientific_journal-757	147	9	above	above	ADV
american_scientific_journal-757	147	10	,	,	PUNCT
american_scientific_journal-757	147	11	the	the	DET
american_scientific_journal-757	147	12	formulas	formula	NOUN
american_scientific_journal-757	147	13	and	and	CCONJ
american_scientific_journal-757	147	14	procedure	procedure	NOUN
american_scientific_journal-757	147	15	we	we	PRON
american_scientific_journal-757	147	16	were	be	AUX
american_scientific_journal-757	147	17	drive	drive	VERB
american_scientific_journal-757	147	18	remain	remain	VERB
american_scientific_journal-757	147	19	valid	valid	ADJ
american_scientific_journal-757	147	20	for	for	ADP
american_scientific_journal-757	147	21	all	all	DET
american_scientific_journal-757	147	22	triangles	triangle	NOUN
american_scientific_journal-757	147	23	and	and	CCONJ
american_scientific_journal-757	147	24	parallelograms	parallelogram	NOUN
american_scientific_journal-757	147	25	.	.	PUNCT
american_scientific_journal-757	148	1	the	the	DET
american_scientific_journal-757	148	2	method	method	NOUN
american_scientific_journal-757	148	3	can	can	AUX
american_scientific_journal-757	148	4	also	also	ADV
american_scientific_journal-757	148	5	be	be	AUX
american_scientific_journal-757	148	6	used	use	VERB
american_scientific_journal-757	148	7	to	to	PART
american_scientific_journal-757	148	8	find	find	VERB
american_scientific_journal-757	148	9	the	the	DET
american_scientific_journal-757	148	10	area	area	NOUN
american_scientific_journal-757	148	11	of	of	ADP
american_scientific_journal-757	148	12	any	any	DET
american_scientific_journal-757	148	13	polygon	polygon	NOUN
american_scientific_journal-757	148	14	by	by	ADP
american_scientific_journal-757	148	15	partitioning	partition	VERB
american_scientific_journal-757	148	16	it	it	PRON
american_scientific_journal-757	148	17	into	into	ADP
american_scientific_journal-757	148	18	a	a	DET
american_scientific_journal-757	148	19	number	number	NOUN
american_scientific_journal-757	148	20	of	of	ADP
american_scientific_journal-757	148	21	triangles	triangle	NOUN
american_scientific_journal-757	148	22	having	have	VERB
american_scientific_journal-757	148	23	common	common	ADJ
american_scientific_journal-757	148	24	vertex	vertex	NOUN
american_scientific_journal-757	148	25	.	.	PUNCT
american_scientific_journal-757	149	1	the	the	DET
american_scientific_journal-757	149	2	new	new	ADJ
american_scientific_journal-757	149	3	approach	approach	NOUN
american_scientific_journal-757	149	4	given	give	VERB
american_scientific_journal-757	149	5	in	in	ADP
american_scientific_journal-757	149	6	this	this	DET
american_scientific_journal-757	149	7	article	article	NOUN
american_scientific_journal-757	149	8	provides	provide	VERB
american_scientific_journal-757	149	9	a	a	DET
american_scientific_journal-757	149	10	more	more	ADV
american_scientific_journal-757	149	11	convenient	convenient	ADJ
american_scientific_journal-757	149	12	and	and	CCONJ
american_scientific_journal-757	149	13	a	a	DET
american_scientific_journal-757	149	14	very	very	ADV
american_scientific_journal-757	149	15	efficient	efficient	ADJ
american_scientific_journal-757	149	16	method	method	NOUN
american_scientific_journal-757	149	17	for	for	ADP
american_scientific_journal-757	149	18	calculating	calculate	VERB
american_scientific_journal-757	149	19	the	the	DET
american_scientific_journal-757	149	20	area	area	NOUN
american_scientific_journal-757	149	21	,	,	PUNCT
american_scientific_journal-757	149	22	as	as	SCONJ
american_scientific_journal-757	149	23	it	it	PRON
american_scientific_journal-757	149	24	uses	use	VERB
american_scientific_journal-757	149	25	coordinates	coordinate	NOUN
american_scientific_journal-757	149	26	of	of	ADP
american_scientific_journal-757	149	27	vertices	vertex	NOUN
american_scientific_journal-757	149	28	of	of	ADP
american_scientific_journal-757	149	29	the	the	DET
american_scientific_journal-757	149	30	triangle	triangle	NOUN
american_scientific_journal-757	149	31	and	and	CCONJ
american_scientific_journal-757	149	32	simple	simple	ADJ
american_scientific_journal-757	149	33	operations	operation	NOUN
american_scientific_journal-757	149	34	of	of	ADP
american_scientific_journal-757	149	35	addition	addition	NOUN
american_scientific_journal-757	149	36	and	and	CCONJ
american_scientific_journal-757	149	37	multiplication	multiplication	NOUN
american_scientific_journal-757	149	38	of	of	ADP
american_scientific_journal-757	149	39	those	those	DET
american_scientific_journal-757	149	40	coordinates	coordinate	NOUN
american_scientific_journal-757	149	41	.	.	PUNCT
american_scientific_journal-757	150	1	hence	hence	ADV
american_scientific_journal-757	150	2	this	this	DET
american_scientific_journal-757	150	3	method	method	NOUN
american_scientific_journal-757	150	4	is	be	AUX
american_scientific_journal-757	150	5	recommended	recommend	VERB
american_scientific_journal-757	150	6	for	for	ADP
american_scientific_journal-757	150	7	solving	solve	VERB
american_scientific_journal-757	150	8	areas	area	NOUN
american_scientific_journal-757	150	9	of	of	ADP
american_scientific_journal-757	150	10	triangles	triangle	NOUN
american_scientific_journal-757	150	11	,	,	PUNCT
american_scientific_journal-757	150	12	parallelograms	parallelogram	NOUN
american_scientific_journal-757	150	13	and	and	CCONJ
american_scientific_journal-757	150	14	quadrilaterals	quadrilateral	NOUN
american_scientific_journal-757	150	15	displayed	display	VERB
american_scientific_journal-757	150	16	in	in	ADP
american_scientific_journal-757	150	17	two	two	NUM
american_scientific_journal-757	150	18	dimensions	dimension	NOUN
american_scientific_journal-757	150	19	.	.	PUNCT
american_scientific_journal-757	151	1	future	future	ADJ
american_scientific_journal-757	151	2	works	work	VERB
american_scientific_journal-757	151	3	to	to	PART
american_scientific_journal-757	151	4	be	be	AUX
american_scientific_journal-757	151	5	done	do	VERB
american_scientific_journal-757	151	6	by	by	ADP
american_scientific_journal-757	151	7	other	other	ADJ
american_scientific_journal-757	151	8	researchers	researcher	NOUN
american_scientific_journal-757	151	9	may	may	AUX
american_scientific_journal-757	151	10	be	be	AUX
american_scientific_journal-757	151	11	finding	find	VERB
american_scientific_journal-757	151	12	the	the	DET
american_scientific_journal-757	151	13	area	area	NOUN
american_scientific_journal-757	151	14	of	of	ADP
american_scientific_journal-757	151	15	a	a	DET
american_scientific_journal-757	151	16	triangle	triangle	NOUN
american_scientific_journal-757	151	17	in	in	ADP
american_scientific_journal-757	151	18	three	three	NUM
american_scientific_journal-757	151	19	dimensions	dimension	NOUN
american_scientific_journal-757	151	20	.	.	PUNCT
american_scientific_journal-757	152	1	i.e.	i.e.	X
american_scientific_journal-757	152	2	extending	extend	VERB
american_scientific_journal-757	152	3	the	the	DET
american_scientific_journal-757	152	4	formula	formula	NOUN
american_scientific_journal-757	152	5	derived	derive	VERB
american_scientific_journal-757	152	6	here	here	ADV
american_scientific_journal-757	152	7	for	for	ADP
american_scientific_journal-757	152	8	triangles	triangle	NOUN
american_scientific_journal-757	152	9	in	in	ADP
american_scientific_journal-757	152	10	space	space	NOUN
american_scientific_journal-757	152	11	.	.	PUNCT
american_scientific_journal-757	153	1	acknowledgements	acknowledgement	NOUN
american_scientific_journal-757	153	2	i	i	PRON
american_scientific_journal-757	153	3	wish	wish	VERB
american_scientific_journal-757	153	4	to	to	PART
american_scientific_journal-757	153	5	thank	thank	VERB
american_scientific_journal-757	153	6	oda	oda	PROPN
american_scientific_journal-757	153	7	jemal	jemal	ADJ
american_scientific_journal-757	153	8	and	and	CCONJ
american_scientific_journal-757	153	9	meseret	meseret	ADJ
american_scientific_journal-757	153	10	tesfaye	tesfaye	NOUN
american_scientific_journal-757	153	11	for	for	ADP
american_scientific_journal-757	153	12	their	their	PRON
american_scientific_journal-757	153	13	consistent	consistent	ADJ
american_scientific_journal-757	153	14	encouragement	encouragement	NOUN
american_scientific_journal-757	153	15	through	through	ADP
american_scientific_journal-757	153	16	the	the	DET
american_scientific_journal-757	153	17	whole	whole	ADJ
american_scientific_journal-757	153	18	study	study	NOUN
american_scientific_journal-757	153	19	.	.	PUNCT
american_scientific_journal-757	154	1	my	my	PRON
american_scientific_journal-757	154	2	thanks	thank	NOUN
american_scientific_journal-757	154	3	go	go	VERB
american_scientific_journal-757	154	4	also	also	ADV
american_scientific_journal-757	154	5	to	to	ADP
american_scientific_journal-757	154	6	gedefa	gedefa	PROPN
american_scientific_journal-757	154	7	adunya	adunya	ADJ
american_scientific_journal-757	154	8	,	,	PUNCT
american_scientific_journal-757	154	9	asnake	asnake	PROPN
american_scientific_journal-757	154	10	imana	imana	PROPN
american_scientific_journal-757	154	11	,	,	PUNCT
american_scientific_journal-757	154	12	adunya	adunya	PROPN
american_scientific_journal-757	154	13	fita	fita	PROPN
american_scientific_journal-757	154	14	and	and	CCONJ
american_scientific_journal-757	154	15	zewdu	zewdu	PROPN
american_scientific_journal-757	154	16	asnake	asnake	PROPN
american_scientific_journal-757	154	17	who	who	PRON
american_scientific_journal-757	154	18	give	give	VERB
american_scientific_journal-757	154	19	me	i	PRON
american_scientific_journal-757	154	20	invaluable	invaluable	ADJ
american_scientific_journal-757	154	21	suggestions	suggestion	NOUN
american_scientific_journal-757	154	22	.	.	PUNCT
american_scientific_journal-757	155	1	references	reference	NOUN
american_scientific_journal-757	155	2	[	[	X
american_scientific_journal-757	155	3	1	1	NUM
american_scientific_journal-757	155	4	]	]	X
american_scientific_journal-757	155	5	laurie	laurie	PROPN
american_scientific_journal-757	155	6	e.	e.	PROPN
american_scientific_journal-757	155	7	bass	bass	PROPN
american_scientific_journal-757	155	8	,	,	PUNCT
american_scientific_journal-757	155	9	charles	charles	PROPN
american_scientific_journal-757	155	10	,	,	PUNCT
american_scientific_journal-757	155	11	basia	basia	PROPN
american_scientific_journal-757	155	12	r.	r.	PROPN
american_scientific_journal-757	155	13	hall	hall	PROPN
american_scientific_journal-757	155	14	,	,	PUNCT
american_scientific_journal-757	155	15	art	art	PROPN
american_scientific_journal-757	155	16	johnson	johnson	PROPN
american_scientific_journal-757	155	17	,	,	PUNCT
american_scientific_journal-757	155	18	and	and	CCONJ
american_scientific_journal-757	155	19	kennedy	kennedy	PROPN
american_scientific_journal-757	155	20	,	,	PUNCT
american_scientific_journal-757	155	21	pretice	pretice	PROPN
american_scientific_journal-757	155	22	hall	hall	NOUN
american_scientific_journal-757	155	23	mathematics	mathematic	NOUN
american_scientific_journal-757	155	24	:	:	PUNCT
american_scientific_journal-757	155	25	geometry	geometry	NOUN
american_scientific_journal-757	155	26	.	.	PUNCT
american_scientific_journal-757	156	1	usa	usa	PROPN
american_scientific_journal-757	156	2	,	,	PUNCT
american_scientific_journal-757	156	3	boston	boston	PROPN
american_scientific_journal-757	156	4	:	:	PUNCT
american_scientific_journal-757	156	5	pearson	pearson	PROPN
american_scientific_journal-757	156	6	prentice	prentice	PROPN
american_scientific_journal-757	156	7	hall	hall	PROPN
american_scientific_journal-757	156	8	.	.	PUNCT
american_scientific_journal-757	157	1	(	(	PUNCT
american_scientific_journal-757	157	2	2007	2007	NUM
american_scientific_journal-757	157	3	)	)	PUNCT
american_scientific_journal-757	157	4	,	,	PUNCT
american_scientific_journal-757	157	5	535	535	NUM
american_scientific_journal-757	157	6	-	-	SYM
american_scientific_journal-757	157	7	538,549,560	538,549,560	NUM
american_scientific_journal-757	157	8	-	-	PUNCT
american_scientific_journal-757	157	9	561	561	NUM
american_scientific_journal-757	158	1	[	[	X
american_scientific_journal-757	158	2	2	2	X
american_scientific_journal-757	158	3	]	]	X
american_scientific_journal-757	158	4	r.s	r.s	PROPN
american_scientific_journal-757	158	5	.	.	PROPN
american_scientific_journal-757	158	6	john	john	PROPN
american_scientific_journal-757	158	7	,	,	PUNCT
american_scientific_journal-757	158	8	geometry	geometry	NOUN
american_scientific_journal-757	158	9	:	:	PUNCT
american_scientific_journal-757	158	10	ancient	ancient	ADJ
american_scientific_journal-757	158	11	&	&	CCONJ
american_scientific_journal-757	158	12	modern	modern	ADJ
american_scientific_journal-757	158	13	.	.	PUNCT
american_scientific_journal-757	159	1	new	new	PROPN
american_scientific_journal-757	159	2	york	york	PROPN
american_scientific_journal-757	159	3	:	:	PUNCT
american_scientific_journal-757	159	4	oxford	oxford	PROPN
american_scientific_journal-757	159	5	university	university	PROPN
american_scientific_journal-757	159	6	press	press	PROPN
american_scientific_journal-757	159	7	inc	inc	PROPN
american_scientific_journal-757	159	8	.	.	PROPN
american_scientific_journal-757	159	9	(	(	PUNCT
american_scientific_journal-757	159	10	2007	2007	NUM
american_scientific_journal-757	159	11	)	)	PUNCT
american_scientific_journal-757	159	12	,	,	PUNCT
american_scientific_journal-757	159	13	62	62	NUM
american_scientific_journal-757	159	14	.	.	PUNCT
american_scientific_journal-757	160	1	[	[	X
american_scientific_journal-757	160	2	3	3	X
american_scientific_journal-757	160	3	]	]	X
american_scientific_journal-757	160	4	r.	r.	PROPN
american_scientific_journal-757	160	5	john	john	PROPN
american_scientific_journal-757	160	6	,	,	PUNCT
american_scientific_journal-757	160	7	elementary	elementary	ADJ
american_scientific_journal-757	160	8	geometry	geometry	NOUN
american_scientific_journal-757	160	9	(	(	PUNCT
american_scientific_journal-757	160	10	1st	1st	ADJ
american_scientific_journal-757	160	11	edition	edition	NOUN
american_scientific_journal-757	160	12	)	)	PUNCT
american_scientific_journal-757	160	13	oxford	oxford	PROPN
american_scientific_journal-757	160	14	:	:	PUNCT
american_scientific_journal-757	160	15	oxford	oxford	PROPN
american_scientific_journal-757	160	16	university	university	PROPN
american_scientific_journal-757	160	17	press	press	PROPN
american_scientific_journal-757	160	18	inc	inc	PROPN
american_scientific_journal-757	160	19	.	.	PROPN
american_scientific_journal-757	160	20	,	,	PUNCT
american_scientific_journal-757	160	21	(	(	PUNCT
american_scientific_journal-757	160	22	1993	1993	NUM
american_scientific_journal-757	160	23	)	)	PUNCT
american_scientific_journal-757	160	24	.	.	PUNCT
american_scientific_journal-757	161	1	195	195	NUM
american_scientific_journal-757	161	2	-	-	SYM
american_scientific_journal-757	161	3	197	197	NUM
american_scientific_journal-757	161	4	[	[	SYM
american_scientific_journal-757	161	5	4	4	NUM
american_scientific_journal-757	161	6	]	]	PUNCT
american_scientific_journal-757	161	7	c.	c.	PROPN
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american_scientific_journal-757	161	9	,	,	PUNCT
american_scientific_journal-757	161	10	g.	g.	PROPN
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american_scientific_journal-757	161	12	,	,	PUNCT
american_scientific_journal-757	161	13	&	&	CCONJ
american_scientific_journal-757	161	14	w.	w.	PROPN
american_scientific_journal-757	161	15	john	john	PROPN
american_scientific_journal-757	161	16	,	,	PUNCT
american_scientific_journal-757	161	17	geometry	geometry	NOUN
american_scientific_journal-757	161	18	:	:	PUNCT
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american_scientific_journal-757	161	20	:	:	PUNCT
american_scientific_journal-757	161	21	houghton	houghton	PROPN
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american_scientific_journal-757	161	24	.	.	PUNCT
american_scientific_journal-757	162	1	(	(	PUNCT
american_scientific_journal-757	162	2	1985),379	1985),379	NUM
american_scientific_journal-757	162	3	-	-	SYM
american_scientific_journal-757	162	4	390	390	NUM
american_scientific_journal-757	162	5	[	[	X
american_scientific_journal-757	162	6	5	5	NUM
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american_scientific_journal-757	162	8	d.	d.	PROPN
american_scientific_journal-757	162	9	gross	gross	PROPN
american_scientific_journal-757	162	10	,	,	PUNCT
american_scientific_journal-757	162	11	w.	w.	PROPN
american_scientific_journal-757	162	12	hauger	hauger	PROPN
american_scientific_journal-757	162	13	,	,	PUNCT
american_scientific_journal-757	162	14	j.	j.	PROPN
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american_scientific_journal-757	162	16	,	,	PUNCT
american_scientific_journal-757	162	17	wall	wall	PROPN
american_scientific_journal-757	162	18	,	,	PUNCT
american_scientific_journal-757	162	19	w.	w.	PROPN
american_scientific_journal-757	162	20	a.	a.	PROPN
american_scientific_journal-757	162	21	&	&	CCONJ
american_scientific_journal-757	162	22	n.	n.	PROPN
american_scientific_journal-757	162	23	rajapakse	rajapakse	PROPN
american_scientific_journal-757	162	24	,	,	PUNCT
american_scientific_journal-757	162	25	engineering	engineering	NOUN
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american_scientific_journal-757	162	27	i	i	PRON
american_scientific_journal-757	162	28	:	:	PUNCT
american_scientific_journal-757	162	29	statics	statics	PROPN
american_scientific_journal-757	162	30	.	.	PUNCT
american_scientific_journal-757	163	1	new	new	PROPN
american_scientific_journal-757	163	2	york	york	PROPN
american_scientific_journal-757	163	3	:	:	PUNCT
american_scientific_journal-757	163	4	springer	springer	NOUN
american_scientific_journal-757	163	5	.	.	PUNCT
american_scientific_journal-757	164	1	(	(	PUNCT
american_scientific_journal-757	164	2	2009	2009	NUM
american_scientific_journal-757	164	3	)	)	PUNCT
american_scientific_journal-757	164	4	,	,	PUNCT
american_scientific_journal-757	164	5	98	98	NUM
american_scientific_journal-757	164	6	-	-	SYM
american_scientific_journal-757	164	7	107	107	NUM
american_scientific_journal-757	164	8	[	[	X
american_scientific_journal-757	164	9	6	6	NUM
american_scientific_journal-757	164	10	]	]	PUNCT
american_scientific_journal-757	164	11	r.	r.	PROPN
american_scientific_journal-757	164	12	c.	c.	PROPN
american_scientific_journal-757	164	13	hibbeler	hibbeler	PROPN
american_scientific_journal-757	164	14	,	,	PUNCT
american_scientific_journal-757	164	15	engineering	engineering	NOUN
american_scientific_journal-757	164	16	mechanics	mechanic	NOUN
american_scientific_journal-757	164	17	:	:	PUNCT
american_scientific_journal-757	164	18	statics	statics	PROPN
american_scientific_journal-757	164	19	.	.	PUNCT
american_scientific_journal-757	165	1	(	(	PUNCT
american_scientific_journal-757	165	2	twelfth	twelfth	ADJ
american_scientific_journal-757	165	3	edition	edition	NOUN
american_scientific_journal-757	165	4	)	)	PUNCT
american_scientific_journal-757	165	5	new	new	PROPN
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american_scientific_journal-757	165	7	:	:	PUNCT
american_scientific_journal-757	165	8	pearson	pearson	PROPN
american_scientific_journal-757	165	9	prentice	prentice	PROPN
american_scientific_journal-757	165	10	hall	hall	PROPN
american_scientific_journal-757	165	11	.	.	PUNCT
american_scientific_journal-757	166	1	59	59	NUM
american_scientific_journal-757	166	2	american	american	ADJ
american_scientific_journal-757	166	3	scientific	scientific	ADJ
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american_scientific_journal-757	166	5	journal	journal	NOUN
american_scientific_journal-757	166	6	for	for	ADP
american_scientific_journal-757	166	7	engineering	engineering	NOUN
american_scientific_journal-757	166	8	,	,	PUNCT
american_scientific_journal-757	166	9	technology	technology	NOUN
american_scientific_journal-757	166	10	,	,	PUNCT
american_scientific_journal-757	166	11	and	and	CCONJ
american_scientific_journal-757	166	12	sciences	science	NOUN
american_scientific_journal-757	166	13	(	(	PUNCT
american_scientific_journal-757	166	14	asrjets	asrjet	NOUN
american_scientific_journal-757	166	15	)	)	PUNCT
american_scientific_journal-757	166	16	(	(	PUNCT
american_scientific_journal-757	166	17	2015	2015	NUM
american_scientific_journal-757	166	18	)	)	PUNCT
american_scientific_journal-757	166	19	volume	volume	NOUN
american_scientific_journal-757	166	20	13	13	NUM
american_scientific_journal-757	166	21	,	,	PUNCT
american_scientific_journal-757	166	22	no	no	DET
american_scientific_journal-757	166	23	1	1	NUM
american_scientific_journal-757	166	24	,	,	PUNCT
american_scientific_journal-757	166	25	pp	pp	ADV
american_scientific_journal-757	166	26	49	49	NUM
american_scientific_journal-757	166	27	-	-	SYM
american_scientific_journal-757	166	28	60	60	NUM
american_scientific_journal-757	166	29	(	(	PUNCT
american_scientific_journal-757	166	30	2010	2010	NUM
american_scientific_journal-757	166	31	)	)	PUNCT
american_scientific_journal-757	166	32	,	,	PUNCT
american_scientific_journal-757	166	33	455	455	NUM
american_scientific_journal-757	167	1	[	[	X
american_scientific_journal-757	167	2	7	7	X
american_scientific_journal-757	167	3	]	]	PUNCT
american_scientific_journal-757	167	4	roland	roland	PROPN
american_scientific_journal-757	167	5	e.	e.	PROPN
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american_scientific_journal-757	167	7	,	,	PUNCT
american_scientific_journal-757	167	8	laura	laura	PROPN
american_scientific_journal-757	167	9	boswell	boswell	PROPN
american_scientific_journal-757	167	10	,	,	PUNCT
american_scientific_journal-757	167	11	and	and	CCONJ
american_scientific_journal-757	167	12	lee	lee	PROPN
american_scientific_journal-757	167	13	stiff	stiff	PROPN
american_scientific_journal-757	167	14	,	,	PUNCT
american_scientific_journal-757	167	15	geometry	geometry	NOUN
american_scientific_journal-757	167	16	:	:	PUNCT
american_scientific_journal-757	167	17	an	an	DET
american_scientific_journal-757	167	18	integrated	integrated	ADJ
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american_scientific_journal-757	167	20	.	.	PUNCT
american_scientific_journal-757	168	1	usa	usa	PROPN
american_scientific_journal-757	168	2	,	,	PUNCT
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american_scientific_journal-757	168	4	,	,	PUNCT
american_scientific_journal-757	168	5	mcdougal	mcdougal	PROPN
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american_scientific_journal-757	168	7	tell	tell	PROPN
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american_scientific_journal-757	168	9	.	.	PROPN
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american_scientific_journal-757	168	14	heath	heath	PROPN
american_scientific_journal-757	168	15	and	and	CCONJ
american_scientific_journal-757	168	16	company.(1998	company.(1998	NOUN
american_scientific_journal-757	168	17	)	)	PUNCT
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american_scientific_journal-757	168	19	-	-	PUNCT
american_scientific_journal-757	168	20	544,553	544,553	NUM
american_scientific_journal-757	168	21	[	[	NOUN
american_scientific_journal-757	168	22	8	8	NUM
american_scientific_journal-757	168	23	]	]	PUNCT
american_scientific_journal-757	168	24	earl	earl	PROPN
american_scientific_journal-757	168	25	w.	w.	PROPN
american_scientific_journal-757	168	26	swokowski	swokowski	PROPN
american_scientific_journal-757	168	27	,	,	PUNCT
american_scientific_journal-757	168	28	jeffery	jeffery	PROPN
american_scientific_journal-757	168	29	a.	a.	PROPN
american_scientific_journal-757	168	30	cole	cole	PROPN
american_scientific_journal-757	168	31	,	,	PUNCT
american_scientific_journal-757	168	32	fundamentals	fundamental	NOUN
american_scientific_journal-757	168	33	of	of	ADP
american_scientific_journal-757	168	34	trigonometry	trigonometry	NOUN
american_scientific_journal-757	168	35	,	,	PUNCT
american_scientific_journal-757	168	36	eighth	eighth	PROPN
american_scientific_journal-757	168	37	edition	edition	PROPN
american_scientific_journal-757	168	38	,	,	PUNCT
american_scientific_journal-757	168	39	usa	usa	PROPN
american_scientific_journal-757	168	40	,	,	PUNCT
american_scientific_journal-757	168	41	boston	boston	PROPN
american_scientific_journal-757	168	42	:	:	PUNCT
american_scientific_journal-757	168	43	pwskenr	pwskenr	PROPN
american_scientific_journal-757	168	44	publishing	publishing	PROPN
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american_scientific_journal-757	168	46	.	.	PUNCT
american_scientific_journal-757	169	1	(	(	PUNCT
american_scientific_journal-757	169	2	1955	1955	NUM
american_scientific_journal-757	169	3	)	)	PUNCT
american_scientific_journal-757	169	4	,	,	PUNCT
american_scientific_journal-757	169	5	234	234	NUM
american_scientific_journal-757	169	6	-	-	SYM
american_scientific_journal-757	169	7	235	235	NUM
american_scientific_journal-757	170	1	[	[	SYM
american_scientific_journal-757	170	2	9	9	NUM
american_scientific_journal-757	170	3	]	]	X
american_scientific_journal-757	170	4	barnett	barnett	PROPN
american_scientific_journal-757	170	5	rich	rich	ADJ
american_scientific_journal-757	170	6	,	,	PUNCT
american_scientific_journal-757	170	7	revised	revise	VERB
american_scientific_journal-757	170	8	by	by	ADP
american_scientific_journal-757	170	9	philip	philip	PROPN
american_scientific_journal-757	170	10	a.	a.	PROPN
american_scientific_journal-757	170	11	schmidt	schmidt	PROPN
american_scientific_journal-757	170	12	,	,	PUNCT
american_scientific_journal-757	170	13	theory	theory	NOUN
american_scientific_journal-757	170	14	and	and	CCONJ
american_scientific_journal-757	170	15	problems	problem	NOUN
american_scientific_journal-757	170	16	of	of	ADP
american_scientific_journal-757	170	17	geometry	geometry	NOUN
american_scientific_journal-757	170	18	:	:	PUNCT
american_scientific_journal-757	170	19	shaum`s	shaum`s	X
american_scientific_journal-757	170	20	outline	outline	NOUN
american_scientific_journal-757	170	21	series	series	NOUN
american_scientific_journal-757	170	22	,	,	PUNCT
american_scientific_journal-757	170	23	includes	include	VERB
american_scientific_journal-757	170	24	plane	plane	NOUN
american_scientific_journal-757	170	25	,	,	PUNCT
american_scientific_journal-757	170	26	analytic	analytic	ADJ
american_scientific_journal-757	170	27	,	,	PUNCT
american_scientific_journal-757	170	28	transformation	transformation	NOUN
american_scientific_journal-757	170	29	,	,	PUNCT
american_scientific_journal-757	170	30	and	and	CCONJ
american_scientific_journal-757	170	31	solid	solid	ADJ
american_scientific_journal-757	170	32	geometry	geometry	NOUN
american_scientific_journal-757	170	33	,	,	PUNCT
american_scientific_journal-757	170	34	new	new	PROPN
american_scientific_journal-757	170	35	york	york	PROPN
american_scientific_journal-757	170	36	:	:	PUNCT
american_scientific_journal-757	170	37	mcgraw	mcgraw	NOUN
american_scientific_journal-757	170	38	-	-	PUNCT
american_scientific_journal-757	170	39	hall	hall	PROPN
american_scientific_journal-757	170	40	,	,	PUNCT
american_scientific_journal-757	170	41	inc	inc	PROPN
american_scientific_journal-757	170	42	.	.	PROPN
american_scientific_journal-757	170	43	(	(	PUNCT
american_scientific_journal-757	170	44	1989	1989	NUM
american_scientific_journal-757	170	45	)	)	PUNCT
american_scientific_journal-757	171	1	[	[	X
american_scientific_journal-757	171	2	10	10	NUM
american_scientific_journal-757	171	3	]	]	X
american_scientific_journal-757	171	4	r.	r.	PROPN
american_scientific_journal-757	171	5	david	david	PROPN
american_scientific_journal-757	171	6	gustafson	gustafson	PROPN
american_scientific_journal-757	171	7	,	,	PUNCT
american_scientific_journal-757	171	8	peter	peter	PROPN
american_scientific_journal-757	171	9	d.	d.	PROPN
american_scientific_journal-757	171	10	frisk	frisk	PROPN
american_scientific_journal-757	171	11	,	,	PUNCT
american_scientific_journal-757	171	12	plane	plane	NOUN
american_scientific_journal-757	171	13	trigonometry	trigonometry	NOUN
american_scientific_journal-757	171	14	.	.	PUNCT
american_scientific_journal-757	172	1	third	third	PROPN
american_scientific_journal-757	172	2	edition	edition	PROPN
american_scientific_journal-757	172	3	,	,	PUNCT
american_scientific_journal-757	172	4	usa	usa	PROPN
american_scientific_journal-757	172	5	,	,	PUNCT
american_scientific_journal-757	172	6	california	california	PROPN
american_scientific_journal-757	172	7	:	:	PUNCT
american_scientific_journal-757	172	8	brooks	brooks	PROPN
american_scientific_journal-757	172	9	/	/	SYM
american_scientific_journal-757	172	10	cole	cole	PROPN
american_scientific_journal-757	172	11	publishing	publishing	PROPN
american_scientific_journal-757	172	12	company	company	NOUN
american_scientific_journal-757	172	13	pacific	pacific	PROPN
american_scientific_journal-757	172	14	grove	grove	PROPN
american_scientific_journal-757	172	15	.	.	PUNCT
american_scientific_journal-757	173	1	(	(	PUNCT
american_scientific_journal-757	173	2	1989	1989	NUM
american_scientific_journal-757	173	3	)	)	PUNCT
american_scientific_journal-757	173	4	,	,	PUNCT
american_scientific_journal-757	173	5	222	222	NUM
american_scientific_journal-757	173	6	-	-	SYM
american_scientific_journal-757	173	7	227	227	NUM
american_scientific_journal-757	173	8	[	[	PUNCT
american_scientific_journal-757	173	9	11	11	NUM
american_scientific_journal-757	173	10	]	]	X
american_scientific_journal-757	173	11	laurie	laurie	PROPN
american_scientific_journal-757	173	12	e.	e.	PROPN
american_scientific_journal-757	173	13	bass	bass	PROPN
american_scientific_journal-757	173	14	,	,	PUNCT
american_scientific_journal-757	173	15	basia	basia	PROPN
american_scientific_journal-757	173	16	r.	r.	PROPN
american_scientific_journal-757	173	17	hall	hall	PROPN
american_scientific_journal-757	173	18	,	,	PUNCT
american_scientific_journal-757	173	19	art	art	PROPN
american_scientific_journal-757	173	20	johnson	johnson	PROPN
american_scientific_journal-757	173	21	,	,	PUNCT
american_scientific_journal-757	173	22	and	and	CCONJ
american_scientific_journal-757	173	23	dorothy	dorothy	PROPN
american_scientific_journal-757	173	24	f.	f.	PROPN
american_scientific_journal-757	173	25	wood	wood	PROPN
american_scientific_journal-757	173	26	,	,	PUNCT
american_scientific_journal-757	173	27	contributed	contribute	VERB
american_scientific_journal-757	173	28	by	by	ADP
american_scientific_journal-757	173	29	simone	simone	PROPN
american_scientific_journal-757	173	30	w.	w.	PROPN
american_scientific_journal-757	173	31	bess	bess	PROPN
american_scientific_journal-757	173	32	,	,	PUNCT
american_scientific_journal-757	173	33	geometry	geometry	NOUN
american_scientific_journal-757	173	34	:	:	PUNCT
american_scientific_journal-757	173	35	texas	texas	PROPN
american_scientific_journal-757	173	36	edition	edition	PROPN
american_scientific_journal-757	173	37	.	.	PUNCT
american_scientific_journal-757	174	1	usa	usa	PROPN
american_scientific_journal-757	174	2	,	,	PUNCT
american_scientific_journal-757	174	3	needham	needham	PROPN
american_scientific_journal-757	174	4	,	,	PUNCT
american_scientific_journal-757	174	5	massachusetts	massachusetts	PROPN
american_scientific_journal-757	174	6	:	:	PUNCT
american_scientific_journal-757	174	7	prentice	prentice	PROPN
american_scientific_journal-757	174	8	hall	hall	PROPN
american_scientific_journal-757	174	9	simon	simon	PROPN
american_scientific_journal-757	174	10	&	&	CCONJ
american_scientific_journal-757	174	11	schusten	schusten	PROPN
american_scientific_journal-757	174	12	education	education	NOUN
american_scientific_journal-757	174	13	group	group	NOUN
american_scientific_journal-757	174	14	.	.	PUNCT
american_scientific_journal-757	175	1	(	(	PUNCT
american_scientific_journal-757	175	2	1998	1998	NUM
american_scientific_journal-757	175	3	)	)	PUNCT
american_scientific_journal-757	175	4	,	,	PUNCT
american_scientific_journal-757	175	5	251	251	NUM
american_scientific_journal-757	175	6	-	-	SYM
american_scientific_journal-757	175	7	254,276,277,294,575	254,276,277,294,575	NUM
american_scientific_journal-757	175	8	-	-	PUNCT
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american_scientific_journal-757	175	10	[	[	X
american_scientific_journal-757	175	11	12	12	NUM
american_scientific_journal-757	175	12	]	]	PUNCT
american_scientific_journal-757	175	13	cindu	cindu	NOUN
american_scientific_journal-757	175	14	j.	j.	PROPN
american_scientific_journal-757	175	15	boyd	boyd	PROPN
american_scientific_journal-757	175	16	,	,	PUNCT
american_scientific_journal-757	175	17	geometry	geometry	NOUN
american_scientific_journal-757	175	18	:	:	PUNCT
american_scientific_journal-757	175	19	integration	integration	NOUN
american_scientific_journal-757	175	20	applications	application	NOUN
american_scientific_journal-757	175	21	connections	connection	NOUN
american_scientific_journal-757	175	22	.	.	PUNCT
american_scientific_journal-757	176	1	texas	texas	PROPN
american_scientific_journal-757	176	2	edition	edition	PROPN
american_scientific_journal-757	176	3	,	,	PUNCT
american_scientific_journal-757	176	4	usa	usa	PROPN
american_scientific_journal-757	176	5	,	,	PUNCT
american_scientific_journal-757	176	6	glencoe	glencoe	PROPN
american_scientific_journal-757	176	7	mcgraw	mcgraw	PROPN
american_scientific_journal-757	176	8	-	-	PUNCT
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american_scientific_journal-757	176	10	.	.	PUNCT
american_scientific_journal-757	177	1	(	(	PUNCT
american_scientific_journal-757	177	2	1998	1998	NUM
american_scientific_journal-757	177	3	)	)	PUNCT
american_scientific_journal-757	177	4	,	,	PUNCT
american_scientific_journal-757	177	5	24,535	24,535	NUM
american_scientific_journal-757	177	6	-	-	SYM
american_scientific_journal-757	177	7	536,538	536,538	NUM
american_scientific_journal-757	177	8	-	-	SYM
american_scientific_journal-757	177	9	540	540	NUM
american_scientific_journal-757	178	1	[	[	SYM
american_scientific_journal-757	178	2	13	13	NUM
american_scientific_journal-757	178	3	]	]	X
american_scientific_journal-757	178	4	rhonda	rhonda	PROPN
american_scientific_journal-757	178	5	baily	baily	PROPN
american_scientific_journal-757	178	6	,	,	PUNCT
american_scientific_journal-757	178	7	roger	roger	PROPN
american_scientific_journal-757	178	8	day	day	PROPN
american_scientific_journal-757	178	9	,	,	PUNCT
american_scientific_journal-757	178	10	patricia	patricia	PROPN
american_scientific_journal-757	178	11	frey	frey	PROPN
american_scientific_journal-757	178	12	,	,	PUNCT
american_scientific_journal-757	178	13	arthur	arthur	PROPN
american_scientific_journal-757	178	14	c.	c.	PROPN
american_scientific_journal-757	178	15	howard	howard	PROPN
american_scientific_journal-757	178	16	,	,	PUNCT
american_scientific_journal-757	178	17	deborah	deborah	PROPN
american_scientific_journal-757	178	18	t.	t.	PROPN
american_scientific_journal-757	178	19	hutchers	hutcher	NOUN
american_scientific_journal-757	178	20	,	,	PUNCT
american_scientific_journal-757	178	21	kay	kay	PROPN
american_scientific_journal-757	178	22	mcclain	mcclain	PROPN
american_scientific_journal-757	178	23	,	,	PUNCT
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american_scientific_journal-757	178	26	harris	harris	PROPN
american_scientific_journal-757	178	27	,	,	PUNCT
american_scientific_journal-757	178	28	jack	jack	PROPN
american_scientific_journal-757	178	29	m.	m.	PROPN
american_scientific_journal-757	178	30	ott	ott	PROPN
american_scientific_journal-757	178	31	,	,	PUNCT
american_scientific_journal-757	178	32	ronald	ronald	PROPN
american_scientific_journal-757	178	33	pelfiney	pelfiney	PROPN
american_scientific_journal-757	178	34	,	,	PUNCT
american_scientific_journal-757	178	35	jack	jack	PROPN
american_scientific_journal-757	178	36	vielholer	vielholer	NOUN
american_scientific_journal-757	178	37	and	and	CCONJ
american_scientific_journal-757	178	38	teri	teri	PROPN
american_scientific_journal-757	178	39	willard	willard	PROPN
american_scientific_journal-757	178	40	,	,	PUNCT
american_scientific_journal-757	178	41	mathematics	mathematic	NOUN
american_scientific_journal-757	178	42	:	:	PUNCT
american_scientific_journal-757	178	43	application	application	NOUN
american_scientific_journal-757	178	44	&	&	CCONJ
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american_scientific_journal-757	178	46	.	.	PUNCT
american_scientific_journal-757	179	1	new	new	PROPN
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american_scientific_journal-757	179	3	,	,	PUNCT
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american_scientific_journal-757	179	5	-	-	PUNCT
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american_scientific_journal-757	179	7	,	,	PUNCT
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american_scientific_journal-757	179	9	.	.	PUNCT
american_scientific_journal-757	180	1	(	(	PUNCT
american_scientific_journal-757	180	2	2005	2005	NUM
american_scientific_journal-757	180	3	)	)	PUNCT
american_scientific_journal-757	180	4	,	,	PUNCT
american_scientific_journal-757	180	5	489	489	NUM
american_scientific_journal-757	181	1	[	[	X
american_scientific_journal-757	181	2	14	14	NUM
american_scientific_journal-757	181	3	]	]	X
american_scientific_journal-757	181	4	paul	paul	PROPN
american_scientific_journal-757	181	5	calter	calter	PROPN
american_scientific_journal-757	181	6	,	,	PUNCT
american_scientific_journal-757	181	7	technical	technical	ADJ
american_scientific_journal-757	181	8	mathematics	mathematic	NOUN
american_scientific_journal-757	181	9	with	with	ADP
american_scientific_journal-757	181	10	calculus	calculus	NOUN
american_scientific_journal-757	181	11	,	,	PUNCT
american_scientific_journal-757	181	12	prentice	prentice	NOUN
american_scientific_journal-757	181	13	hall	hall	PROPN
american_scientific_journal-757	181	14	.	.	PUNCT
american_scientific_journal-757	182	1	englewood	englewood	PROPN
american_scientific_journal-757	182	2	cliffs	cliffs	PROPN
american_scientific_journal-757	182	3	,	,	PUNCT
american_scientific_journal-757	182	4	njo783	njo783	NOUN
american_scientific_journal-757	182	5	(	(	PUNCT
american_scientific_journal-757	182	6	1990	1990	NUM
american_scientific_journal-757	182	7	)	)	PUNCT
american_scientific_journal-757	182	8	,	,	PUNCT
american_scientific_journal-757	182	9	136	136	NUM
american_scientific_journal-757	182	10	-	-	SYM
american_scientific_journal-757	182	11	137	137	NUM
american_scientific_journal-757	183	1	[	[	X
american_scientific_journal-757	183	2	15	15	NUM
american_scientific_journal-757	183	3	]	]	X
american_scientific_journal-757	183	4	dennis	dennis	PROPN
american_scientific_journal-757	183	5	g.	g.	PROPN
american_scientific_journal-757	183	6	zill	zill	PROPN
american_scientific_journal-757	183	7	,	,	PUNCT
american_scientific_journal-757	183	8	jacqueline	jacqueline	PROPN
american_scientific_journal-757	183	9	m.	m.	PROPN
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american_scientific_journal-757	183	11	,	,	PUNCT
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american_scientific_journal-757	183	13	,	,	PUNCT
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american_scientific_journal-757	183	15	edition	edition	NOUN
american_scientific_journal-757	183	16	.	.	PUNCT
american_scientific_journal-757	184	1	new	new	PROPN
american_scientific_journal-757	184	2	york	york	PROPN
american_scientific_journal-757	184	3	,	,	PUNCT
american_scientific_journal-757	184	4	mcgraw	mcgraw	PROPN
american_scientific_journal-757	184	5	-	-	PUNCT
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american_scientific_journal-757	184	7	publishing	publish	VERB
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american_scientific_journal-757	184	9	(	(	PUNCT
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american_scientific_journal-757	184	11	)	)	PUNCT
american_scientific_journal-757	184	12	.	.	PUNCT
american_scientific_journal-757	185	1	122	122	NUM
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american_scientific_journal-757	186	3	]	]	PUNCT
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american_scientific_journal-757	186	5	vygodsky	vygodsky	NOUN
american_scientific_journal-757	186	6	,	,	PUNCT
american_scientific_journal-757	186	7	mathematical	mathematical	ADJ
american_scientific_journal-757	186	8	hand	hand	NOUN
american_scientific_journal-757	186	9	book	book	NOUN
american_scientific_journal-757	186	10	:	:	PUNCT
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american_scientific_journal-757	186	13	.	.	PUNCT
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american_scientific_journal-757	187	2	:	:	PUNCT
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american_scientific_journal-757	187	4	publishers	publisher	NOUN
american_scientific_journal-757	187	5	.	.	PUNCT
american_scientific_journal-757	188	1	(	(	PUNCT
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american_scientific_journal-757	188	3	)	)	PUNCT
american_scientific_journal-757	188	4	,	,	PUNCT
american_scientific_journal-757	188	5	27	27	NUM
american_scientific_journal-757	188	6	-	-	SYM
american_scientific_journal-757	188	7	28	28	NUM
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american_scientific_journal-757	189	3	]	]	PUNCT
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american_scientific_journal-757	189	6	,	,	PUNCT
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american_scientific_journal-757	189	8	of	of	ADP
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american_scientific_journal-757	189	10	&	&	CCONJ
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american_scientific_journal-757	189	12	.	.	PUNCT
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american_scientific_journal-757	190	3	.	.	PUNCT
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american_scientific_journal-757	191	3	:	:	PUNCT
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