id	sid	tid	token	lemma	pos
cana-3334	1	1	communications	communication	NOUN
cana-3334	1	2	on	on	ADP
cana-3334	1	3	applied	apply	VERB
cana-3334	1	4	nonlinear	nonlinear	ADJ
cana-3334	1	5	analysis	analysis	NOUN
cana-3334	1	6	issn	issn	NOUN
cana-3334	1	7	:	:	PUNCT
cana-3334	1	8	1074	1074	NUM
cana-3334	1	9	-	-	PUNCT
cana-3334	1	10	133x	133x	NUM
cana-3334	1	11	vol	vol	NOUN
cana-3334	1	12	32	32	NUM
cana-3334	1	13	no	no	NOUN
cana-3334	1	14	.	.	PUNCT
cana-3334	2	1	7s	7	NOUN
cana-3334	2	2	(	(	PUNCT
cana-3334	2	3	2025	2025	NUM
cana-3334	2	4	)	)	PUNCT
cana-3334	2	5	1	1	NUM
cana-3334	2	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-3334	2	7	diophantine	diophantine	NOUN
cana-3334	2	8	kites	kite	VERB
cana-3334	2	9	:	:	PUNCT
cana-3334	2	10	rational	rational	ADJ
cana-3334	2	11	diagonals	diagonal	NOUN
cana-3334	2	12	and	and	CCONJ
cana-3334	2	13	integer	integer	NOUN
cana-3334	2	14	area	area	NOUN
cana-3334	2	15	constructions	construction	NOUN
cana-3334	2	16	1	1	NUM
cana-3334	2	17	m.	m.	NOUN
cana-3334	2	18	mahalakshmi	mahalakshmi	PROPN
cana-3334	2	19	,	,	PUNCT
cana-3334	2	20	*	*	NOUN
cana-3334	2	21	2j	2j	NOUN
cana-3334	2	22	.	.	PUNCT
cana-3334	3	1	kannan	kannan	PROPN
cana-3334	3	2	,	,	PUNCT
cana-3334	3	3	3a	3a	NUM
cana-3334	3	4	.	.	PUNCT
cana-3334	3	5	deepshika	deepshika	PROPN
cana-3334	3	6	,	,	PUNCT
cana-3334	3	7	4manju	4manju	NUM
cana-3334	3	8	somanath	somanath	NOUN
cana-3334	3	9	,	,	PUNCT
cana-3334	3	10	5p	5p	NUM
cana-3334	3	11	.	.	PUNCT
cana-3334	4	1	vijaya	vijaya	PROPN
cana-3334	4	2	shanthi	shanthi	PROPN
cana-3334	4	3	and	and	CCONJ
cana-3334	4	4	6k	6k	PROPN
cana-3334	4	5	.	.	PUNCT
cana-3334	5	1	kaleeswari	kaleeswari	PROPN
cana-3334	5	2	1,3,6ph.d	1,3,6ph.d	NUM
cana-3334	5	3	.	.	PUNCT
cana-3334	5	4	research	research	NOUN
cana-3334	5	5	scholar	scholar	NOUN
cana-3334	5	6	,	,	PUNCT
cana-3334	5	7	department	department	NOUN
cana-3334	5	8	of	of	ADP
cana-3334	5	9	mathematics	mathematics	PROPN
cana-3334	5	10	,	,	PUNCT
cana-3334	5	11	ayya	ayya	PROPN
cana-3334	5	12	nadar	nadar	PROPN
cana-3334	5	13	janaki	janaki	PROPN
cana-3334	5	14	ammal	ammal	PROPN
cana-3334	5	15	college	college	PROPN
cana-3334	5	16	(	(	PUNCT
cana-3334	5	17	autonomous	autonomous	ADJ
cana-3334	5	18	,	,	PUNCT
cana-3334	5	19	affiliated	affiliate	VERB
cana-3334	5	20	to	to	PART
cana-3334	5	21	madurai	madurai	VERB
cana-3334	5	22	kamaraj	kamaraj	ADJ
cana-3334	5	23	university	university	NOUN
cana-3334	5	24	)	)	PUNCT
cana-3334	5	25	,	,	PUNCT
cana-3334	5	26	sivakasi	sivakasi	NOUN
cana-3334	5	27	–	–	PUNCT
cana-3334	5	28	626124	626124	NUM
cana-3334	5	29	,	,	PUNCT
cana-3334	5	30	tamil	tamil	PROPN
cana-3334	5	31	nadu	nadu	PROPN
cana-3334	5	32	,	,	PUNCT
cana-3334	5	33	india	india	PROPN
cana-3334	5	34	.	.	PUNCT
cana-3334	6	1	2assistant	2assistant	NUM
cana-3334	6	2	professor	professor	NOUN
cana-3334	6	3	,	,	PUNCT
cana-3334	6	4	department	department	NOUN
cana-3334	6	5	of	of	ADP
cana-3334	6	6	mathematics	mathematics	PROPN
cana-3334	6	7	,	,	PUNCT
cana-3334	6	8	ayya	ayya	PROPN
cana-3334	6	9	nadar	nadar	PROPN
cana-3334	6	10	janaki	janaki	PROPN
cana-3334	6	11	ammal	ammal	PROPN
cana-3334	6	12	college	college	PROPN
cana-3334	6	13	(	(	PUNCT
cana-3334	6	14	autonomous	autonomous	ADJ
cana-3334	6	15	,	,	PUNCT
cana-3334	6	16	affiliated	affiliate	VERB
cana-3334	6	17	to	to	PART
cana-3334	6	18	madurai	madurai	VERB
cana-3334	6	19	kamaraj	kamaraj	ADJ
cana-3334	6	20	university	university	NOUN
cana-3334	6	21	)	)	PUNCT
cana-3334	6	22	,	,	PUNCT
cana-3334	6	23	sivakasi	sivakasi	NOUN
cana-3334	6	24	–	–	PUNCT
cana-3334	6	25	626124	626124	NUM
cana-3334	6	26	,	,	PUNCT
cana-3334	6	27	tamil	tamil	PROPN
cana-3334	6	28	nadu	nadu	PROPN
cana-3334	6	29	,	,	PUNCT
cana-3334	6	30	india	india	PROPN
cana-3334	6	31	.	.	PUNCT
cana-3334	7	1	4associate	4associate	NUM
cana-3334	7	2	professor	professor	NOUN
cana-3334	7	3	,	,	PUNCT
cana-3334	7	4	pg	pg	NOUN
cana-3334	7	5	and	and	CCONJ
cana-3334	7	6	research	research	PROPN
cana-3334	7	7	department	department	PROPN
cana-3334	7	8	of	of	ADP
cana-3334	7	9	mathematics	mathematics	PROPN
cana-3334	7	10	,	,	PUNCT
cana-3334	7	11	national	national	PROPN
cana-3334	7	12	college	college	PROPN
cana-3334	7	13	(	(	PUNCT
cana-3334	7	14	autonomous	autonomous	ADJ
cana-3334	7	15	,	,	PUNCT
cana-3334	7	16	affiliated	affiliate	VERB
cana-3334	7	17	to	to	PART
cana-3334	7	18	bharathidasan	bharathidasan	VERB
cana-3334	7	19	university	university	NOUN
cana-3334	7	20	)	)	PUNCT
cana-3334	7	21	,	,	PUNCT
cana-3334	7	22	trichy	trichy	NOUN
cana-3334	7	23	–	–	PUNCT
cana-3334	7	24	620	620	NUM
cana-3334	7	25	001	001	NUM
cana-3334	7	26	,	,	PUNCT
cana-3334	7	27	tamil	tamil	PROPN
cana-3334	7	28	nadu	nadu	PROPN
cana-3334	7	29	,	,	PUNCT
cana-3334	7	30	india	india	PROPN
cana-3334	7	31	.	.	PUNCT
cana-3334	8	1	5assistant	5assistant	NUM
cana-3334	8	2	professor	professor	NOUN
cana-3334	8	3	,	,	PUNCT
cana-3334	8	4	pg	pg	PROPN
cana-3334	8	5	and	and	CCONJ
cana-3334	8	6	researh	researh	VERB
cana-3334	8	7	department	department	NOUN
cana-3334	8	8	of	of	ADP
cana-3334	8	9	mathematics	mathematic	NOUN
cana-3334	8	10	,	,	PUNCT
cana-3334	8	11	a.p.c	a.p.c	PROPN
cana-3334	8	12	.	.	PUNCT
cana-3334	8	13	mahalaxmi	mahalaxmi	PROPN
cana-3334	8	14	college	college	NOUN
cana-3334	8	15	for	for	ADP
cana-3334	8	16	women	woman	NOUN
cana-3334	8	17	(	(	PUNCT
cana-3334	8	18	affiliated	affiliate	VERB
cana-3334	8	19	to	to	ADP
cana-3334	8	20	manonmaniam	manonmaniam	PROPN
cana-3334	8	21	sundaranar	sundaranar	PROPN
cana-3334	8	22	university	university	PROPN
cana-3334	8	23	)	)	PUNCT
cana-3334	8	24	,	,	PUNCT
cana-3334	8	25	thoothukudi	thoothukudi	PROPN
cana-3334	8	26	–	–	PUNCT
cana-3334	8	27	628	628	NUM
cana-3334	8	28	002	002	NUM
cana-3334	8	29	,	,	PUNCT
cana-3334	8	30	tamil	tamil	PROPN
cana-3334	8	31	nadu	nadu	PROPN
cana-3334	8	32	,	,	PUNCT
cana-3334	8	33	india	india	PROPN
cana-3334	8	34	.	.	PUNCT
cana-3334	9	1	article	article	PROPN
cana-3334	9	2	history	history	NOUN
cana-3334	9	3	:	:	PUNCT
cana-3334	9	4	received	receive	VERB
cana-3334	9	5	:	:	PUNCT
cana-3334	9	6	25	25	NUM
cana-3334	9	7	-	-	SYM
cana-3334	9	8	10	10	NUM
cana-3334	9	9	-	-	PUNCT
cana-3334	9	10	2024	2024	NUM
cana-3334	9	11	revised	revise	VERB
cana-3334	9	12	:	:	PUNCT
cana-3334	9	13	02	02	NUM
cana-3334	9	14	-	-	SYM
cana-3334	9	15	12	12	NUM
cana-3334	9	16	-	-	PUNCT
cana-3334	9	17	2024	2024	NUM
cana-3334	9	18	accepted	accept	VERB
cana-3334	9	19	:	:	PUNCT
cana-3334	9	20	12	12	NUM
cana-3334	9	21	-	-	SYM
cana-3334	9	22	12	12	NUM
cana-3334	9	23	-	-	PUNCT
cana-3334	9	24	2024	2024	NUM
cana-3334	9	25	abstract	abstract	NOUN
cana-3334	9	26	:	:	PUNCT
cana-3334	9	27	in	in	ADP
cana-3334	9	28	this	this	DET
cana-3334	9	29	paper	paper	NOUN
cana-3334	9	30	,	,	PUNCT
cana-3334	9	31	we	we	PRON
cana-3334	9	32	aim	aim	VERB
cana-3334	9	33	to	to	PART
cana-3334	9	34	collect	collect	VERB
cana-3334	9	35	all	all	DET
cana-3334	9	36	kites	kite	NOUN
cana-3334	9	37	with	with	ADP
cana-3334	9	38	certain	certain	ADJ
cana-3334	9	39	fixed	fix	VERB
cana-3334	9	40	sides	side	NOUN
cana-3334	9	41	in	in	ADP
cana-3334	9	42	integers	integer	NOUN
cana-3334	9	43	,	,	PUNCT
cana-3334	9	44	rational	rational	ADJ
cana-3334	9	45	diagonals	diagonal	NOUN
cana-3334	9	46	and	and	CCONJ
cana-3334	9	47	integer	integer	NOUN
cana-3334	9	48	areas	area	NOUN
cana-3334	9	49	.	.	PUNCT
cana-3334	10	1	we	we	PRON
cana-3334	10	2	develop	develop	VERB
cana-3334	10	3	mathematical	mathematical	ADJ
cana-3334	10	4	procedure	procedure	NOUN
cana-3334	10	5	and	and	CCONJ
cana-3334	10	6	python	python	NOUN
cana-3334	10	7	programming	programming	NOUN
cana-3334	10	8	to	to	PART
cana-3334	10	9	collect	collect	VERB
cana-3334	10	10	all	all	DET
cana-3334	10	11	those	those	DET
cana-3334	10	12	kites	kite	NOUN
cana-3334	10	13	.	.	PUNCT
cana-3334	11	1	also	also	ADV
cana-3334	11	2	,	,	PUNCT
cana-3334	11	3	experimental	experimental	ADJ
cana-3334	11	4	analyses	analysis	NOUN
cana-3334	11	5	are	be	AUX
cana-3334	11	6	done	do	VERB
cana-3334	11	7	by	by	ADP
cana-3334	11	8	means	mean	NOUN
cana-3334	11	9	of	of	ADP
cana-3334	11	10	examples	example	NOUN
cana-3334	11	11	.	.	PUNCT
cana-3334	12	1	keywords	keyword	NOUN
cana-3334	12	2	:	:	PUNCT
cana-3334	12	3	diophantine	diophantine	VERB
cana-3334	12	4	equations	equation	NOUN
cana-3334	12	5	,	,	PUNCT
cana-3334	12	6	geometrical	geometrical	ADJ
cana-3334	12	7	shape	shape	NOUN
cana-3334	12	8	,	,	PUNCT
cana-3334	12	9	integer	integer	NOUN
cana-3334	12	10	area	area	NOUN
cana-3334	12	11	,	,	PUNCT
cana-3334	12	12	kite	kite	NOUN
cana-3334	12	13	,	,	PUNCT
cana-3334	12	14	rational	rational	ADJ
cana-3334	12	15	area	area	NOUN
cana-3334	12	16	,	,	PUNCT
cana-3334	12	17	rational	rational	ADJ
cana-3334	12	18	diagonals	diagonal	NOUN
cana-3334	12	19	.	.	PUNCT
cana-3334	13	1	2010	2010	NUM
cana-3334	13	2	msc	msc	PROPN
cana-3334	13	3	subject	subject	PROPN
cana-3334	13	4	classification	classification	NOUN
cana-3334	13	5	:	:	PUNCT
cana-3334	13	6	57n25	57n25	NUM
cana-3334	13	7	,	,	PUNCT
cana-3334	13	8	97g30	97g30	NUM
cana-3334	13	9	,	,	PUNCT
cana-3334	13	10	97f40	97f40	NUM
cana-3334	13	11	,	,	PUNCT
cana-3334	13	12	11d09	11d09	NUM
cana-3334	13	13	,	,	PUNCT
cana-3334	13	14	11d99	11d99	NUM
cana-3334	13	15	.	.	PUNCT
cana-3334	14	1	1	1	X
cana-3334	14	2	.	.	X
cana-3334	14	3	introduction	introduction	NOUN
cana-3334	14	4	geometry	geometry	NOUN
cana-3334	14	5	is	be	AUX
cana-3334	14	6	one	one	NUM
cana-3334	14	7	of	of	ADP
cana-3334	14	8	the	the	DET
cana-3334	14	9	most	most	ADV
cana-3334	14	10	interesting	interesting	ADJ
cana-3334	14	11	areas	area	NOUN
cana-3334	14	12	of	of	ADP
cana-3334	14	13	mathematics	mathematic	NOUN
cana-3334	14	14	.	.	PUNCT
cana-3334	15	1	the	the	DET
cana-3334	15	2	basic	basic	ADJ
cana-3334	15	3	geometry	geometry	NOUN
cana-3334	15	4	covers	cover	VERB
cana-3334	15	5	a	a	DET
cana-3334	15	6	range	range	NOUN
cana-3334	15	7	of	of	ADP
cana-3334	15	8	shapes	shape	NOUN
cana-3334	15	9	and	and	CCONJ
cana-3334	15	10	deals	deal	NOUN
cana-3334	15	11	with	with	ADP
cana-3334	15	12	their	their	PRON
cana-3334	15	13	properties	property	NOUN
cana-3334	15	14	along	along	ADP
cana-3334	15	15	with	with	ADP
cana-3334	15	16	the	the	DET
cana-3334	15	17	applications	application	NOUN
cana-3334	15	18	.	.	PUNCT
cana-3334	16	1	in	in	ADP
cana-3334	16	2	earlier	early	ADJ
cana-3334	16	3	days	day	NOUN
cana-3334	16	4	itself	itself	PRON
cana-3334	16	5	,	,	PUNCT
cana-3334	16	6	mathematicians	mathematician	NOUN
cana-3334	16	7	involved	involve	VERB
cana-3334	16	8	themselves	themselves	PRON
cana-3334	16	9	in	in	ADP
cana-3334	16	10	finding	find	VERB
cana-3334	16	11	some	some	DET
cana-3334	16	12	parameters	parameter	NOUN
cana-3334	16	13	regarding	regard	VERB
cana-3334	16	14	such	such	ADJ
cana-3334	16	15	shapes	shape	NOUN
cana-3334	16	16	.	.	PUNCT
cana-3334	17	1	some	some	DET
cana-3334	17	2	basic	basic	ADJ
cana-3334	17	3	shapes	shape	NOUN
cana-3334	17	4	are	be	AUX
cana-3334	17	5	square	square	ADJ
cana-3334	17	6	,	,	PUNCT
cana-3334	17	7	triangle	triangle	NOUN
cana-3334	17	8	,	,	PUNCT
cana-3334	17	9	rectangle	rectangle	NOUN
cana-3334	17	10	,	,	PUNCT
cana-3334	17	11	and	and	CCONJ
cana-3334	17	12	circle	circle	PROPN
cana-3334	17	13	.	.	PUNCT
cana-3334	18	1	area	area	NOUN
cana-3334	18	2	and	and	CCONJ
cana-3334	18	3	perimeter	perimeter	NOUN
cana-3334	18	4	are	be	AUX
cana-3334	18	5	the	the	DET
cana-3334	18	6	most	most	ADV
cana-3334	18	7	used	used	ADJ
cana-3334	18	8	parameters	parameter	NOUN
cana-3334	18	9	by	by	ADP
cana-3334	18	10	common	common	ADJ
cana-3334	18	11	people	people	NOUN
cana-3334	18	12	.	.	PUNCT
cana-3334	19	1	to	to	PART
cana-3334	19	2	make	make	VERB
cana-3334	19	3	the	the	DET
cana-3334	19	4	process	process	NOUN
cana-3334	19	5	of	of	ADP
cana-3334	19	6	finding	find	VERB
cana-3334	19	7	the	the	DET
cana-3334	19	8	area	area	NOUN
cana-3334	19	9	and	and	CCONJ
cana-3334	19	10	perimeter	perimeter	NOUN
cana-3334	19	11	much	much	ADV
cana-3334	19	12	easier	easy	ADJ
cana-3334	19	13	,	,	PUNCT
cana-3334	19	14	early	early	ADJ
cana-3334	19	15	mathematicians	mathematician	NOUN
cana-3334	19	16	launched	launch	VERB
cana-3334	19	17	formulas	formula	NOUN
cana-3334	19	18	using	use	VERB
cana-3334	19	19	the	the	DET
cana-3334	19	20	terms	term	NOUN
cana-3334	19	21	which	which	PRON
cana-3334	19	22	are	be	AUX
cana-3334	19	23	needed	need	VERB
cana-3334	19	24	to	to	PART
cana-3334	19	25	construct	construct	VERB
cana-3334	19	26	that	that	DET
cana-3334	19	27	particular	particular	ADJ
cana-3334	19	28	shape	shape	NOUN
cana-3334	19	29	.	.	PUNCT
cana-3334	20	1	for	for	ADP
cana-3334	20	2	example	example	NOUN
cana-3334	20	3	,	,	PUNCT
cana-3334	20	4	if	if	SCONJ
cana-3334	20	5	the	the	DET
cana-3334	20	6	side	side	NOUN
cana-3334	20	7	of	of	ADP
cana-3334	20	8	a	a	DET
cana-3334	20	9	square	square	NOUN
cana-3334	20	10	is	be	AUX
cana-3334	20	11	𝑎	𝑎	NOUN
cana-3334	20	12	,	,	PUNCT
cana-3334	20	13	then	then	ADV
cana-3334	20	14	its	its	PRON
cana-3334	20	15	area	area	NOUN
cana-3334	20	16	is	be	AUX
cana-3334	20	17	𝑎2	𝑎2	NOUN
cana-3334	20	18	and	and	CCONJ
cana-3334	20	19	perimeter	perimeter	NOUN
cana-3334	20	20	is	be	AUX
cana-3334	20	21	4𝑎.	4𝑎.	NUM
cana-3334	20	22	so	so	ADV
cana-3334	20	23	many	many	ADJ
cana-3334	20	24	regular	regular	ADJ
cana-3334	20	25	shapes	shape	NOUN
cana-3334	20	26	are	be	AUX
cana-3334	20	27	seen	see	VERB
cana-3334	20	28	along	along	ADP
cana-3334	20	29	with	with	ADP
cana-3334	20	30	those	those	DET
cana-3334	20	31	formulas	formula	NOUN
cana-3334	20	32	.	.	PUNCT
cana-3334	21	1	as	as	ADP
cana-3334	21	2	an	an	DET
cana-3334	21	3	extension	extension	NOUN
cana-3334	21	4	,	,	PUNCT
cana-3334	21	5	researchers	researcher	NOUN
cana-3334	21	6	constructed	construct	VERB
cana-3334	21	7	some	some	DET
cana-3334	21	8	new	new	ADJ
cana-3334	21	9	shapes	shape	NOUN
cana-3334	21	10	by	by	ADP
cana-3334	21	11	adjoining	adjoin	VERB
cana-3334	21	12	existing	exist	VERB
cana-3334	21	13	known	know	VERB
cana-3334	21	14	shapes	shape	NOUN
cana-3334	21	15	.	.	PUNCT
cana-3334	22	1	also	also	ADV
cana-3334	22	2	,	,	PUNCT
cana-3334	22	3	they	they	PRON
cana-3334	22	4	paved	pave	VERB
cana-3334	22	5	an	an	DET
cana-3334	22	6	unchallenging	unchallenging	ADJ
cana-3334	22	7	way	way	NOUN
cana-3334	22	8	to	to	PART
cana-3334	22	9	calculate	calculate	VERB
cana-3334	22	10	its	its	PRON
cana-3334	22	11	area	area	NOUN
cana-3334	22	12	.	.	PUNCT
cana-3334	23	1	one	one	NUM
cana-3334	23	2	such	such	ADJ
cana-3334	23	3	shape	shape	NOUN
cana-3334	23	4	is	be	AUX
cana-3334	23	5	kite	kite	NOUN
cana-3334	23	6	.	.	PUNCT
cana-3334	24	1	it	it	PRON
cana-3334	24	2	looks	look	VERB
cana-3334	24	3	like	like	ADP
cana-3334	24	4	the	the	DET
cana-3334	24	5	joining	joining	NOUN
cana-3334	24	6	of	of	ADP
cana-3334	24	7	two	two	NUM
cana-3334	24	8	triangles	triangle	NOUN
cana-3334	24	9	under	under	ADP
cana-3334	24	10	some	some	DET
cana-3334	24	11	considerations	consideration	NOUN
cana-3334	24	12	.	.	PUNCT
cana-3334	25	1	using	use	VERB
cana-3334	25	2	diagonals	diagonal	NOUN
cana-3334	25	3	of	of	ADP
cana-3334	25	4	kites	kite	NOUN
cana-3334	25	5	,	,	PUNCT
cana-3334	25	6	we	we	PRON
cana-3334	25	7	can	can	AUX
cana-3334	25	8	easily	easily	ADV
cana-3334	25	9	calculate	calculate	VERB
cana-3334	25	10	its	its	PRON
cana-3334	25	11	area	area	NOUN
cana-3334	25	12	.	.	PUNCT
cana-3334	26	1	but	but	CCONJ
cana-3334	26	2	here	here	ADV
cana-3334	26	3	the	the	DET
cana-3334	26	4	task	task	NOUN
cana-3334	26	5	is	be	AUX
cana-3334	26	6	to	to	PART
cana-3334	26	7	find	find	VERB
cana-3334	26	8	the	the	DET
cana-3334	26	9	area	area	NOUN
cana-3334	26	10	of	of	ADP
cana-3334	26	11	the	the	DET
cana-3334	26	12	kite	kite	NOUN
cana-3334	26	13	by	by	ADP
cana-3334	26	14	splitting	split	VERB
cana-3334	26	15	it	it	PRON
cana-3334	26	16	into	into	ADP
cana-3334	26	17	two	two	NUM
cana-3334	26	18	isosceles	isoscele	NOUN
cana-3334	26	19	triangles	triangle	NOUN
cana-3334	26	20	,	,	PUNCT
cana-3334	26	21	then	then	ADV
cana-3334	26	22	find	find	VERB
cana-3334	26	23	those	those	DET
cana-3334	26	24	triangle	triangle	NOUN
cana-3334	26	25	's	's	PART
cana-3334	26	26	area	area	NOUN
cana-3334	26	27	,	,	PUNCT
cana-3334	26	28	and	and	CCONJ
cana-3334	26	29	adding	add	VERB
cana-3334	26	30	them	they	PRON
cana-3334	26	31	up	up	ADP
cana-3334	26	32	.	.	PUNCT
cana-3334	27	1	heron	heron	PROPN
cana-3334	27	2	's	's	PART
cana-3334	27	3	formula	formula	NOUN
cana-3334	27	4	is	be	AUX
cana-3334	27	5	used	use	VERB
cana-3334	27	6	to	to	PART
cana-3334	27	7	find	find	VERB
cana-3334	27	8	the	the	DET
cana-3334	27	9	area	area	NOUN
cana-3334	27	10	of	of	ADP
cana-3334	27	11	those	those	DET
cana-3334	27	12	triangles	triangle	NOUN
cana-3334	27	13	,	,	PUNCT
cana-3334	27	14	which	which	PRON
cana-3334	27	15	is	be	AUX
cana-3334	27	16	stated	state	VERB
cana-3334	27	17	as	as	ADP
cana-3334	27	18	`	`	PUNCT
cana-3334	27	19	`	`	PUNCT
cana-3334	27	20	if	if	SCONJ
cana-3334	27	21	𝑎	𝑎	ADP
cana-3334	27	22	,	,	PUNCT
cana-3334	27	23	𝑏	𝑏	PROPN
cana-3334	27	24	and	and	CCONJ
cana-3334	27	25	𝑐	𝑐	PROPN
cana-3334	27	26	are	be	AUX
cana-3334	27	27	sides	side	NOUN
cana-3334	27	28	of	of	ADP
cana-3334	27	29	a	a	DET
cana-3334	27	30	triangle	triangle	NOUN
cana-3334	27	31	,	,	PUNCT
cana-3334	27	32	then	then	ADV
cana-3334	27	33	its	its	PRON
cana-3334	27	34	area	area	NOUN
cana-3334	27	35	is	be	AUX
cana-3334	27	36	given	give	VERB
cana-3334	27	37	as	as	ADP
cana-3334	27	38	√𝑠(𝑠	√𝑠(𝑠	NOUN
cana-3334	27	39	−	−	NUM
cana-3334	27	40	𝑎)(𝑠	𝑎)(𝑠	NOUN
cana-3334	27	41	−	−	PROPN
cana-3334	27	42	𝑏)(𝑠	𝑏)(𝑠	ADP
cana-3334	27	43	−	−	PROPN
cana-3334	27	44	𝑐	𝑐	NOUN
cana-3334	27	45	)	)	PUNCT
cana-3334	27	46	where	where	SCONJ
cana-3334	27	47	𝑠	𝑠	PROPN
cana-3334	27	48	=	=	SYM
cana-3334	27	49	𝑎+𝑏+𝑐	𝑎+𝑏+𝑐	NOUN
cana-3334	27	50	2	2	NUM
cana-3334	27	51	"	"	PUNCT
cana-3334	27	52	.	.	PUNCT
cana-3334	28	1	communications	communication	NOUN
cana-3334	28	2	on	on	ADP
cana-3334	28	3	applied	apply	VERB
cana-3334	28	4	nonlinear	nonlinear	ADJ
cana-3334	28	5	analysis	analysis	NOUN
cana-3334	28	6	issn	issn	NOUN
cana-3334	28	7	:	:	PUNCT
cana-3334	28	8	1074	1074	NUM
cana-3334	28	9	-	-	PUNCT
cana-3334	28	10	133x	133x	NUM
cana-3334	28	11	vol	vol	NOUN
cana-3334	28	12	32	32	NUM
cana-3334	28	13	no	no	NOUN
cana-3334	28	14	.	.	PUNCT
cana-3334	29	1	7s	7	NOUN
cana-3334	29	2	(	(	PUNCT
cana-3334	29	3	2025	2025	NUM
cana-3334	29	4	)	)	PUNCT
cana-3334	29	5	2	2	NUM
cana-3334	29	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3334	29	7	in	in	ADP
cana-3334	29	8	[	[	X
cana-3334	29	9	14	14	NUM
cana-3334	29	10	]	]	PUNCT
cana-3334	29	11	,	,	PUNCT
cana-3334	29	12	(	(	PUNCT
cana-3334	29	13	rusin	rusin	NOUN
cana-3334	29	14	,	,	PUNCT
cana-3334	29	15	1998	1998	NUM
cana-3334	29	16	)	)	PUNCT
cana-3334	29	17	collected	collect	VERB
cana-3334	29	18	rational	rational	ADJ
cana-3334	29	19	triangles	triangle	NOUN
cana-3334	29	20	with	with	ADP
cana-3334	29	21	equal	equal	ADJ
cana-3334	29	22	area	area	NOUN
cana-3334	29	23	.	.	PUNCT
cana-3334	30	1	inspired	inspire	VERB
cana-3334	30	2	by	by	ADP
cana-3334	30	3	his	his	PRON
cana-3334	30	4	work	work	NOUN
cana-3334	30	5	,	,	PUNCT
cana-3334	30	6	this	this	DET
cana-3334	30	7	paper	paper	NOUN
cana-3334	30	8	was	be	AUX
cana-3334	30	9	developed	develop	VERB
cana-3334	30	10	.	.	PUNCT
cana-3334	31	1	also	also	ADV
cana-3334	31	2	in	in	ADP
cana-3334	31	3	[	[	X
cana-3334	31	4	3	3	NUM
cana-3334	31	5	]	]	PUNCT
cana-3334	31	6	,	,	PUNCT
cana-3334	31	7	(	(	PUNCT
cana-3334	31	8	dickson	dickson	PROPN
cana-3334	31	9	,	,	PUNCT
cana-3334	31	10	2013	2013	NUM
cana-3334	31	11	)	)	PUNCT
cana-3334	31	12	provided	provide	VERB
cana-3334	31	13	some	some	DET
cana-3334	31	14	key	key	ADJ
cana-3334	31	15	ideas	idea	NOUN
cana-3334	31	16	for	for	ADP
cana-3334	31	17	the	the	DET
cana-3334	31	18	creation	creation	NOUN
cana-3334	31	19	of	of	ADP
cana-3334	31	20	this	this	DET
cana-3334	31	21	problem	problem	NOUN
cana-3334	31	22	.	.	PUNCT
cana-3334	32	1	also	also	ADV
cana-3334	32	2	[	[	PUNCT
cana-3334	32	3	(	(	PUNCT
cana-3334	32	4	aassila	aassila	NOUN
cana-3334	32	5	,	,	PUNCT
cana-3334	32	6	2001	2001	NUM
cana-3334	32	7	)	)	PUNCT
cana-3334	32	8	,	,	PUNCT
cana-3334	32	9	(	(	PUNCT
cana-3334	32	10	hendrik	hendrik	PROPN
cana-3334	32	11	w.	w.	PROPN
cana-3334	32	12	lenstra	lenstra	PROPN
cana-3334	32	13	,	,	PUNCT
cana-3334	32	14	2002	2002	NUM
cana-3334	32	15	)	)	PUNCT
cana-3334	32	16	,	,	PUNCT
cana-3334	32	17	(	(	PUNCT
cana-3334	32	18	nelsen	nelsen	INTJ
cana-3334	32	19	,	,	PUNCT
cana-3334	32	20	2020	2020	NUM
cana-3334	32	21	)	)	PUNCT
cana-3334	32	22	,	,	PUNCT
cana-3334	32	23	(	(	PUNCT
cana-3334	32	24	robin	robin	PROPN
cana-3334	32	25	mclean	mclean	PROPN
cana-3334	32	26	,	,	PUNCT
cana-3334	32	27	1988	1988	NUM
cana-3334	32	28	)	)	PUNCT
cana-3334	32	29	,	,	PUNCT
cana-3334	32	30	(	(	PUNCT
cana-3334	32	31	robin	robin	PROPN
cana-3334	32	32	mclean	mclean	PROPN
cana-3334	32	33	,	,	PUNCT
cana-3334	32	34	1988	1988	NUM
cana-3334	32	35	)	)	PUNCT
cana-3334	32	36	,	,	PUNCT
cana-3334	32	37	(	(	PUNCT
cana-3334	32	38	rusin	rusin	NOUN
cana-3334	32	39	,	,	PUNCT
cana-3334	32	40	1998	1998	NUM
cana-3334	32	41	)	)	PUNCT
cana-3334	32	42	,	,	PUNCT
cana-3334	32	43	(	(	PUNCT
cana-3334	32	44	gopalan	gopalan	PROPN
cana-3334	32	45	,	,	PUNCT
cana-3334	32	46	kannan	kannan	PROPN
cana-3334	32	47	,	,	PUNCT
cana-3334	32	48	manju	manju	PROPN
cana-3334	32	49	,	,	PUNCT
cana-3334	32	50	&	&	CCONJ
cana-3334	32	51	raja	raja	PROPN
cana-3334	32	52	,	,	PUNCT
cana-3334	32	53	2016	2016	NUM
cana-3334	32	54	)	)	PUNCT
cana-3334	32	55	,	,	PUNCT
cana-3334	32	56	(	(	PUNCT
cana-3334	32	57	manju	manju	PROPN
cana-3334	32	58	,	,	PUNCT
cana-3334	32	59	kannan	kannan	PROPN
cana-3334	32	60	,	,	PUNCT
cana-3334	32	61	&	&	CCONJ
cana-3334	32	62	raja	raja	PROPN
cana-3334	32	63	,	,	PUNCT
cana-3334	32	64	2017	2017	NUM
cana-3334	32	65	)	)	PUNCT
cana-3334	32	66	,	,	PUNCT
cana-3334	32	67	(	(	PUNCT
cana-3334	32	68	mahalakshmi	mahalakshmi	PROPN
cana-3334	32	69	,	,	PUNCT
cana-3334	32	70	kannan	kannan	PROPN
cana-3334	32	71	,	,	PUNCT
cana-3334	32	72	&	&	CCONJ
cana-3334	32	73	narasimman	narasimman	NOUN
cana-3334	32	74	,	,	PUNCT
cana-3334	32	75	2022	2022	NUM
cana-3334	32	76	)	)	PUNCT
cana-3334	32	77	,	,	PUNCT
cana-3334	32	78	(	(	PUNCT
cana-3334	32	79	kannan	kannan	PROPN
cana-3334	32	80	&	&	CCONJ
cana-3334	32	81	mahalakshmi	mahalakshmi	PROPN
cana-3334	32	82	,	,	PUNCT
cana-3334	32	83	some	some	DET
cana-3334	32	84	annotations	annotation	NOUN
cana-3334	32	85	on	on	ADP
cana-3334	32	86	almost	almost	ADV
cana-3334	32	87	and	and	CCONJ
cana-3334	32	88	pseudo	pseudo	NOUN
cana-3334	32	89	almost	almost	ADV
cana-3334	32	90	equilateral	equilateral	ADJ
cana-3334	32	91	rational	rational	ADJ
cana-3334	32	92	rectangles	rectangle	NOUN
cana-3334	32	93	,	,	PUNCT
cana-3334	32	94	2022	2022	NUM
cana-3334	32	95	)	)	PUNCT
cana-3334	32	96	]	]	PUNCT
cana-3334	32	97	are	be	AUX
cana-3334	32	98	considered	consider	VERB
cana-3334	32	99	as	as	ADP
cana-3334	32	100	roots	root	NOUN
cana-3334	32	101	for	for	ADP
cana-3334	32	102	this	this	DET
cana-3334	32	103	paper	paper	NOUN
cana-3334	32	104	.	.	PUNCT
cana-3334	33	1	to	to	PART
cana-3334	33	2	do	do	VERB
cana-3334	33	3	our	our	PRON
cana-3334	33	4	work	work	NOUN
cana-3334	33	5	,	,	PUNCT
cana-3334	33	6	we	we	PRON
cana-3334	33	7	demand	demand	VERB
cana-3334	33	8	the	the	DET
cana-3334	33	9	need	need	NOUN
cana-3334	33	10	of	of	ADP
cana-3334	33	11	classical	classical	ADJ
cana-3334	33	12	branch	branch	NOUN
cana-3334	33	13	of	of	ADP
cana-3334	33	14	mathematics	mathematic	NOUN
cana-3334	33	15	,	,	PUNCT
cana-3334	33	16	the	the	DET
cana-3334	33	17	number	number	NOUN
cana-3334	33	18	theory	theory	NOUN
cana-3334	33	19	.	.	PUNCT
cana-3334	34	1	throughout	throughout	ADP
cana-3334	34	2	this	this	DET
cana-3334	34	3	paper	paper	NOUN
cana-3334	34	4	,	,	PUNCT
cana-3334	34	5	the	the	DET
cana-3334	34	6	vast	vast	ADJ
cana-3334	34	7	research	research	NOUN
cana-3334	34	8	area	area	NOUN
cana-3334	34	9	diophantine	diophantine	VERB
cana-3334	34	10	analysis	analysis	NOUN
cana-3334	34	11	,	,	PUNCT
cana-3334	34	12	the	the	DET
cana-3334	34	13	study	study	NOUN
cana-3334	34	14	of	of	ADP
cana-3334	34	15	diophantine	diophantine	NOUN
cana-3334	34	16	equations	equation	NOUN
cana-3334	34	17	,	,	PUNCT
cana-3334	34	18	its	its	PRON
cana-3334	34	19	solutions	solution	NOUN
cana-3334	34	20	and	and	CCONJ
cana-3334	34	21	its	its	PRON
cana-3334	34	22	applications	application	NOUN
cana-3334	34	23	,	,	PUNCT
cana-3334	34	24	is	be	AUX
cana-3334	34	25	employed	employ	VERB
cana-3334	34	26	(	(	PUNCT
cana-3334	34	27	dickson	dickson	PROPN
cana-3334	34	28	,	,	PUNCT
cana-3334	34	29	2013	2013	NUM
cana-3334	34	30	)	)	PUNCT
cana-3334	34	31	.	.	PUNCT
cana-3334	35	1	especially	especially	ADV
cana-3334	35	2	,	,	PUNCT
cana-3334	35	3	the	the	DET
cana-3334	35	4	well	well	ADV
cana-3334	35	5	-	-	PUNCT
cana-3334	35	6	known	know	VERB
cana-3334	35	7	pythagorean	pythagorean	NOUN
cana-3334	35	8	equations	equation	NOUN
cana-3334	35	9	and	and	CCONJ
cana-3334	35	10	its	its	PRON
cana-3334	35	11	solutions	solution	NOUN
cana-3334	35	12	are	be	AUX
cana-3334	35	13	used	use	VERB
cana-3334	35	14	to	to	PART
cana-3334	35	15	collect	collect	VERB
cana-3334	35	16	the	the	DET
cana-3334	35	17	required	require	VERB
cana-3334	35	18	kites	kite	NOUN
cana-3334	35	19	.	.	PUNCT
cana-3334	36	1	in	in	ADP
cana-3334	36	2	this	this	DET
cana-3334	36	3	paper	paper	NOUN
cana-3334	36	4	,	,	PUNCT
cana-3334	36	5	we	we	PRON
cana-3334	36	6	work	work	VERB
cana-3334	36	7	on	on	ADP
cana-3334	36	8	four	four	NUM
cana-3334	36	9	types	type	NOUN
cana-3334	36	10	of	of	ADP
cana-3334	36	11	kites	kite	NOUN
cana-3334	36	12	(	(	PUNCT
cana-3334	36	13	based	base	VERB
cana-3334	36	14	on	on	ADP
cana-3334	36	15	sides	side	NOUN
cana-3334	36	16	)	)	PUNCT
cana-3334	36	17	.	.	PUNCT
cana-3334	37	1	in	in	ADP
cana-3334	37	2	section	section	NOUN
cana-3334	37	3	2	2	NUM
cana-3334	37	4	,	,	PUNCT
cana-3334	37	5	we	we	PRON
cana-3334	37	6	display	display	VERB
cana-3334	37	7	the	the	DET
cana-3334	37	8	preliminary	preliminary	ADJ
cana-3334	37	9	concepts	concept	NOUN
cana-3334	37	10	needed	need	VERB
cana-3334	37	11	for	for	ADP
cana-3334	37	12	this	this	DET
cana-3334	37	13	work	work	NOUN
cana-3334	37	14	.	.	PUNCT
cana-3334	38	1	section	section	NOUN
cana-3334	38	2	3	3	NUM
cana-3334	38	3	collects	collect	VERB
cana-3334	38	4	all	all	DET
cana-3334	38	5	kites	kite	NOUN
cana-3334	38	6	with	with	ADP
cana-3334	38	7	sides	side	NOUN
cana-3334	38	8	𝑛	𝑛	PRON
cana-3334	38	9	and	and	CCONJ
cana-3334	38	10	𝑛	𝑛	PRON
cana-3334	38	11	+	+	NUM
cana-3334	38	12	1	1	NUM
cana-3334	38	13	and	and	CCONJ
cana-3334	38	14	having	have	VERB
cana-3334	38	15	rational	rational	ADJ
cana-3334	38	16	diagonal	diagonal	ADJ
cana-3334	38	17	and	and	CCONJ
cana-3334	38	18	integer	integer	NOUN
cana-3334	38	19	area	area	NOUN
cana-3334	38	20	whereas	whereas	SCONJ
cana-3334	38	21	in	in	ADP
cana-3334	38	22	section	section	NOUN
cana-3334	38	23	4	4	NUM
cana-3334	38	24	,	,	PUNCT
cana-3334	38	25	kites	kite	VERB
cana-3334	38	26	with	with	ADP
cana-3334	38	27	sides	side	NOUN
cana-3334	38	28	𝑛	𝑛	PRON
cana-3334	38	29	and	and	CCONJ
cana-3334	38	30	𝑛	𝑛	PRON
cana-3334	38	31	−	−	PROPN
cana-3334	38	32	1	1	NUM
cana-3334	38	33	and	and	CCONJ
cana-3334	38	34	with	with	ADP
cana-3334	38	35	integer	integer	NOUN
cana-3334	38	36	area	area	NOUN
cana-3334	38	37	are	be	AUX
cana-3334	38	38	gathered	gather	VERB
cana-3334	38	39	.	.	PUNCT
cana-3334	39	1	in	in	ADP
cana-3334	39	2	sections	section	NOUN
cana-3334	39	3	5	5	NUM
cana-3334	39	4	and	and	CCONJ
cana-3334	39	5	6	6	NUM
cana-3334	39	6	,	,	PUNCT
cana-3334	39	7	we	we	PRON
cana-3334	39	8	focus	focus	VERB
cana-3334	39	9	on	on	ADP
cana-3334	39	10	the	the	DET
cana-3334	39	11	same	same	ADJ
cana-3334	39	12	but	but	CCONJ
cana-3334	39	13	with	with	ADP
cana-3334	39	14	sides	side	NOUN
cana-3334	39	15	𝑛	𝑛	PROPN
cana-3334	39	16	,	,	PUNCT
cana-3334	39	17	𝑛	𝑛	DET
cana-3334	39	18	±	±	NUM
cana-3334	39	19	𝑟	𝑟	NOUN
cana-3334	39	20	respectively	respectively	ADV
cana-3334	39	21	.	.	PUNCT
cana-3334	40	1	in	in	ADP
cana-3334	40	2	each	each	DET
cana-3334	40	3	section	section	NOUN
cana-3334	40	4	,	,	PUNCT
cana-3334	40	5	we	we	PRON
cana-3334	40	6	include	include	VERB
cana-3334	40	7	python	python	NOUN
cana-3334	40	8	coding	code	VERB
cana-3334	40	9	to	to	PART
cana-3334	40	10	collect	collect	VERB
cana-3334	40	11	all	all	DET
cana-3334	40	12	required	require	VERB
cana-3334	40	13	kites	kite	NOUN
cana-3334	40	14	along	along	ADP
cana-3334	40	15	with	with	ADP
cana-3334	40	16	the	the	DET
cana-3334	40	17	output	output	NOUN
cana-3334	40	18	and	and	CCONJ
cana-3334	40	19	experimental	experimental	ADJ
cana-3334	40	20	analysis	analysis	NOUN
cana-3334	40	21	by	by	ADP
cana-3334	40	22	an	an	DET
cana-3334	40	23	example	example	NOUN
cana-3334	40	24	.	.	PUNCT
cana-3334	41	1	2	2	X
cana-3334	41	2	.	.	X
cana-3334	41	3	preliminaries	preliminary	NOUN
cana-3334	41	4	pythagorean	pythagorean	PROPN
cana-3334	41	5	equations	equation	NOUN
cana-3334	41	6	are	be	AUX
cana-3334	41	7	among	among	ADP
cana-3334	41	8	the	the	DET
cana-3334	41	9	most	most	ADJ
cana-3334	41	10	pre	pre	ADJ
cana-3334	41	11	-	-	ADJ
cana-3334	41	12	eminent	eminent	ADJ
cana-3334	41	13	diophantine	diophantine	NOUN
cana-3334	41	14	equations	equation	NOUN
cana-3334	41	15	.	.	PUNCT
cana-3334	42	1	these	these	DET
cana-3334	42	2	equations	equation	NOUN
cana-3334	42	3	are	be	AUX
cana-3334	42	4	of	of	ADP
cana-3334	42	5	the	the	DET
cana-3334	42	6	form	form	NOUN
cana-3334	42	7	𝑥2	𝑥2	NOUN
cana-3334	42	8	+	+	CCONJ
cana-3334	42	9	𝑦2	𝑦2	NOUN
cana-3334	42	10	=	=	SYM
cana-3334	42	11	𝑧2	𝑧2	PROPN
cana-3334	42	12	.	.	PUNCT
cana-3334	43	1	(	(	PUNCT
cana-3334	43	2	titu	titu	PROPN
cana-3334	43	3	,	,	PUNCT
cana-3334	43	4	dorin	dorin	PROPN
cana-3334	43	5	,	,	PUNCT
cana-3334	43	6	&	&	CCONJ
cana-3334	43	7	ion	ion	NOUN
cana-3334	43	8	,	,	PUNCT
cana-3334	43	9	2010	2010	NUM
cana-3334	43	10	)	)	PUNCT
cana-3334	43	11	depicts	depict	VERB
cana-3334	43	12	that	that	SCONJ
cana-3334	43	13	the	the	DET
cana-3334	43	14	general	general	ADJ
cana-3334	43	15	solution	solution	NOUN
cana-3334	43	16	of	of	ADP
cana-3334	43	17	the	the	DET
cana-3334	43	18	pythagorean	pythagorean	PROPN
cana-3334	43	19	equation	equation	NOUN
cana-3334	43	20	𝑥2	𝑥2	NOUN
cana-3334	43	21	+	+	CCONJ
cana-3334	43	22	𝑦2	𝑦2	NOUN
cana-3334	43	23	=	=	SYM
cana-3334	43	24	𝑧2	𝑧2	PROPN
cana-3334	43	25	over	over	ADP
cana-3334	43	26	integers	integer	NOUN
cana-3334	43	27	is	be	AUX
cana-3334	43	28	of	of	ADP
cana-3334	43	29	the	the	DET
cana-3334	43	30	form	form	NOUN
cana-3334	44	1	𝑥	𝑥	NOUN
cana-3334	44	2	=	=	SYM
cana-3334	44	3	𝑘(𝑚2	𝑘(𝑚2	ADJ
cana-3334	44	4	−	−	PROPN
cana-3334	44	5	𝑙2	𝑙2	PROPN
cana-3334	44	6	)	)	PUNCT
cana-3334	44	7	,	,	PUNCT
cana-3334	44	8	𝑦	𝑦	NOUN
cana-3334	44	9	=	=	NOUN
cana-3334	44	10	2𝑘𝑚𝑙	2𝑘𝑚𝑙	NUM
cana-3334	44	11	and	and	CCONJ
cana-3334	44	12	𝑧	𝑧	PRON
cana-3334	44	13	=	=	ADJ
cana-3334	44	14	𝑘(𝑚2	𝑘(𝑚2	PROPN
cana-3334	44	15	+	+	NUM
cana-3334	44	16	𝑙2	𝑙2	NOUN
cana-3334	44	17	)	)	PUNCT
cana-3334	44	18	where	where	SCONJ
cana-3334	44	19	𝑘	𝑘	X
cana-3334	44	20	,	,	PUNCT
cana-3334	44	21	𝑚	𝑚	PROPN
cana-3334	44	22	,	,	PUNCT
cana-3334	44	23	𝑙	𝑙	PROPN
cana-3334	44	24	∈	∈	PROPN
cana-3334	44	25	ℤ	ℤ	PROPN
cana-3334	44	26	and	and	CCONJ
cana-3334	44	27	𝑚	𝑚	X
cana-3334	44	28	>	>	X
cana-3334	44	29	𝑙.	𝑙.	NOUN
cana-3334	45	1	a	a	DET
cana-3334	45	2	quadrilateral	quadrilateral	NOUN
cana-3334	45	3	known	know	VERB
cana-3334	45	4	as	as	ADP
cana-3334	45	5	a	a	DET
cana-3334	45	6	kite	kite	NOUN
cana-3334	45	7	has	have	VERB
cana-3334	45	8	four	four	NUM
cana-3334	45	9	sides	side	NOUN
cana-3334	45	10	that	that	PRON
cana-3334	45	11	are	be	AUX
cana-3334	45	12	grouped	group	VERB
cana-3334	45	13	into	into	ADP
cana-3334	45	14	two	two	NUM
cana-3334	45	15	adjacent	adjacent	ADJ
cana-3334	45	16	pairs	pair	NOUN
cana-3334	45	17	of	of	ADP
cana-3334	45	18	equallength	equallength	NOUN
cana-3334	45	19	sides	side	NOUN
cana-3334	45	20	,	,	PUNCT
cana-3334	45	21	and	and	CCONJ
cana-3334	45	22	the	the	DET
cana-3334	45	23	diagonals	diagonal	NOUN
cana-3334	45	24	cross	cross	VERB
cana-3334	45	25	each	each	DET
cana-3334	45	26	other	other	ADJ
cana-3334	45	27	at	at	ADP
cana-3334	45	28	right	right	ADJ
cana-3334	45	29	angles	angle	NOUN
cana-3334	45	30	.	.	PUNCT
cana-3334	46	1	figure	figure	NOUN
cana-3334	46	2	1	1	NUM
cana-3334	46	3	:	:	PUNCT
cana-3334	46	4	example	example	NOUN
cana-3334	46	5	of	of	ADP
cana-3334	46	6	a	a	DET
cana-3334	46	7	kite	kite	NOUN
cana-3334	46	8	note	note	NOUN
cana-3334	46	9	2.1	2.1	NUM
cana-3334	46	10	.	.	PUNCT
cana-3334	46	11	:	:	PUNCT
cana-3334	47	1	throughout	throughout	ADP
cana-3334	47	2	this	this	DET
cana-3334	47	3	paper	paper	NOUN
cana-3334	47	4	,	,	PUNCT
cana-3334	47	5	𝑛	𝑛	DET
cana-3334	47	6	∈	∈	PROPN
cana-3334	47	7	ℕ	ℕ	PROPN
cana-3334	47	8	and	and	CCONJ
cana-3334	47	9	𝑟	𝑟	PRON
cana-3334	47	10	∈	∈	PROPN
cana-3334	47	11	ℕ	ℕ	PROPN
cana-3334	47	12	−	−	PROPN
cana-3334	47	13	{	{	PUNCT
cana-3334	47	14	1	1	NUM
cana-3334	47	15	}	}	PUNCT
cana-3334	47	16	.	.	PUNCT
cana-3334	48	1	3	3	X
cana-3334	48	2	.	.	X
cana-3334	48	3	kite	kite	NOUN
cana-3334	48	4	with	with	ADP
cana-3334	48	5	sides	side	NOUN
cana-3334	48	6	𝒏	𝒏	PROPN
cana-3334	48	7	,	,	PUNCT
cana-3334	48	8	𝒏	𝒏	PROPN
cana-3334	48	9	+	+	CCONJ
cana-3334	48	10	𝟏	𝟏	NUM
cana-3334	48	11	we	we	PRON
cana-3334	48	12	address	address	VERB
cana-3334	48	13	the	the	DET
cana-3334	48	14	kites	kite	NOUN
cana-3334	48	15	with	with	ADP
cana-3334	48	16	sides	side	NOUN
cana-3334	48	17	𝑛	𝑛	PRON
cana-3334	48	18	and	and	CCONJ
cana-3334	48	19	𝑛	𝑛	PRON
cana-3334	49	1	+	+	NOUN
cana-3334	49	2	1	1	NUM
cana-3334	49	3	in	in	ADP
cana-3334	49	4	this	this	DET
cana-3334	49	5	part	part	NOUN
cana-3334	49	6	and	and	CCONJ
cana-3334	49	7	gather	gather	VERB
cana-3334	49	8	all	all	DET
cana-3334	49	9	kites	kite	NOUN
cana-3334	49	10	with	with	ADP
cana-3334	49	11	rational	rational	ADJ
cana-3334	49	12	diagonal	diagonal	ADJ
cana-3334	49	13	and	and	CCONJ
cana-3334	49	14	integer	integer	NOUN
cana-3334	49	15	area	area	NOUN
cana-3334	49	16	by	by	ADP
cana-3334	49	17	employing	employ	VERB
cana-3334	49	18	the	the	DET
cana-3334	49	19	pythagorean	pythagorean	PROPN
cana-3334	49	20	equation	equation	NOUN
cana-3334	49	21	and	and	CCONJ
cana-3334	49	22	its	its	PRON
cana-3334	49	23	solutions	solution	NOUN
cana-3334	49	24	.	.	PUNCT
cana-3334	50	1	communications	communication	NOUN
cana-3334	50	2	on	on	ADP
cana-3334	50	3	applied	apply	VERB
cana-3334	50	4	nonlinear	nonlinear	ADJ
cana-3334	50	5	analysis	analysis	NOUN
cana-3334	50	6	issn	issn	NOUN
cana-3334	50	7	:	:	PUNCT
cana-3334	50	8	1074	1074	NUM
cana-3334	50	9	-	-	PUNCT
cana-3334	50	10	133x	133x	NUM
cana-3334	50	11	vol	vol	NOUN
cana-3334	50	12	32	32	NUM
cana-3334	50	13	no	no	NOUN
cana-3334	50	14	.	.	PUNCT
cana-3334	51	1	7s	7	NOUN
cana-3334	51	2	(	(	PUNCT
cana-3334	51	3	2025	2025	NUM
cana-3334	51	4	)	)	PUNCT
cana-3334	51	5	3	3	NUM
cana-3334	51	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3334	51	7	let	let	VERB
cana-3334	51	8	us	we	PRON
cana-3334	51	9	consider	consider	VERB
cana-3334	51	10	a	a	DET
cana-3334	51	11	kite	kite	NOUN
cana-3334	51	12	abcd	abcd	NOUN
cana-3334	51	13	with	with	ADP
cana-3334	51	14	sides	side	NOUN
cana-3334	51	15	𝑛	𝑛	PRON
cana-3334	51	16	and	and	CCONJ
cana-3334	51	17	𝑛	𝑛	PRON
cana-3334	52	1	+	+	NOUN
cana-3334	52	2	1	1	NUM
cana-3334	52	3	(	(	PUNCT
cana-3334	52	4	figure	figure	NOUN
cana-3334	52	5	2	2	NUM
cana-3334	52	6	)	)	PUNCT
cana-3334	52	7	.	.	PUNCT
cana-3334	53	1	figure	figure	NOUN
cana-3334	53	2	2	2	NUM
cana-3334	53	3	:	:	PUNCT
cana-3334	53	4	kite	kite	NOUN
cana-3334	53	5	used	use	VERB
cana-3334	53	6	in	in	ADP
cana-3334	53	7	sections	section	NOUN
cana-3334	53	8	3	3	NUM
cana-3334	53	9	and	and	CCONJ
cana-3334	53	10	5	5	NUM
cana-3334	53	11	take	take	VERB
cana-3334	53	12	𝐴𝐵	𝐴𝐵	NOUN
cana-3334	53	13	=	=	SYM
cana-3334	53	14	𝑛	𝑛	NOUN
cana-3334	53	15	=	=	SYM
cana-3334	53	16	𝐵𝐶	𝐵𝐶	PROPN
cana-3334	53	17	and	and	CCONJ
cana-3334	53	18	𝐴𝐷	𝐴𝐷	PROPN
cana-3334	53	19	=	=	SYM
cana-3334	53	20	𝑛	𝑛	PROPN
cana-3334	54	1	+	+	NOUN
cana-3334	54	2	1	1	NUM
cana-3334	54	3	=	=	SYM
cana-3334	54	4	𝐷𝐶.	𝐷𝐶.	NOUN
cana-3334	54	5	let	let	VERB
cana-3334	54	6	𝐴𝐶	𝐴𝐶	PROPN
cana-3334	54	7	=	=	SYM
cana-3334	54	8	𝑑.	𝑑.	NOUN
cana-3334	54	9	then	then	ADV
cana-3334	54	10	the	the	DET
cana-3334	54	11	kite	kite	NOUN
cana-3334	54	12	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	54	13	can	can	AUX
cana-3334	54	14	be	be	AUX
cana-3334	54	15	split	split	VERB
cana-3334	54	16	into	into	ADP
cana-3334	54	17	two	two	NUM
cana-3334	54	18	isosceles	isoscele	NOUN
cana-3334	54	19	triangles	triangle	NOUN
cana-3334	54	20	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	54	21	and	and	CCONJ
cana-3334	54	22	𝐴𝐷𝐶.	𝐴𝐷𝐶.	X
cana-3334	54	23	thus	thus	ADV
cana-3334	54	24	area	area	NOUN
cana-3334	54	25	of	of	ADP
cana-3334	54	26	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	54	27	=	=	PUNCT
cana-3334	54	28	area	area	NOUN
cana-3334	54	29	of	of	ADP
cana-3334	54	30	δ	δ	PROPN
cana-3334	54	31	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	54	32	+	+	PROPN
cana-3334	54	33	area	area	NOUN
cana-3334	54	34	of	of	ADP
cana-3334	54	35	δ	δ	PROPN
cana-3334	54	36	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	54	37	the	the	DET
cana-3334	54	38	semi	semi	ADJ
cana-3334	54	39	perimeter	perimeter	NOUN
cana-3334	54	40	for	for	ADP
cana-3334	54	41	δ	δ	PROPN
cana-3334	54	42	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	54	43	is	be	AUX
cana-3334	54	44	𝑠	𝑠	ADP
cana-3334	54	45	=	=	PRON
cana-3334	54	46	𝑛+𝑛+𝑑	𝑛+𝑛+𝑑	NOUN
cana-3334	54	47	2	2	NUM
cana-3334	54	48	=	=	SYM
cana-3334	54	49	2𝑛+𝑑	2𝑛+𝑑	NUM
cana-3334	54	50	2	2	NUM
cana-3334	54	51	.	.	PUNCT
cana-3334	55	1	thus	thus	ADV
cana-3334	55	2	by	by	ADP
cana-3334	55	3	applying	apply	VERB
cana-3334	55	4	heron	heron	NOUN
cana-3334	55	5	's	's	PART
cana-3334	55	6	formula	formula	NOUN
cana-3334	55	7	,	,	PUNCT
cana-3334	55	8	we	we	PRON
cana-3334	55	9	obtain	obtain	VERB
cana-3334	55	10	area	area	NOUN
cana-3334	55	11	of	of	ADP
cana-3334	55	12	δ	δ	PROPN
cana-3334	55	13	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	55	14	=	=	PROPN
cana-3334	55	15	𝑑	𝑑	PROPN
cana-3334	55	16	4	4	NUM
cana-3334	55	17	√4𝑛2	√4𝑛2	NOUN
cana-3334	55	18	−	−	PROPN
cana-3334	55	19	𝑑2	𝑑2	NOUN
cana-3334	55	20	(	(	PUNCT
cana-3334	55	21	1	1	X
cana-3334	55	22	)	)	PUNCT
cana-3334	55	23	the	the	DET
cana-3334	55	24	semi	semi	ADJ
cana-3334	55	25	perimeter	perimeter	NOUN
cana-3334	55	26	for	for	ADP
cana-3334	55	27	δ	δ	PROPN
cana-3334	55	28	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	55	29	is	be	AUX
cana-3334	55	30	𝑠	𝑠	PROPN
cana-3334	55	31	=	=	PUNCT
cana-3334	55	32	𝑛+1+𝑛+1+𝑑	𝑛+1+𝑛+1+𝑑	PROPN
cana-3334	55	33	2	2	NUM
cana-3334	55	34	=	=	SYM
cana-3334	55	35	2𝑛+2+𝑑	2𝑛+2+𝑑	NUM
cana-3334	55	36	2	2	NUM
cana-3334	55	37	.	.	PUNCT
cana-3334	56	1	thus	thus	ADV
cana-3334	56	2	by	by	ADP
cana-3334	56	3	applying	apply	VERB
cana-3334	56	4	heron	heron	NOUN
cana-3334	56	5	's	's	PART
cana-3334	56	6	formula	formula	NOUN
cana-3334	56	7	,	,	PUNCT
cana-3334	56	8	we	we	PRON
cana-3334	56	9	obtain	obtain	VERB
cana-3334	56	10	area	area	NOUN
cana-3334	56	11	of	of	ADP
cana-3334	56	12	δ	δ	PROPN
cana-3334	56	13	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	56	14	=	=	PRON
cana-3334	56	15	𝑑	𝑑	PROPN
cana-3334	56	16	4	4	NUM
cana-3334	56	17	√(2𝑛	√(2𝑛	NOUN
cana-3334	57	1	+	+	CCONJ
cana-3334	57	2	2)2	2)2	NUM
cana-3334	57	3	−	−	NOUN
cana-3334	57	4	𝑑2	𝑑2	NOUN
cana-3334	57	5	(	(	PUNCT
cana-3334	57	6	2	2	X
cana-3334	57	7	)	)	PUNCT
cana-3334	57	8	this	this	PRON
cana-3334	57	9	implies	imply	VERB
cana-3334	57	10	the	the	DET
cana-3334	57	11	fact	fact	NOUN
cana-3334	57	12	that	that	SCONJ
cana-3334	57	13	the	the	DET
cana-3334	57	14	area	area	NOUN
cana-3334	57	15	of	of	ADP
cana-3334	57	16	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	57	17	∈	∈	PROPN
cana-3334	57	18	ℤ	ℤ	PROPN
cana-3334	57	19	,	,	PUNCT
cana-3334	57	20	if	if	SCONJ
cana-3334	57	21	and	and	CCONJ
cana-3334	57	22	only	only	ADV
cana-3334	57	23	if	if	SCONJ
cana-3334	57	24	the	the	DET
cana-3334	57	25	area	area	NOUN
cana-3334	57	26	of	of	ADP
cana-3334	57	27	δ	δ	PROPN
cana-3334	57	28	𝐴𝐵𝐷	𝐴𝐵𝐷	PROPN
cana-3334	57	29	and	and	CCONJ
cana-3334	57	30	area	area	NOUN
cana-3334	57	31	of	of	ADP
cana-3334	57	32	δ	δ	PROPN
cana-3334	57	33	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	57	34	both	both	PRON
cana-3334	57	35	must	must	AUX
cana-3334	57	36	be	be	AUX
cana-3334	57	37	rational	rational	ADJ
cana-3334	57	38	numbers	number	NOUN
cana-3334	57	39	.	.	PUNCT
cana-3334	58	1	area	area	NOUN
cana-3334	58	2	of	of	ADP
cana-3334	58	3	𝚫	𝚫	PROPN
cana-3334	58	4	𝑨𝑩𝑪	𝑨𝑩𝑪	PROPN
cana-3334	58	5	over	over	ADP
cana-3334	58	6	ℚ	ℚ	PROPN
cana-3334	58	7	`	`	PUNCT
cana-3334	58	8	`	`	PUNCT
cana-3334	58	9	equation	equation	NOUN
cana-3334	58	10	(	(	PUNCT
cana-3334	58	11	1	1	NUM
cana-3334	58	12	)	)	PUNCT
cana-3334	58	13	''	''	PUNCT
cana-3334	58	14	implies	imply	VERB
cana-3334	58	15	that	that	DET
cana-3334	58	16	area	area	NOUN
cana-3334	58	17	of	of	ADP
cana-3334	58	18	δ	δ	PROPN
cana-3334	58	19	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	58	20	∈	∈	PROPN
cana-3334	58	21	ℚ	ℚ	PROPN
cana-3334	58	22	if	if	SCONJ
cana-3334	58	23	4𝑛2	4𝑛2	NUM
cana-3334	58	24	−	−	ADP
cana-3334	58	25	𝑑2	𝑑2	NOUN
cana-3334	58	26	=	=	SYM
cana-3334	58	27	𝑡1	𝑡1	NOUN
cana-3334	58	28	2	2	NUM
cana-3334	58	29	for	for	ADP
cana-3334	58	30	some	some	DET
cana-3334	58	31	𝑡1	𝑡1	NOUN
cana-3334	58	32	∈	∈	PROPN
cana-3334	58	33	ℚ	ℚ	PROPN
cana-3334	58	34	.	.	PUNCT
cana-3334	59	1	now	now	ADV
cana-3334	59	2	we	we	PRON
cana-3334	59	3	reduced	reduce	VERB
cana-3334	59	4	the	the	DET
cana-3334	59	5	problem	problem	NOUN
cana-3334	59	6	of	of	ADP
cana-3334	59	7	finding	find	VERB
cana-3334	59	8	rational	rational	ADJ
cana-3334	59	9	area	area	NOUN
cana-3334	59	10	for	for	SCONJ
cana-3334	59	11	δ	δ	PROPN
cana-3334	59	12	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	59	13	to	to	PART
cana-3334	59	14	solve	solve	VERB
cana-3334	59	15	the	the	DET
cana-3334	59	16	equation	equation	NOUN
cana-3334	59	17	𝑡1	𝑡1	NOUN
cana-3334	59	18	2	2	NUM
cana-3334	59	19	+	+	CCONJ
cana-3334	59	20	𝑑2	𝑑2	NOUN
cana-3334	59	21	=	=	SYM
cana-3334	59	22	(	(	PUNCT
cana-3334	59	23	2𝑛)2	2𝑛)2	NUM
cana-3334	59	24	over	over	ADP
cana-3334	59	25	ℚ.	ℚ.	PROPN
cana-3334	59	26	let	let	VERB
cana-3334	59	27	's	us	PRON
cana-3334	59	28	first	first	ADJ
cana-3334	59	29	solve	solve	VERB
cana-3334	59	30	the	the	DET
cana-3334	59	31	equation	equation	NOUN
cana-3334	59	32	𝑡1	𝑡1	NOUN
cana-3334	59	33	2	2	NUM
cana-3334	59	34	+	+	CCONJ
cana-3334	59	35	𝑑2	𝑑2	NOUN
cana-3334	59	36	=	=	SYM
cana-3334	59	37	1	1	NUM
cana-3334	59	38	over	over	ADP
cana-3334	59	39	ℚ	ℚ	PROPN
cana-3334	59	40	to	to	PART
cana-3334	59	41	get	get	AUX
cana-3334	59	42	started	start	VERB
cana-3334	59	43	.	.	PUNCT
cana-3334	60	1	assume	assume	VERB
cana-3334	60	2	that	that	SCONJ
cana-3334	60	3	𝑡1	𝑡1	NOUN
cana-3334	60	4	=	=	SYM
cana-3334	60	5	𝑝	𝑝	NOUN
cana-3334	60	6	𝑞	𝑞	NOUN
cana-3334	60	7	and	and	CCONJ
cana-3334	60	8	𝑑	𝑑	PROPN
cana-3334	60	9	=	=	ADJ
cana-3334	60	10	𝑟	𝑟	X
cana-3334	60	11	𝑠	𝑠	INTJ
cana-3334	60	12	for	for	ADP
cana-3334	60	13	some	some	DET
cana-3334	60	14	𝑝	𝑝	PROPN
cana-3334	60	15	,	,	PUNCT
cana-3334	60	16	𝑞	𝑞	PROPN
cana-3334	60	17	,	,	PUNCT
cana-3334	60	18	𝑟	𝑟	X
cana-3334	60	19	,	,	PUNCT
cana-3334	60	20	𝑠	𝑠	PROPN
cana-3334	60	21	∈	∈	PROPN
cana-3334	60	22	ℤ	ℤ	PROPN
cana-3334	60	23	.	.	PUNCT
cana-3334	61	1	then	then	ADV
cana-3334	61	2	we	we	PRON
cana-3334	61	3	acquire	acquire	VERB
cana-3334	61	4	the	the	DET
cana-3334	61	5	pythagorean	pythagorean	PROPN
cana-3334	61	6	type	type	NOUN
cana-3334	61	7	equation	equation	NOUN
cana-3334	61	8	(	(	PUNCT
cana-3334	61	9	𝑝𝑠)2	𝑝𝑠)2	PROPN
cana-3334	61	10	+	+	CCONJ
cana-3334	61	11	(	(	PUNCT
cana-3334	61	12	𝑞𝑟)2	𝑞𝑟)2	PROPN
cana-3334	61	13	=	=	SYM
cana-3334	61	14	(	(	PUNCT
cana-3334	61	15	𝑞𝑠)2	𝑞𝑠)2	PROPN
cana-3334	61	16	.	.	PUNCT
cana-3334	62	1	this	this	DET
cana-3334	62	2	equation	equation	NOUN
cana-3334	62	3	has	have	VERB
cana-3334	62	4	to	to	PART
cana-3334	62	5	be	be	AUX
cana-3334	62	6	solved	solve	VERB
cana-3334	62	7	over	over	ADP
cana-3334	62	8	integers	integer	NOUN
cana-3334	62	9	.	.	PUNCT
cana-3334	63	1	from	from	ADP
cana-3334	63	2	section	section	NOUN
cana-3334	63	3	2	2	NUM
cana-3334	63	4	,	,	PUNCT
cana-3334	63	5	we	we	PRON
cana-3334	63	6	have	have	VERB
cana-3334	63	7	𝑡1	𝑡1	NOUN
cana-3334	63	8	=	=	SYM
cana-3334	63	9	𝑝	𝑝	NOUN
cana-3334	63	10	𝑞	𝑞	X
cana-3334	63	11	=	=	SYM
cana-3334	63	12	𝑚2−𝑙2	𝑚2−𝑙2	PROPN
cana-3334	63	13	𝑚2+𝑙2	𝑚2+𝑙2	PROPN
cana-3334	63	14	and	and	CCONJ
cana-3334	63	15	𝑑	𝑑	PROPN
cana-3334	63	16	=	=	ADJ
cana-3334	63	17	𝑟	𝑟	NOUN
cana-3334	63	18	𝑠	𝑠	X
cana-3334	63	19	=	=	SYM
cana-3334	63	20	2𝑚𝑙	2𝑚𝑙	PROPN
cana-3334	63	21	𝑚2+𝑙2	𝑚2+𝑙2	PROPN
cana-3334	63	22	for	for	ADP
cana-3334	63	23	some	some	DET
cana-3334	63	24	𝑚	𝑚	NOUN
cana-3334	63	25	,	,	PUNCT
cana-3334	63	26	𝑙	𝑙	PROPN
cana-3334	63	27	∈	∈	PROPN
cana-3334	63	28	ℤ	ℤ	PROPN
cana-3334	63	29	.	.	PUNCT
cana-3334	64	1	hence	hence	ADV
cana-3334	64	2	the	the	DET
cana-3334	64	3	rational	rational	ADJ
cana-3334	64	4	solutions	solution	NOUN
cana-3334	64	5	for	for	ADP
cana-3334	64	6	the	the	DET
cana-3334	64	7	equation	equation	NOUN
cana-3334	64	8	𝑡1	𝑡1	NOUN
cana-3334	64	9	2	2	NUM
cana-3334	64	10	+	+	CCONJ
cana-3334	64	11	𝑑2	𝑑2	NOUN
cana-3334	64	12	=	=	SYM
cana-3334	64	13	(	(	PUNCT
cana-3334	64	14	2𝑛)2	2𝑛)2	NUM
cana-3334	64	15	are	be	AUX
cana-3334	64	16	𝑡1	𝑡1	NOUN
cana-3334	64	17	=	=	SYM
cana-3334	64	18	2𝑛	2𝑛	PROPN
cana-3334	64	19	(	(	PUNCT
cana-3334	64	20	𝑚2−𝑙2	𝑚2−𝑙2	PROPN
cana-3334	64	21	𝑚2+𝑙2	𝑚2+𝑙2	PROPN
cana-3334	64	22	)	)	PUNCT
cana-3334	64	23	and	and	CCONJ
cana-3334	64	24	𝑑	𝑑	PROPN
cana-3334	64	25	=	=	X
cana-3334	64	26	4𝑛	4𝑛	PROPN
cana-3334	64	27	(	(	PUNCT
cana-3334	64	28	𝑚𝑙	𝑚𝑙	NOUN
cana-3334	64	29	𝑚2+𝑙2	𝑚2+𝑙2	PROPN
cana-3334	64	30	)	)	PUNCT
cana-3334	64	31	for	for	ADP
cana-3334	64	32	some	some	DET
cana-3334	64	33	𝑚	𝑚	NOUN
cana-3334	64	34	,	,	PUNCT
cana-3334	64	35	𝑙	𝑙	PROPN
cana-3334	64	36	∈	∈	PROPN
cana-3334	64	37	ℤ	ℤ	PROPN
cana-3334	64	38	and	and	CCONJ
cana-3334	64	39	𝑚	𝑚	X
cana-3334	64	40	>	>	X
cana-3334	64	41	𝑙.	𝑙.	ADJ
cana-3334	64	42	communications	communication	NOUN
cana-3334	64	43	on	on	ADP
cana-3334	64	44	applied	apply	VERB
cana-3334	64	45	nonlinear	nonlinear	ADJ
cana-3334	64	46	analysis	analysis	NOUN
cana-3334	64	47	issn	issn	NOUN
cana-3334	64	48	:	:	PUNCT
cana-3334	64	49	1074	1074	NUM
cana-3334	64	50	-	-	PUNCT
cana-3334	64	51	133x	133x	NUM
cana-3334	64	52	vol	vol	NOUN
cana-3334	64	53	32	32	NUM
cana-3334	64	54	no	no	NOUN
cana-3334	64	55	.	.	PUNCT
cana-3334	65	1	7s	7	NOUN
cana-3334	65	2	(	(	PUNCT
cana-3334	65	3	2025	2025	NUM
cana-3334	65	4	)	)	PUNCT
cana-3334	65	5	4	4	NUM
cana-3334	65	6	https://internationalpubls.com	https://internationalpubls.com	NOUN
cana-3334	65	7	area	area	NOUN
cana-3334	65	8	of	of	ADP
cana-3334	65	9	𝚫	𝚫	PROPN
cana-3334	65	10	𝑨𝑫𝑪	𝑨𝑫𝑪	NOUN
cana-3334	65	11	over	over	ADP
cana-3334	65	12	ℚ	ℚ	PROPN
cana-3334	65	13	`	`	PUNCT
cana-3334	65	14	`	`	PUNCT
cana-3334	65	15	equation	equation	NOUN
cana-3334	65	16	(	(	PUNCT
cana-3334	65	17	2	2	NUM
cana-3334	65	18	)	)	PUNCT
cana-3334	65	19	''	''	PUNCT
cana-3334	65	20	implies	imply	VERB
cana-3334	65	21	that	that	DET
cana-3334	65	22	area	area	NOUN
cana-3334	65	23	of	of	ADP
cana-3334	65	24	δ	δ	PROPN
cana-3334	65	25	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	65	26	∈	∈	PROPN
cana-3334	65	27	ℚ	ℚ	PROPN
cana-3334	65	28	if	if	SCONJ
cana-3334	65	29	(	(	PUNCT
cana-3334	65	30	2𝑛	2𝑛	NOUN
cana-3334	65	31	+	+	CCONJ
cana-3334	65	32	2)2	2)2	NUM
cana-3334	65	33	−	−	NOUN
cana-3334	65	34	𝑑2	𝑑2	NOUN
cana-3334	65	35	=	=	SYM
cana-3334	65	36	𝑡2	𝑡2	ADJ
cana-3334	65	37	2	2	NUM
cana-3334	65	38	for	for	ADP
cana-3334	65	39	some	some	DET
cana-3334	65	40	𝑡2	𝑡2	PROPN
cana-3334	65	41	∈	∈	PROPN
cana-3334	65	42	ℚ	ℚ	PROPN
cana-3334	65	43	.	.	PUNCT
cana-3334	66	1	as	as	ADP
cana-3334	66	2	in	in	ADP
cana-3334	66	3	the	the	DET
cana-3334	66	4	above	above	ADJ
cana-3334	66	5	case	case	NOUN
cana-3334	66	6	,	,	PUNCT
cana-3334	66	7	we	we	PRON
cana-3334	66	8	have	have	VERB
cana-3334	66	9	𝑡2	𝑡2	NOUN
cana-3334	66	10	=	=	SYM
cana-3334	66	11	(	(	PUNCT
cana-3334	66	12	2𝑛	2𝑛	NOUN
cana-3334	66	13	+	+	CCONJ
cana-3334	67	1	2	2	X
cana-3334	67	2	)	)	PUNCT
cana-3334	67	3	(	(	PUNCT
cana-3334	67	4	𝑎2−𝑏2	𝑎2−𝑏2	NUM
cana-3334	67	5	𝑎2+𝑏2	𝑎2+𝑏2	PROPN
cana-3334	67	6	)	)	PUNCT
cana-3334	67	7	and	and	CCONJ
cana-3334	67	8	𝑑	𝑑	PROPN
cana-3334	67	9	=	=	X
cana-3334	67	10	(	(	PUNCT
cana-3334	67	11	2𝑛	2𝑛	NOUN
cana-3334	67	12	+	+	CCONJ
cana-3334	67	13	2	2	X
cana-3334	67	14	)	)	PUNCT
cana-3334	67	15	(	(	PUNCT
cana-3334	67	16	2𝑎𝑏	2𝑎𝑏	PROPN
cana-3334	67	17	𝑎2+𝑏2	𝑎2+𝑏2	PROPN
cana-3334	67	18	)	)	PUNCT
cana-3334	67	19	for	for	ADP
cana-3334	67	20	some	some	DET
cana-3334	67	21	𝑎	𝑎	NOUN
cana-3334	67	22	,	,	PUNCT
cana-3334	67	23	𝑏	𝑏	PROPN
cana-3334	67	24	∈	∈	PROPN
cana-3334	67	25	ℤ	ℤ	PROPN
cana-3334	67	26	and	and	CCONJ
cana-3334	67	27	𝑎	𝑎	ADP
cana-3334	67	28	>	>	X
cana-3334	67	29	𝑏.	𝑏.	NOUN
cana-3334	67	30	to	to	PART
cana-3334	67	31	find	find	VERB
cana-3334	67	32	required	required	ADJ
cana-3334	67	33	𝒏	𝒏	PROPN
cana-3334	67	34	since	since	SCONJ
cana-3334	67	35	the	the	DET
cana-3334	67	36	value	value	NOUN
cana-3334	67	37	𝑑	𝑑	NOUN
cana-3334	67	38	is	be	AUX
cana-3334	67	39	equal	equal	ADJ
cana-3334	67	40	in	in	ADP
cana-3334	67	41	both	both	CCONJ
cana-3334	67	42	the	the	DET
cana-3334	67	43	areas	area	NOUN
cana-3334	67	44	,	,	PUNCT
cana-3334	67	45	we	we	PRON
cana-3334	67	46	can	can	AUX
cana-3334	67	47	equate	equate	VERB
cana-3334	67	48	them	they	PRON
cana-3334	67	49	and	and	CCONJ
cana-3334	67	50	find	find	VERB
cana-3334	67	51	𝑛	𝑛	PRON
cana-3334	67	52	as	as	ADP
cana-3334	67	53	𝑛	𝑛	NOUN
cana-3334	67	54	=	=	SYM
cana-3334	67	55	𝑎𝑏(𝑚2	𝑎𝑏(𝑚2	PROPN
cana-3334	68	1	+	+	CCONJ
cana-3334	68	2	𝑙2	𝑙2	NOUN
cana-3334	68	3	)	)	PUNCT
cana-3334	68	4	𝑚𝑙(𝑎2	𝑚𝑙(𝑎2	NOUN
cana-3334	69	1	+	+	CCONJ
cana-3334	69	2	𝑏2	𝑏2	NOUN
cana-3334	69	3	)	)	PUNCT
cana-3334	69	4	−	−	PROPN
cana-3334	69	5	𝑎𝑏(𝑚2	𝑎𝑏(𝑚2	PROPN
cana-3334	70	1	+	+	CCONJ
cana-3334	70	2	𝑙2	𝑙2	PROPN
cana-3334	70	3	)	)	PUNCT
cana-3334	70	4	3.1	3.1	NUM
cana-3334	70	5	.	.	PUNCT
cana-3334	71	1	python	python	NOUN
cana-3334	71	2	coding	coding	NOUN
cana-3334	71	3	for	for	ADP
cana-3334	71	4	generation	generation	NOUN
cana-3334	71	5	of	of	ADP
cana-3334	71	6	required	require	VERB
cana-3334	71	7	kites	kite	NOUN
cana-3334	71	8	with	with	ADP
cana-3334	71	9	sides	side	NOUN
cana-3334	71	10	𝒏	𝒏	PROPN
cana-3334	71	11	and	and	CCONJ
cana-3334	71	12	𝒏	𝒏	PROPN
cana-3334	71	13	+	+	CCONJ
cana-3334	71	14	𝟏	𝟏	NUM
cana-3334	71	15	in	in	ADP
cana-3334	71	16	this	this	DET
cana-3334	71	17	section	section	NOUN
cana-3334	71	18	we	we	PRON
cana-3334	71	19	display	display	VERB
cana-3334	71	20	python	python	NOUN
cana-3334	71	21	coding	code	VERB
cana-3334	71	22	to	to	PART
cana-3334	71	23	collect	collect	VERB
cana-3334	71	24	kites	kite	NOUN
cana-3334	71	25	with	with	ADP
cana-3334	71	26	sides	side	NOUN
cana-3334	71	27	𝑛	𝑛	PROPN
cana-3334	71	28	,	,	PUNCT
cana-3334	71	29	𝑛	𝑛	PRON
cana-3334	71	30	+	+	NOUN
cana-3334	71	31	1	1	NUM
cana-3334	71	32	,	,	PUNCT
cana-3334	71	33	rational	rational	ADJ
cana-3334	71	34	diagonals	diagonal	NOUN
cana-3334	71	35	and	and	CCONJ
cana-3334	71	36	integer	integer	NOUN
cana-3334	71	37	area	area	NOUN
cana-3334	71	38	followed	follow	VERB
cana-3334	71	39	by	by	ADP
cana-3334	71	40	its	its	PRON
cana-3334	71	41	output	output	NOUN
cana-3334	71	42	.	.	PUNCT
cana-3334	72	1	figure	figure	VERB
cana-3334	72	2	3	3	NUM
cana-3334	72	3	:	:	PUNCT
cana-3334	72	4	coding	code	VERB
cana-3334	72	5	1	1	NUM
cana-3334	72	6	:	:	PUNCT
cana-3334	72	7	kite	kite	NOUN
cana-3334	72	8	with	with	ADP
cana-3334	72	9	sides	side	NOUN
cana-3334	72	10	𝑛	𝑛	PROPN
cana-3334	72	11	,	,	PUNCT
cana-3334	72	12	𝑛	𝑛	PRON
cana-3334	72	13	+	+	ADJ
cana-3334	72	14	1	1	NUM
cana-3334	72	15	communications	communication	NOUN
cana-3334	72	16	on	on	ADP
cana-3334	72	17	applied	apply	VERB
cana-3334	72	18	nonlinear	nonlinear	ADJ
cana-3334	72	19	analysis	analysis	NOUN
cana-3334	72	20	issn	issn	NOUN
cana-3334	72	21	:	:	PUNCT
cana-3334	72	22	1074	1074	NUM
cana-3334	72	23	-	-	PUNCT
cana-3334	72	24	133x	133x	NUM
cana-3334	72	25	vol	vol	NOUN
cana-3334	72	26	32	32	NUM
cana-3334	72	27	no	no	NOUN
cana-3334	72	28	.	.	PUNCT
cana-3334	73	1	7s	7	NOUN
cana-3334	73	2	(	(	PUNCT
cana-3334	73	3	2025	2025	NUM
cana-3334	73	4	)	)	PUNCT
cana-3334	73	5	5	5	NUM
cana-3334	73	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3334	73	7	figure	figure	NOUN
cana-3334	73	8	4	4	NUM
cana-3334	73	9	:	:	PUNCT
cana-3334	73	10	output	output	NOUN
cana-3334	73	11	:	:	PUNCT
cana-3334	73	12	coding	code	VERB
cana-3334	73	13	1	1	NUM
cana-3334	73	14	3.2	3.2	NUM
cana-3334	73	15	.	.	PUNCT
cana-3334	74	1	experimental	experimental	ADJ
cana-3334	74	2	analysis	analysis	NOUN
cana-3334	74	3	by	by	ADP
cana-3334	74	4	an	an	DET
cana-3334	74	5	example	example	NOUN
cana-3334	74	6	usual	usual	ADJ
cana-3334	74	7	formula	formula	NOUN
cana-3334	74	8	for	for	ADP
cana-3334	74	9	area	area	NOUN
cana-3334	74	10	of	of	ADP
cana-3334	74	11	kite	kite	NOUN
cana-3334	74	12	is	be	AUX
cana-3334	74	13	1	1	NUM
cana-3334	74	14	2	2	NUM
cana-3334	74	15	𝑑𝑑1	𝑑𝑑1	NOUN
cana-3334	74	16	,	,	PUNCT
cana-3334	74	17	where	where	SCONJ
cana-3334	74	18	𝑑	𝑑	NOUN
cana-3334	74	19	and	and	CCONJ
cana-3334	74	20	𝑑1	𝑑1	NOUN
cana-3334	74	21	are	be	AUX
cana-3334	74	22	diagonals	diagonal	NOUN
cana-3334	74	23	.	.	PUNCT
cana-3334	75	1	in	in	ADP
cana-3334	75	2	figure	figure	NOUN
cana-3334	75	3	1	1	NUM
cana-3334	75	4	,	,	PUNCT
cana-3334	75	5	take	take	VERB
cana-3334	75	6	the	the	DET
cana-3334	75	7	diagonals	diagonal	NOUN
cana-3334	75	8	as	as	ADP
cana-3334	75	9	𝐵𝐷(=	𝐵𝐷(=	NOUN
cana-3334	75	10	𝑑	𝑑	NOUN
cana-3334	75	11	)	)	PUNCT
cana-3334	75	12	,	,	PUNCT
cana-3334	75	13	𝐴𝐶(=	𝐴𝐶(=	CCONJ
cana-3334	75	14	𝑑1	𝑑1	NOUN
cana-3334	75	15	)	)	PUNCT
cana-3334	75	16	and	and	CCONJ
cana-3334	75	17	the	the	DET
cana-3334	75	18	sides	side	NOUN
cana-3334	75	19	as	as	ADP
cana-3334	75	20	𝐴𝐷	𝐴𝐷	PROPN
cana-3334	75	21	=	=	SYM
cana-3334	75	22	𝑛	𝑛	NOUN
cana-3334	75	23	=	=	SYM
cana-3334	75	24	𝐴𝐵	𝐴𝐵	PROPN
cana-3334	75	25	and	and	CCONJ
cana-3334	75	26	𝐵𝐶	𝐵𝐶	PROPN
cana-3334	75	27	=	=	SYM
cana-3334	75	28	𝑛	𝑛	PROPN
cana-3334	75	29	+	+	NOUN
cana-3334	75	30	1	1	NUM
cana-3334	75	31	=	=	NOUN
cana-3334	75	32	𝐶𝐷.	𝐶𝐷.	NOUN
cana-3334	75	33	applying	apply	VERB
cana-3334	75	34	pythagoras	pythagoras	PROPN
cana-3334	75	35	theorem	theorem	VERB
cana-3334	75	36	for	for	ADP
cana-3334	75	37	δ	δ	PROPN
cana-3334	75	38	𝐴𝑂𝐵	𝐴𝑂𝐵	PROPN
cana-3334	75	39	and	and	CCONJ
cana-3334	75	40	δ	δ	PROPN
cana-3334	75	41	𝐵𝑂𝐶	𝐵𝑂𝐶	PROPN
cana-3334	75	42	,	,	PUNCT
cana-3334	75	43	we	we	PRON
cana-3334	75	44	get	get	VERB
cana-3334	75	45	𝑂𝐴	𝑂𝐴	PROPN
cana-3334	75	46	=	=	SYM
cana-3334	75	47	1	1	NUM
cana-3334	75	48	2	2	NUM
cana-3334	75	49	√4𝑛2	√4𝑛2	NOUN
cana-3334	75	50	−	−	NOUN
cana-3334	75	51	𝑑2	𝑑2	NOUN
cana-3334	75	52	and	and	CCONJ
cana-3334	75	53	𝑂𝐶	𝑂𝐶	PROPN
cana-3334	75	54	=	=	SYM
cana-3334	75	55	1	1	NUM
cana-3334	75	56	2	2	NUM
cana-3334	75	57	√4(𝑛	√4(𝑛	VERB
cana-3334	75	58	+	+	CCONJ
cana-3334	75	59	1)2	1)2	NUM
cana-3334	75	60	−	−	NOUN
cana-3334	75	61	𝑑2	𝑑2	NOUN
cana-3334	75	62	respectively	respectively	ADV
cana-3334	75	63	.	.	PUNCT
cana-3334	76	1	this	this	PRON
cana-3334	76	2	gives	give	VERB
cana-3334	76	3	𝑑1	𝑑1	NOUN
cana-3334	76	4	=	=	PUNCT
cana-3334	76	5	𝑂𝐴	𝑂𝐴	PROPN
cana-3334	76	6	+	+	CCONJ
cana-3334	76	7	𝑂𝐶	𝑂𝐶	NOUN
cana-3334	76	8	=	=	SYM
cana-3334	76	9	1	1	NUM
cana-3334	76	10	2	2	NUM
cana-3334	76	11	[	[	X
cana-3334	76	12	√4𝑛2	√4𝑛2	NOUN
cana-3334	76	13	−	−	PROPN
cana-3334	76	14	𝑑2	𝑑2	NOUN
cana-3334	76	15	+	+	CCONJ
cana-3334	76	16	√4(𝑛	√4(𝑛	VERB
cana-3334	76	17	+	+	X
cana-3334	76	18	1)2	1)2	NUM
cana-3334	76	19	−	−	NOUN
cana-3334	76	20	𝑑2	𝑑2	NOUN
cana-3334	76	21	]	]	PUNCT
cana-3334	76	22	.	.	PUNCT
cana-3334	77	1	so	so	ADV
cana-3334	77	2	the	the	DET
cana-3334	77	3	area	area	NOUN
cana-3334	77	4	is	be	AUX
cana-3334	77	5	1	1	NUM
cana-3334	77	6	4	4	NUM
cana-3334	77	7	𝑑	𝑑	NOUN
cana-3334	77	8	[	[	X
cana-3334	77	9	√4𝑛2	√4𝑛2	NOUN
cana-3334	77	10	−	−	PROPN
cana-3334	77	11	𝑑2	𝑑2	NOUN
cana-3334	77	12	+	+	CCONJ
cana-3334	77	13	√4(𝑛	√4(𝑛	VERB
cana-3334	77	14	+	+	X
cana-3334	77	15	1)2	1)2	NUM
cana-3334	77	16	−	−	NOUN
cana-3334	77	17	𝑑2	𝑑2	NOUN
cana-3334	77	18	]	]	PUNCT
cana-3334	77	19	.	.	PUNCT
cana-3334	78	1	now	now	ADV
cana-3334	78	2	,	,	PUNCT
cana-3334	78	3	let	let	VERB
cana-3334	78	4	us	we	PRON
cana-3334	78	5	verify	verify	VERB
cana-3334	78	6	this	this	PRON
cana-3334	78	7	by	by	ADP
cana-3334	78	8	an	an	DET
cana-3334	78	9	example	example	NOUN
cana-3334	78	10	.	.	PUNCT
cana-3334	79	1	take	take	VERB
cana-3334	79	2	𝑛	𝑛	NOUN
cana-3334	79	3	=	=	SYM
cana-3334	79	4	20	20	NUM
cana-3334	79	5	and	and	CCONJ
cana-3334	79	6	𝑑	𝑑	PROPN
cana-3334	79	7	=	=	ADJ
cana-3334	79	8	840	840	NUM
cana-3334	79	9	29	29	NUM
cana-3334	79	10	.	.	PUNCT
cana-3334	80	1	then	then	ADV
cana-3334	80	2	we	we	PRON
cana-3334	80	3	obtain	obtain	VERB
cana-3334	80	4	𝑑1	𝑑1	NOUN
cana-3334	80	5	=	=	NOUN
cana-3334	80	6	29	29	NUM
cana-3334	80	7	.	.	PUNCT
cana-3334	81	1	this	this	PRON
cana-3334	81	2	gives	give	VERB
cana-3334	81	3	the	the	DET
cana-3334	81	4	area	area	NOUN
cana-3334	81	5	420	420	NUM
cana-3334	81	6	,	,	PUNCT
cana-3334	81	7	is	be	AUX
cana-3334	81	8	same	same	ADJ
cana-3334	81	9	as	as	ADP
cana-3334	81	10	the	the	DET
cana-3334	81	11	one	one	NUM
cana-3334	81	12	found	find	VERB
cana-3334	81	13	from	from	ADP
cana-3334	81	14	the	the	DET
cana-3334	81	15	python	python	NOUN
cana-3334	81	16	coding	coding	NOUN
cana-3334	81	17	.	.	PUNCT
cana-3334	82	1	4	4	X
cana-3334	82	2	.	.	X
cana-3334	82	3	kite	kite	NOUN
cana-3334	82	4	with	with	ADP
cana-3334	82	5	sides	side	NOUN
cana-3334	82	6	𝒏	𝒏	PROPN
cana-3334	82	7	,	,	PUNCT
cana-3334	82	8	𝒏	𝒏	PROPN
cana-3334	82	9	−	−	PROPN
cana-3334	82	10	𝟏	𝟏	PRON
cana-3334	82	11	utilizing	utilize	VERB
cana-3334	82	12	the	the	DET
cana-3334	82	13	pythagorean	pythagorean	PROPN
cana-3334	82	14	equation	equation	NOUN
cana-3334	82	15	and	and	CCONJ
cana-3334	82	16	its	its	PRON
cana-3334	82	17	solutions	solution	NOUN
cana-3334	82	18	,	,	PUNCT
cana-3334	82	19	we	we	PRON
cana-3334	82	20	examine	examine	VERB
cana-3334	82	21	the	the	DET
cana-3334	82	22	kites	kite	NOUN
cana-3334	82	23	with	with	ADP
cana-3334	82	24	sides	side	NOUN
cana-3334	82	25	𝑛	𝑛	PRON
cana-3334	82	26	and	and	CCONJ
cana-3334	82	27	𝑛	𝑛	PRON
cana-3334	82	28	−	−	PROPN
cana-3334	82	29	1	1	NUM
cana-3334	82	30	in	in	ADP
cana-3334	82	31	this	this	DET
cana-3334	82	32	section	section	NOUN
cana-3334	82	33	and	and	CCONJ
cana-3334	82	34	generate	generate	VERB
cana-3334	82	35	all	all	DET
cana-3334	82	36	kites	kite	NOUN
cana-3334	82	37	with	with	ADP
cana-3334	82	38	integer	integer	PROPN
cana-3334	82	39	area	area	NOUN
cana-3334	82	40	.	.	PUNCT
cana-3334	83	1	let	let	VERB
cana-3334	83	2	us	we	PRON
cana-3334	83	3	consider	consider	VERB
cana-3334	83	4	a	a	DET
cana-3334	83	5	kite	kite	NOUN
cana-3334	83	6	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	NOUN
cana-3334	83	7	with	with	ADP
cana-3334	83	8	sides	side	NOUN
cana-3334	83	9	𝑛	𝑛	PRON
cana-3334	83	10	and	and	CCONJ
cana-3334	83	11	𝑛	𝑛	PRON
cana-3334	83	12	−	−	PROPN
cana-3334	83	13	1	1	NUM
cana-3334	83	14	(	(	PUNCT
cana-3334	83	15	figure	figure	NOUN
cana-3334	83	16	5	5	NUM
cana-3334	83	17	)	)	PUNCT
cana-3334	83	18	.	.	PUNCT
cana-3334	84	1	take	take	VERB
cana-3334	84	2	𝐴𝐵	𝐴𝐵	NOUN
cana-3334	84	3	=	=	SYM
cana-3334	84	4	𝑛	𝑛	NOUN
cana-3334	84	5	=	=	SYM
cana-3334	84	6	𝐵𝐶	𝐵𝐶	PROPN
cana-3334	84	7	and	and	CCONJ
cana-3334	84	8	𝐴𝐷	𝐴𝐷	PROPN
cana-3334	84	9	=	=	SYM
cana-3334	85	1	𝑛	𝑛	DET
cana-3334	85	2	−	−	NUM
cana-3334	85	3	1	1	NUM
cana-3334	85	4	=	=	SYM
cana-3334	85	5	𝐷𝐶.	𝐷𝐶.	NOUN
cana-3334	85	6	let	let	VERB
cana-3334	85	7	𝐴𝐶	𝐴𝐶	PROPN
cana-3334	85	8	=	=	SYM
cana-3334	85	9	𝑑.	𝑑.	NOUN
cana-3334	85	10	then	then	ADV
cana-3334	85	11	the	the	DET
cana-3334	85	12	kite	kite	NOUN
cana-3334	85	13	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	85	14	can	can	AUX
cana-3334	85	15	be	be	AUX
cana-3334	85	16	split	split	VERB
cana-3334	85	17	into	into	ADP
cana-3334	85	18	two	two	NUM
cana-3334	85	19	isosceles	isoscele	NOUN
cana-3334	85	20	triangles	triangle	NOUN
cana-3334	85	21	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	85	22	and	and	CCONJ
cana-3334	85	23	𝐴𝐷𝐶.	𝐴𝐷𝐶.	X
cana-3334	85	24	thus	thus	ADV
cana-3334	85	25	,	,	PUNCT
cana-3334	85	26	area	area	NOUN
cana-3334	85	27	of	of	ADP
cana-3334	85	28	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	85	29	=	=	PUNCT
cana-3334	85	30	area	area	NOUN
cana-3334	85	31	of	of	ADP
cana-3334	85	32	δ	δ	PROPN
cana-3334	85	33	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	85	34	+	+	NUM
cana-3334	85	35	area	area	NOUN
cana-3334	85	36	of	of	ADP
cana-3334	85	37	δ	δ	PROPN
cana-3334	85	38	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	85	39	communications	communication	NOUN
cana-3334	85	40	on	on	ADP
cana-3334	85	41	applied	apply	VERB
cana-3334	85	42	nonlinear	nonlinear	ADJ
cana-3334	85	43	analysis	analysis	NOUN
cana-3334	85	44	issn	issn	NOUN
cana-3334	85	45	:	:	PUNCT
cana-3334	85	46	1074	1074	NUM
cana-3334	85	47	-	-	PUNCT
cana-3334	85	48	133x	133x	NUM
cana-3334	85	49	vol	vol	NOUN
cana-3334	85	50	32	32	NUM
cana-3334	85	51	no	no	NOUN
cana-3334	85	52	.	.	PUNCT
cana-3334	86	1	7s	7	NOUN
cana-3334	86	2	(	(	PUNCT
cana-3334	86	3	2025	2025	NUM
cana-3334	86	4	)	)	PUNCT
cana-3334	86	5	6	6	NUM
cana-3334	86	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3334	86	7	figure	figure	NOUN
cana-3334	86	8	5	5	NUM
cana-3334	86	9	:	:	PUNCT
cana-3334	86	10	kite	kite	NOUN
cana-3334	86	11	used	use	VERB
cana-3334	86	12	in	in	ADP
cana-3334	86	13	sections	section	NOUN
cana-3334	86	14	4	4	NUM
cana-3334	86	15	and	and	CCONJ
cana-3334	86	16	6	6	NUM
cana-3334	86	17	the	the	DET
cana-3334	86	18	semi	semi	ADJ
cana-3334	86	19	perimeter	perimeter	NOUN
cana-3334	86	20	for	for	ADP
cana-3334	86	21	δ	δ	PROPN
cana-3334	86	22	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	86	23	is	be	AUX
cana-3334	86	24	𝑠	𝑠	ADP
cana-3334	86	25	=	=	PRON
cana-3334	86	26	𝑛+𝑛+𝑑	𝑛+𝑛+𝑑	NOUN
cana-3334	86	27	2	2	NUM
cana-3334	86	28	=	=	SYM
cana-3334	86	29	2𝑛+𝑑	2𝑛+𝑑	NUM
cana-3334	86	30	𝑑	𝑑	NOUN
cana-3334	86	31	.	.	PUNCT
cana-3334	87	1	thus	thus	ADV
cana-3334	87	2	by	by	ADP
cana-3334	87	3	applying	apply	VERB
cana-3334	87	4	heron	heron	NOUN
cana-3334	87	5	's	's	PART
cana-3334	87	6	formula	formula	NOUN
cana-3334	87	7	,	,	PUNCT
cana-3334	87	8	we	we	PRON
cana-3334	87	9	obtain	obtain	VERB
cana-3334	87	10	area	area	NOUN
cana-3334	87	11	of	of	ADP
cana-3334	87	12	δ	δ	PROPN
cana-3334	87	13	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	87	14	=	=	PROPN
cana-3334	87	15	𝑑	𝑑	PROPN
cana-3334	87	16	4	4	NUM
cana-3334	87	17	√4𝑛2	√4𝑛2	NOUN
cana-3334	87	18	−	−	PROPN
cana-3334	87	19	𝑑2	𝑑2	NOUN
cana-3334	87	20	(	(	PUNCT
cana-3334	87	21	3	3	X
cana-3334	87	22	)	)	PUNCT
cana-3334	87	23	the	the	DET
cana-3334	87	24	semi	semi	ADJ
cana-3334	87	25	perimeter	perimeter	NOUN
cana-3334	87	26	for	for	ADP
cana-3334	87	27	δ	δ	PROPN
cana-3334	87	28	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	87	29	is	be	AUX
cana-3334	87	30	𝑠	𝑠	PROPN
cana-3334	87	31	=	=	PUNCT
cana-3334	87	32	𝑛−1+𝑛−1+𝑑	𝑛−1+𝑛−1+𝑑	NOUN
cana-3334	87	33	2	2	NUM
cana-3334	87	34	=	=	SYM
cana-3334	87	35	2𝑛−2+𝑑	2𝑛−2+𝑑	NUM
cana-3334	87	36	2	2	NUM
cana-3334	87	37	.	.	PUNCT
cana-3334	88	1	thus	thus	ADV
cana-3334	88	2	by	by	ADP
cana-3334	88	3	applying	apply	VERB
cana-3334	88	4	heron	heron	NOUN
cana-3334	88	5	's	's	PART
cana-3334	88	6	formula	formula	NOUN
cana-3334	88	7	,	,	PUNCT
cana-3334	88	8	we	we	PRON
cana-3334	88	9	obtain	obtain	VERB
cana-3334	88	10	area	area	NOUN
cana-3334	88	11	of	of	ADP
cana-3334	88	12	δ	δ	PROPN
cana-3334	88	13	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	88	14	=	=	PRON
cana-3334	89	1	𝑑	𝑑	PROPN
cana-3334	89	2	4	4	NUM
cana-3334	89	3	√(2𝑛	√(2𝑛	NOUN
cana-3334	89	4	−	−	PROPN
cana-3334	89	5	2)2	2)2	NUM
cana-3334	89	6	−	−	NOUN
cana-3334	89	7	𝑑2	𝑑2	NOUN
cana-3334	89	8	(	(	PUNCT
cana-3334	89	9	4	4	X
cana-3334	89	10	)	)	PUNCT
cana-3334	89	11	this	this	PRON
cana-3334	89	12	implies	imply	VERB
cana-3334	89	13	the	the	DET
cana-3334	89	14	fact	fact	NOUN
cana-3334	89	15	that	that	SCONJ
cana-3334	89	16	the	the	DET
cana-3334	89	17	area	area	NOUN
cana-3334	89	18	of	of	ADP
cana-3334	89	19	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	89	20	∈	∈	PROPN
cana-3334	89	21	ℤ	ℤ	PROPN
cana-3334	89	22	,	,	PUNCT
cana-3334	89	23	if	if	SCONJ
cana-3334	89	24	and	and	CCONJ
cana-3334	89	25	only	only	ADV
cana-3334	89	26	if	if	SCONJ
cana-3334	89	27	the	the	DET
cana-3334	89	28	area	area	NOUN
cana-3334	89	29	of	of	ADP
cana-3334	89	30	δ	δ	PROPN
cana-3334	89	31	𝐴𝐵𝐷	𝐴𝐵𝐷	PROPN
cana-3334	89	32	and	and	CCONJ
cana-3334	89	33	area	area	NOUN
cana-3334	89	34	of	of	ADP
cana-3334	89	35	δ	δ	PROPN
cana-3334	89	36	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	89	37	both	both	PRON
cana-3334	89	38	must	must	AUX
cana-3334	89	39	be	be	AUX
cana-3334	89	40	rational	rational	ADJ
cana-3334	89	41	numbers	number	NOUN
cana-3334	89	42	.	.	PUNCT
cana-3334	90	1	area	area	NOUN
cana-3334	90	2	of	of	ADP
cana-3334	90	3	𝚫	𝚫	PROPN
cana-3334	90	4	𝑨𝑩𝑪	𝑨𝑩𝑪	PROPN
cana-3334	90	5	over	over	ADP
cana-3334	90	6	ℚ	ℚ	PROPN
cana-3334	90	7	`	`	PUNCT
cana-3334	90	8	`	`	PUNCT
cana-3334	90	9	equation	equation	NOUN
cana-3334	90	10	(	(	PUNCT
cana-3334	90	11	3	3	NUM
cana-3334	90	12	)	)	PUNCT
cana-3334	90	13	''	''	PUNCT
cana-3334	90	14	implies	imply	VERB
cana-3334	90	15	that	that	DET
cana-3334	90	16	area	area	NOUN
cana-3334	90	17	of	of	ADP
cana-3334	90	18	δ	δ	PROPN
cana-3334	90	19	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	90	20	∈	∈	PROPN
cana-3334	90	21	ℚ	ℚ	PROPN
cana-3334	90	22	if	if	SCONJ
cana-3334	90	23	𝑡1	𝑡1	NOUN
cana-3334	90	24	=	=	SYM
cana-3334	90	25	2𝑛	2𝑛	PROPN
cana-3334	90	26	(	(	PUNCT
cana-3334	90	27	𝑚2−𝑙2	𝑚2−𝑙2	PROPN
cana-3334	90	28	𝑚2+𝑙2	𝑚2+𝑙2	PROPN
cana-3334	90	29	)	)	PUNCT
cana-3334	90	30	and	and	CCONJ
cana-3334	90	31	𝑑	𝑑	PROPN
cana-3334	90	32	=	=	X
cana-3334	90	33	4𝑛	4𝑛	PROPN
cana-3334	90	34	(	(	PUNCT
cana-3334	90	35	𝑚𝑙	𝑚𝑙	NOUN
cana-3334	90	36	𝑚2+𝑙2	𝑚2+𝑙2	PROPN
cana-3334	90	37	)	)	PUNCT
cana-3334	90	38	for	for	ADP
cana-3334	90	39	some	some	DET
cana-3334	90	40	𝑚	𝑚	NOUN
cana-3334	90	41	,	,	PUNCT
cana-3334	90	42	𝑙	𝑙	PROPN
cana-3334	90	43	∈	∈	PROPN
cana-3334	90	44	ℤ	ℤ	PROPN
cana-3334	90	45	and	and	CCONJ
cana-3334	90	46	𝑚	𝑚	X
cana-3334	90	47	>	>	X
cana-3334	90	48	𝑙.	𝑙.	ADJ
cana-3334	90	49	area	area	NOUN
cana-3334	90	50	of	of	ADP
cana-3334	90	51	𝚫	𝚫	PROPN
cana-3334	90	52	𝑨𝑫𝑪	𝑨𝑫𝑪	NOUN
cana-3334	90	53	over	over	ADP
cana-3334	90	54	ℚ	ℚ	PROPN
cana-3334	90	55	`	`	PUNCT
cana-3334	90	56	`	`	PUNCT
cana-3334	90	57	equation	equation	NOUN
cana-3334	90	58	(	(	PUNCT
cana-3334	90	59	4	4	NUM
cana-3334	90	60	)	)	PUNCT
cana-3334	90	61	''	''	PUNCT
cana-3334	90	62	implies	imply	VERB
cana-3334	90	63	that	that	DET
cana-3334	90	64	area	area	NOUN
cana-3334	90	65	of	of	ADP
cana-3334	90	66	δ	δ	PROPN
cana-3334	90	67	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	90	68	∈	∈	PROPN
cana-3334	90	69	ℚ	ℚ	PROPN
cana-3334	90	70	if	if	SCONJ
cana-3334	90	71	(	(	PUNCT
cana-3334	90	72	2𝑛	2𝑛	PROPN
cana-3334	90	73	−	−	PROPN
cana-3334	90	74	2)2	2)2	NUM
cana-3334	90	75	−	−	NOUN
cana-3334	90	76	𝑑2	𝑑2	NOUN
cana-3334	90	77	=	=	SYM
cana-3334	90	78	𝑡2	𝑡2	ADJ
cana-3334	90	79	2	2	NUM
cana-3334	90	80	for	for	ADP
cana-3334	90	81	some	some	DET
cana-3334	90	82	𝑡2	𝑡2	PROPN
cana-3334	90	83	∈	∈	PROPN
cana-3334	90	84	ℚ	ℚ	PROPN
cana-3334	90	85	.	.	PUNCT
cana-3334	91	1	as	as	ADP
cana-3334	91	2	in	in	ADP
cana-3334	91	3	the	the	DET
cana-3334	91	4	above	above	ADJ
cana-3334	91	5	case	case	NOUN
cana-3334	91	6	,	,	PUNCT
cana-3334	91	7	we	we	PRON
cana-3334	91	8	have	have	VERB
cana-3334	91	9	𝑡2	𝑡2	NOUN
cana-3334	91	10	=	=	SYM
cana-3334	91	11	(	(	PUNCT
cana-3334	91	12	2𝑛	2𝑛	PROPN
cana-3334	91	13	−	−	PROPN
cana-3334	91	14	2	2	NUM
cana-3334	91	15	)	)	PUNCT
cana-3334	91	16	(	(	PUNCT
cana-3334	91	17	𝑎2−𝑏2	𝑎2−𝑏2	ADV
cana-3334	91	18	)	)	PUNCT
cana-3334	91	19	(	(	PUNCT
cana-3334	91	20	𝑎2+𝑏2	𝑎2+𝑏2	PROPN
cana-3334	91	21	)	)	PUNCT
cana-3334	91	22	and	and	CCONJ
cana-3334	91	23	𝑑	𝑑	PROPN
cana-3334	91	24	=	=	X
cana-3334	91	25	(	(	PUNCT
cana-3334	91	26	2𝑛	2𝑛	NOUN
cana-3334	91	27	−	−	PROPN
cana-3334	91	28	2	2	NUM
cana-3334	91	29	)	)	PUNCT
cana-3334	91	30	(	(	PUNCT
cana-3334	91	31	2𝑎𝑏	2𝑎𝑏	PROPN
cana-3334	91	32	𝑎2+𝑏2	𝑎2+𝑏2	PROPN
cana-3334	91	33	)	)	PUNCT
cana-3334	91	34	for	for	ADP
cana-3334	91	35	some	some	DET
cana-3334	91	36	𝑎	𝑎	NOUN
cana-3334	91	37	,	,	PUNCT
cana-3334	91	38	𝑏	𝑏	PROPN
cana-3334	91	39	∈	∈	PROPN
cana-3334	91	40	ℤ	ℤ	PROPN
cana-3334	91	41	and	and	CCONJ
cana-3334	91	42	𝑎	𝑎	ADP
cana-3334	91	43	>	>	X
cana-3334	91	44	𝑏.	𝑏.	NOUN
cana-3334	91	45	to	to	PART
cana-3334	91	46	find	find	VERB
cana-3334	91	47	required	require	VERB
cana-3334	91	48	n	n	NOUN
cana-3334	91	49	since	since	SCONJ
cana-3334	91	50	the	the	DET
cana-3334	91	51	value	value	NOUN
cana-3334	91	52	𝑑	𝑑	NOUN
cana-3334	91	53	is	be	AUX
cana-3334	91	54	equal	equal	ADJ
cana-3334	91	55	in	in	ADP
cana-3334	91	56	both	both	CCONJ
cana-3334	91	57	the	the	DET
cana-3334	91	58	areas	area	NOUN
cana-3334	91	59	,	,	PUNCT
cana-3334	91	60	we	we	PRON
cana-3334	91	61	can	can	AUX
cana-3334	91	62	equate	equate	VERB
cana-3334	91	63	them	they	PRON
cana-3334	91	64	and	and	CCONJ
cana-3334	91	65	find	find	VERB
cana-3334	91	66	𝑛	𝑛	PRON
cana-3334	91	67	as	as	ADP
cana-3334	91	68	𝑛	𝑛	NOUN
cana-3334	91	69	=	=	SYM
cana-3334	91	70	𝑎𝑏(𝑚2	𝑎𝑏(𝑚2	PROPN
cana-3334	92	1	+	+	CCONJ
cana-3334	92	2	𝑙2	𝑙2	NOUN
cana-3334	92	3	)	)	PUNCT
cana-3334	92	4	𝑎𝑏(𝑚2	𝑎𝑏(𝑚2	PROPN
cana-3334	93	1	+	+	CCONJ
cana-3334	93	2	𝑙2	𝑙2	NOUN
cana-3334	93	3	)	)	PUNCT
cana-3334	93	4	−	−	ADP
cana-3334	93	5	𝑚𝑙(𝑎2	𝑚𝑙(𝑎2	NOUN
cana-3334	94	1	+	+	NUM
cana-3334	94	2	𝑏2	𝑏2	NOUN
cana-3334	94	3	)	)	PUNCT
cana-3334	94	4	4.1	4.1	NUM
cana-3334	94	5	.	.	PUNCT
cana-3334	95	1	python	python	NOUN
cana-3334	95	2	coding	coding	NOUN
cana-3334	95	3	for	for	ADP
cana-3334	95	4	generation	generation	NOUN
cana-3334	95	5	of	of	ADP
cana-3334	95	6	required	require	VERB
cana-3334	95	7	kites	kite	NOUN
cana-3334	95	8	with	with	ADP
cana-3334	95	9	sides	side	NOUN
cana-3334	95	10	𝒏	𝒏	PROPN
cana-3334	95	11	and	and	CCONJ
cana-3334	95	12	𝒏	𝒏	PROPN
cana-3334	95	13	−	−	PROPN
cana-3334	95	14	𝟏	𝟏	NUM
cana-3334	95	15	in	in	ADP
cana-3334	95	16	this	this	DET
cana-3334	95	17	section	section	NOUN
cana-3334	95	18	we	we	PRON
cana-3334	95	19	display	display	VERB
cana-3334	95	20	python	python	NOUN
cana-3334	95	21	coding	code	VERB
cana-3334	95	22	to	to	PART
cana-3334	95	23	collect	collect	VERB
cana-3334	95	24	kites	kite	NOUN
cana-3334	95	25	with	with	ADP
cana-3334	95	26	sides	side	NOUN
cana-3334	95	27	𝑛	𝑛	PROPN
cana-3334	95	28	,	,	PUNCT
cana-3334	95	29	𝑛	𝑛	PRON
cana-3334	95	30	−	−	PROPN
cana-3334	95	31	1	1	NUM
cana-3334	95	32	,	,	PUNCT
cana-3334	95	33	rational	rational	ADJ
cana-3334	95	34	diagonals	diagonal	NOUN
cana-3334	95	35	and	and	CCONJ
cana-3334	95	36	integer	integer	NOUN
cana-3334	95	37	area	area	NOUN
cana-3334	95	38	followed	follow	VERB
cana-3334	95	39	by	by	ADP
cana-3334	95	40	its	its	PRON
cana-3334	95	41	output	output	NOUN
cana-3334	95	42	.	.	PUNCT
cana-3334	96	1	communications	communication	NOUN
cana-3334	96	2	on	on	ADP
cana-3334	96	3	applied	apply	VERB
cana-3334	96	4	nonlinear	nonlinear	ADJ
cana-3334	96	5	analysis	analysis	NOUN
cana-3334	96	6	issn	issn	NOUN
cana-3334	96	7	:	:	PUNCT
cana-3334	96	8	1074	1074	NUM
cana-3334	96	9	-	-	PUNCT
cana-3334	96	10	133x	133x	NUM
cana-3334	96	11	vol	vol	NOUN
cana-3334	96	12	32	32	NUM
cana-3334	96	13	no	no	NOUN
cana-3334	96	14	.	.	PUNCT
cana-3334	97	1	7s	7	NOUN
cana-3334	97	2	(	(	PUNCT
cana-3334	97	3	2025	2025	NUM
cana-3334	97	4	)	)	PUNCT
cana-3334	97	5	7	7	NUM
cana-3334	97	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3334	97	7	figure	figure	NOUN
cana-3334	97	8	6	6	NUM
cana-3334	97	9	:	:	PUNCT
cana-3334	97	10	coding	code	VERB
cana-3334	97	11	2	2	NUM
cana-3334	97	12	:	:	PUNCT
cana-3334	97	13	kite	kite	NOUN
cana-3334	97	14	with	with	ADP
cana-3334	97	15	sides	side	NOUN
cana-3334	97	16	𝑛	𝑛	PROPN
cana-3334	97	17	,	,	PUNCT
cana-3334	97	18	𝑛	𝑛	PRON
cana-3334	97	19	−	−	NUM
cana-3334	97	20	1	1	NUM
cana-3334	97	21	figure	figure	NOUN
cana-3334	97	22	7	7	NUM
cana-3334	97	23	:	:	PUNCT
cana-3334	97	24	output	output	NOUN
cana-3334	97	25	:	:	PUNCT
cana-3334	97	26	coding	code	VERB
cana-3334	97	27	2	2	NUM
cana-3334	97	28	4.2	4.2	NUM
cana-3334	97	29	.	.	PUNCT
cana-3334	98	1	experimental	experimental	ADJ
cana-3334	98	2	analysis	analysis	NOUN
cana-3334	98	3	by	by	ADP
cana-3334	98	4	an	an	DET
cana-3334	98	5	example	example	NOUN
cana-3334	98	6	in	in	ADP
cana-3334	98	7	figure	figure	NOUN
cana-3334	98	8	1	1	NUM
cana-3334	98	9	,	,	PUNCT
cana-3334	98	10	take	take	VERB
cana-3334	98	11	the	the	DET
cana-3334	98	12	diagonals	diagonal	NOUN
cana-3334	98	13	as	as	ADP
cana-3334	98	14	𝐵𝐷(=	𝐵𝐷(=	NOUN
cana-3334	98	15	𝑑	𝑑	NOUN
cana-3334	98	16	)	)	PUNCT
cana-3334	98	17	,	,	PUNCT
cana-3334	98	18	𝐴𝐶(=	𝐴𝐶(=	CCONJ
cana-3334	98	19	𝑑1	𝑑1	NOUN
cana-3334	98	20	)	)	PUNCT
cana-3334	98	21	and	and	CCONJ
cana-3334	98	22	the	the	DET
cana-3334	98	23	sides	side	NOUN
cana-3334	98	24	as	as	ADP
cana-3334	98	25	𝐶𝐵	𝐶𝐵	PROPN
cana-3334	98	26	=	=	SYM
cana-3334	98	27	𝑛	𝑛	NOUN
cana-3334	98	28	=	=	PUNCT
cana-3334	98	29	𝐶𝐷	𝐶𝐷	PROPN
cana-3334	98	30	and	and	CCONJ
cana-3334	98	31	𝐴𝐷	𝐴𝐷	PROPN
cana-3334	98	32	=	=	SYM
cana-3334	99	1	𝑛	𝑛	PRON
cana-3334	99	2	−	−	NUM
cana-3334	99	3	1	1	NUM
cana-3334	99	4	=	=	SYM
cana-3334	99	5	𝐴𝐵.	𝐴𝐵.	NOUN
cana-3334	99	6	doing	do	VERB
cana-3334	99	7	the	the	DET
cana-3334	99	8	same	same	ADJ
cana-3334	99	9	procedure	procedure	NOUN
cana-3334	99	10	as	as	ADP
cana-3334	99	11	in	in	ADP
cana-3334	99	12	subsection	subsection	NOUN
cana-3334	99	13	3.2	3.2	NUM
cana-3334	99	14	,	,	PUNCT
cana-3334	99	15	we	we	PRON
cana-3334	99	16	get	get	VERB
cana-3334	99	17	𝑑1	𝑑1	NOUN
cana-3334	99	18	=	=	NOUN
cana-3334	99	19	1	1	NUM
cana-3334	99	20	2	2	NUM
cana-3334	99	21	[	[	X
cana-3334	99	22	√4𝑛2	√4𝑛2	NOUN
cana-3334	99	23	−	−	PROPN
cana-3334	99	24	𝑑2	𝑑2	NOUN
cana-3334	99	25	+	+	CCONJ
cana-3334	99	26	√4(𝑛	√4(𝑛	VERB
cana-3334	99	27	−	−	PROPN
cana-3334	99	28	1)2	1)2	NUM
cana-3334	99	29	−	−	NOUN
cana-3334	99	30	𝑑2	𝑑2	NOUN
cana-3334	99	31	]	]	PUNCT
cana-3334	99	32	.	.	PUNCT
cana-3334	100	1	so	so	ADV
cana-3334	100	2	the	the	DET
cana-3334	100	3	area	area	NOUN
cana-3334	100	4	is	be	AUX
cana-3334	100	5	1	1	NUM
cana-3334	100	6	4	4	NUM
cana-3334	100	7	𝑑	𝑑	NOUN
cana-3334	100	8	[	[	X
cana-3334	100	9	√4𝑛2	√4𝑛2	NOUN
cana-3334	100	10	−	−	PROPN
cana-3334	100	11	𝑑2	𝑑2	NOUN
cana-3334	100	12	+	+	CCONJ
cana-3334	100	13	√4(𝑛	√4(𝑛	VERB
cana-3334	100	14	−	−	PROPN
cana-3334	100	15	1)2	1)2	NUM
cana-3334	100	16	−	−	NOUN
cana-3334	100	17	𝑑2	𝑑2	NOUN
cana-3334	100	18	]	]	PUNCT
cana-3334	100	19	.	.	PUNCT
cana-3334	101	1	now	now	ADV
cana-3334	101	2	,	,	PUNCT
cana-3334	101	3	let	let	VERB
cana-3334	101	4	us	we	PRON
cana-3334	101	5	verify	verify	VERB
cana-3334	101	6	this	this	PRON
cana-3334	101	7	by	by	ADP
cana-3334	101	8	an	an	DET
cana-3334	101	9	example	example	NOUN
cana-3334	101	10	.	.	PUNCT
cana-3334	102	1	take	take	VERB
cana-3334	102	2	𝑛	𝑛	NOUN
cana-3334	102	3	=	=	SYM
cana-3334	102	4	4	4	NUM
cana-3334	102	5	and	and	CCONJ
cana-3334	102	6	𝑑	𝑑	NOUN
cana-3334	102	7	=	=	ADJ
cana-3334	102	8	24	24	NUM
cana-3334	102	9	5	5	NUM
cana-3334	102	10	.	.	PUNCT
cana-3334	103	1	then	then	ADV
cana-3334	103	2	we	we	PRON
cana-3334	103	3	obtain	obtain	VERB
cana-3334	103	4	𝑑1	𝑑1	NOUN
cana-3334	103	5	=	=	NOUN
cana-3334	103	6	5	5	X
cana-3334	103	7	.	.	PUNCT
cana-3334	104	1	this	this	PRON
cana-3334	104	2	gives	give	VERB
cana-3334	104	3	the	the	DET
cana-3334	104	4	area	area	NOUN
cana-3334	104	5	12	12	NUM
cana-3334	104	6	,	,	PUNCT
cana-3334	104	7	is	be	AUX
cana-3334	104	8	same	same	ADJ
cana-3334	104	9	as	as	ADP
cana-3334	104	10	the	the	DET
cana-3334	104	11	one	one	NUM
cana-3334	104	12	found	find	VERB
cana-3334	104	13	from	from	ADP
cana-3334	104	14	the	the	DET
cana-3334	104	15	python	python	NOUN
cana-3334	104	16	coding	coding	NOUN
cana-3334	104	17	.	.	PUNCT
cana-3334	105	1	communications	communication	NOUN
cana-3334	105	2	on	on	ADP
cana-3334	105	3	applied	apply	VERB
cana-3334	105	4	nonlinear	nonlinear	ADJ
cana-3334	105	5	analysis	analysis	NOUN
cana-3334	105	6	issn	issn	NOUN
cana-3334	105	7	:	:	PUNCT
cana-3334	105	8	1074	1074	NUM
cana-3334	105	9	-	-	PUNCT
cana-3334	105	10	133x	133x	NUM
cana-3334	105	11	vol	vol	NOUN
cana-3334	105	12	32	32	NUM
cana-3334	105	13	no	no	NOUN
cana-3334	105	14	.	.	PUNCT
cana-3334	106	1	7s	7	NOUN
cana-3334	106	2	(	(	PUNCT
cana-3334	106	3	2025	2025	NUM
cana-3334	106	4	)	)	PUNCT
cana-3334	106	5	8	8	NUM
cana-3334	106	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3334	106	7	5	5	NUM
cana-3334	106	8	.	.	PUNCT
cana-3334	107	1	kite	kite	NOUN
cana-3334	107	2	with	with	ADP
cana-3334	107	3	sides	side	NOUN
cana-3334	107	4	𝒏	𝒏	PROPN
cana-3334	107	5	,	,	PUNCT
cana-3334	107	6	𝒏	𝒏	PROPN
cana-3334	107	7	+	+	CCONJ
cana-3334	107	8	𝒓	𝒓	PROPN
cana-3334	107	9	in	in	ADP
cana-3334	107	10	this	this	DET
cana-3334	107	11	section	section	NOUN
cana-3334	107	12	,	,	PUNCT
cana-3334	107	13	we	we	PRON
cana-3334	107	14	work	work	VERB
cana-3334	107	15	on	on	ADP
cana-3334	107	16	kites	kite	NOUN
cana-3334	107	17	with	with	ADP
cana-3334	107	18	sides	side	NOUN
cana-3334	107	19	𝑛	𝑛	PRON
cana-3334	107	20	and	and	CCONJ
cana-3334	107	21	𝑛	𝑛	PRON
cana-3334	107	22	+	+	ADJ
cana-3334	107	23	𝑟	𝑟	NOUN
cana-3334	107	24	,	,	PUNCT
cana-3334	107	25	as	as	ADP
cana-3334	107	26	above	above	ADV
cana-3334	107	27	.	.	PUNCT
cana-3334	108	1	let	let	VERB
cana-3334	108	2	us	we	PRON
cana-3334	108	3	consider	consider	VERB
cana-3334	108	4	a	a	DET
cana-3334	108	5	kite	kite	NOUN
cana-3334	108	6	a𝐵𝐶𝐷	a𝐵𝐶𝐷	PROPN
cana-3334	108	7	with	with	ADP
cana-3334	108	8	sides	side	NOUN
cana-3334	108	9	𝑛	𝑛	PRON
cana-3334	108	10	and	and	CCONJ
cana-3334	108	11	𝑛	𝑛	PRON
cana-3334	108	12	+	+	CCONJ
cana-3334	108	13	𝑟.	𝑟.	NOUN
cana-3334	108	14	in	in	ADP
cana-3334	108	15	fig	fig	NOUN
cana-3334	108	16	2	2	NUM
cana-3334	108	17	,	,	PUNCT
cana-3334	108	18	take	take	VERB
cana-3334	108	19	𝐴𝐵	𝐴𝐵	NOUN
cana-3334	108	20	=	=	SYM
cana-3334	108	21	𝑛	𝑛	NOUN
cana-3334	108	22	=	=	SYM
cana-3334	108	23	𝐵𝐶	𝐵𝐶	PROPN
cana-3334	108	24	and	and	CCONJ
cana-3334	108	25	𝐴𝐷	𝐴𝐷	PROPN
cana-3334	108	26	=	=	SYM
cana-3334	108	27	𝑛	𝑛	PROPN
cana-3334	108	28	+	+	NUM
cana-3334	108	29	𝑟	𝑟	NOUN
cana-3334	108	30	=	=	NOUN
cana-3334	108	31	𝐷𝐶.	𝐷𝐶.	NOUN
cana-3334	108	32	let	let	VERB
cana-3334	108	33	𝐴𝐶	𝐴𝐶	PROPN
cana-3334	108	34	=	=	SYM
cana-3334	108	35	𝑑.	𝑑.	NOUN
cana-3334	108	36	then	then	ADV
cana-3334	108	37	the	the	DET
cana-3334	108	38	kite	kite	NOUN
cana-3334	108	39	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	108	40	can	can	AUX
cana-3334	108	41	be	be	AUX
cana-3334	108	42	split	split	VERB
cana-3334	108	43	into	into	ADP
cana-3334	108	44	two	two	NUM
cana-3334	108	45	isosceles	isoscele	NOUN
cana-3334	108	46	triangles	triangle	NOUN
cana-3334	108	47	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	108	48	and	and	CCONJ
cana-3334	108	49	𝐴𝐷𝐶.	𝐴𝐷𝐶.	X
cana-3334	108	50	thus	thus	ADV
cana-3334	108	51	,	,	PUNCT
cana-3334	108	52	area	area	NOUN
cana-3334	108	53	of	of	ADP
cana-3334	108	54	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	108	55	=	=	PUNCT
cana-3334	108	56	area	area	NOUN
cana-3334	108	57	of	of	ADP
cana-3334	108	58	δ	δ	PROPN
cana-3334	108	59	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	108	60	+	+	PROPN
cana-3334	108	61	area	area	NOUN
cana-3334	108	62	of	of	ADP
cana-3334	108	63	δ	δ	PROPN
cana-3334	108	64	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	108	65	as	as	ADP
cana-3334	108	66	in	in	ADP
cana-3334	108	67	the	the	DET
cana-3334	108	68	previous	previous	ADJ
cana-3334	108	69	sections	section	NOUN
cana-3334	108	70	,	,	PUNCT
cana-3334	108	71	we	we	PRON
cana-3334	108	72	get	get	VERB
cana-3334	108	73	δ	δ	PROPN
cana-3334	108	74	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	108	75	area	area	NOUN
cana-3334	108	76	of	of	ADP
cana-3334	108	77	δ	δ	PROPN
cana-3334	109	1	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	109	2	=	=	PROPN
cana-3334	109	3	𝑑	𝑑	PROPN
cana-3334	109	4	4	4	NUM
cana-3334	109	5	√4𝑛2	√4𝑛2	NOUN
cana-3334	109	6	−	−	PROPN
cana-3334	109	7	𝑑2	𝑑2	NOUN
cana-3334	109	8	(	(	PUNCT
cana-3334	109	9	5	5	NUM
cana-3334	109	10	)	)	PUNCT
cana-3334	109	11	the	the	DET
cana-3334	109	12	semi	semi	ADJ
cana-3334	109	13	perimeter	perimeter	NOUN
cana-3334	109	14	for	for	ADP
cana-3334	109	15	δ	δ	PROPN
cana-3334	109	16	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	109	17	is	be	AUX
cana-3334	109	18	𝑠	𝑠	ADP
cana-3334	109	19	=	=	SYM
cana-3334	109	20	𝑛+𝑟+𝑛+𝑟+𝑑	𝑛+𝑟+𝑛+𝑟+𝑑	ADJ
cana-3334	109	21	2	2	NUM
cana-3334	109	22	=	=	SYM
cana-3334	109	23	2𝑛+2𝑟+𝑑	2𝑛+2𝑟+𝑑	NUM
cana-3334	109	24	2	2	NUM
cana-3334	109	25	.	.	PUNCT
cana-3334	110	1	thus	thus	ADV
cana-3334	110	2	by	by	ADP
cana-3334	110	3	applying	apply	VERB
cana-3334	110	4	heron	heron	NOUN
cana-3334	110	5	's	's	PART
cana-3334	110	6	formula	formula	NOUN
cana-3334	110	7	,	,	PUNCT
cana-3334	110	8	we	we	PRON
cana-3334	110	9	obtain	obtain	VERB
cana-3334	110	10	,	,	PUNCT
cana-3334	110	11	area	area	NOUN
cana-3334	110	12	of	of	ADP
cana-3334	110	13	δ	δ	PROPN
cana-3334	110	14	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	110	15	=	=	PRON
cana-3334	110	16	𝑑	𝑑	PROPN
cana-3334	110	17	4	4	NUM
cana-3334	110	18	√(2𝑛	√(2𝑛	NOUN
cana-3334	111	1	+	+	CCONJ
cana-3334	111	2	2𝑟)2	2𝑟)2	NUM
cana-3334	111	3	−	−	NOUN
cana-3334	111	4	𝑑2	𝑑2	NOUN
cana-3334	111	5	(	(	PUNCT
cana-3334	111	6	6	6	NUM
cana-3334	111	7	)	)	PUNCT
cana-3334	111	8	this	this	PRON
cana-3334	111	9	implies	imply	VERB
cana-3334	111	10	the	the	DET
cana-3334	111	11	fact	fact	NOUN
cana-3334	111	12	that	that	SCONJ
cana-3334	111	13	the	the	DET
cana-3334	111	14	area	area	NOUN
cana-3334	111	15	of	of	ADP
cana-3334	111	16	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	111	17	∈	∈	PROPN
cana-3334	111	18	ℤ	ℤ	PROPN
cana-3334	111	19	,	,	PUNCT
cana-3334	111	20	if	if	SCONJ
cana-3334	111	21	and	and	CCONJ
cana-3334	111	22	only	only	ADV
cana-3334	111	23	if	if	SCONJ
cana-3334	111	24	the	the	DET
cana-3334	111	25	area	area	NOUN
cana-3334	111	26	of	of	ADP
cana-3334	111	27	δ	δ	PROPN
cana-3334	111	28	𝐴𝐵𝐷	𝐴𝐵𝐷	PROPN
cana-3334	111	29	and	and	CCONJ
cana-3334	111	30	area	area	NOUN
cana-3334	111	31	of	of	ADP
cana-3334	111	32	δ	δ	PROPN
cana-3334	111	33	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	111	34	both	both	PRON
cana-3334	111	35	must	must	AUX
cana-3334	111	36	be	be	AUX
cana-3334	111	37	rational	rational	ADJ
cana-3334	111	38	numbers	number	NOUN
cana-3334	111	39	.	.	PUNCT
cana-3334	112	1	area	area	NOUN
cana-3334	112	2	of	of	ADP
cana-3334	112	3	𝚫	𝚫	PROPN
cana-3334	112	4	𝑨𝑩𝑪	𝑨𝑩𝑪	PROPN
cana-3334	112	5	over	over	ADP
cana-3334	112	6	ℚ	ℚ	PROPN
cana-3334	112	7	`	`	PUNCT
cana-3334	112	8	`	`	PUNCT
cana-3334	112	9	equation	equation	NOUN
cana-3334	112	10	(	(	PUNCT
cana-3334	112	11	5	5	NUM
cana-3334	112	12	)	)	PUNCT
cana-3334	112	13	''	''	PUNCT
cana-3334	112	14	implies	imply	VERB
cana-3334	112	15	that	that	DET
cana-3334	112	16	area	area	NOUN
cana-3334	112	17	of	of	ADP
cana-3334	112	18	δ	δ	PROPN
cana-3334	112	19	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	112	20	∈	∈	PROPN
cana-3334	112	21	ℚ	ℚ	PROPN
cana-3334	112	22	if	if	SCONJ
cana-3334	112	23	𝑡1	𝑡1	NOUN
cana-3334	112	24	=	=	SYM
cana-3334	112	25	2𝑛	2𝑛	PROPN
cana-3334	112	26	(	(	PUNCT
cana-3334	112	27	𝑚2−𝑙2	𝑚2−𝑙2	PROPN
cana-3334	112	28	𝑚2+𝑙2	𝑚2+𝑙2	PROPN
cana-3334	112	29	)	)	PUNCT
cana-3334	112	30	and	and	CCONJ
cana-3334	112	31	𝑑	𝑑	PROPN
cana-3334	112	32	=	=	X
cana-3334	112	33	4𝑛	4𝑛	PROPN
cana-3334	112	34	(	(	PUNCT
cana-3334	112	35	𝑚𝑙	𝑚𝑙	NOUN
cana-3334	112	36	𝑚2+𝑙2	𝑚2+𝑙2	PROPN
cana-3334	112	37	)	)	PUNCT
cana-3334	112	38	for	for	ADP
cana-3334	112	39	some	some	DET
cana-3334	112	40	𝑚	𝑚	NOUN
cana-3334	112	41	,	,	PUNCT
cana-3334	112	42	𝑙	𝑙	PROPN
cana-3334	112	43	∈	∈	PROPN
cana-3334	112	44	ℤ	ℤ	PROPN
cana-3334	112	45	and	and	CCONJ
cana-3334	112	46	𝑚	𝑚	X
cana-3334	112	47	>	>	X
cana-3334	112	48	𝑙.	𝑙.	ADJ
cana-3334	112	49	area	area	NOUN
cana-3334	112	50	of	of	ADP
cana-3334	112	51	𝚫	𝚫	PROPN
cana-3334	112	52	𝑨𝑫𝑪	𝑨𝑫𝑪	NOUN
cana-3334	112	53	over	over	ADP
cana-3334	112	54	ℚ	ℚ	PROPN
cana-3334	112	55	`	`	PUNCT
cana-3334	112	56	`	`	PUNCT
cana-3334	112	57	equation	equation	NOUN
cana-3334	112	58	(	(	PUNCT
cana-3334	112	59	6	6	NUM
cana-3334	112	60	)	)	PUNCT
cana-3334	112	61	''	''	PUNCT
cana-3334	112	62	implies	imply	VERB
cana-3334	112	63	that	that	DET
cana-3334	112	64	area	area	NOUN
cana-3334	112	65	of	of	ADP
cana-3334	112	66	δ	δ	PROPN
cana-3334	112	67	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	112	68	∈	∈	PROPN
cana-3334	112	69	ℚ	ℚ	PROPN
cana-3334	112	70	if	if	SCONJ
cana-3334	112	71	(	(	PUNCT
cana-3334	112	72	2𝑛	2𝑛	NOUN
cana-3334	112	73	+	+	CCONJ
cana-3334	112	74	2𝑟)2	2𝑟)2	NUM
cana-3334	112	75	−	−	NOUN
cana-3334	112	76	𝑑2	𝑑2	NOUN
cana-3334	112	77	=	=	SYM
cana-3334	112	78	𝑡2	𝑡2	ADJ
cana-3334	112	79	2	2	NUM
cana-3334	112	80	for	for	ADP
cana-3334	112	81	some	some	DET
cana-3334	112	82	𝑡2	𝑡2	PROPN
cana-3334	112	83	∈	∈	PROPN
cana-3334	112	84	ℚ	ℚ	PROPN
cana-3334	112	85	.	.	PUNCT
cana-3334	113	1	as	as	ADP
cana-3334	113	2	in	in	ADP
cana-3334	113	3	the	the	DET
cana-3334	113	4	above	above	ADJ
cana-3334	113	5	case	case	NOUN
cana-3334	113	6	,	,	PUNCT
cana-3334	113	7	we	we	PRON
cana-3334	113	8	have	have	VERB
cana-3334	113	9	𝑡2	𝑡2	NOUN
cana-3334	113	10	=	=	SYM
cana-3334	113	11	(	(	PUNCT
cana-3334	113	12	2𝑛	2𝑛	PROPN
cana-3334	113	13	+	+	CCONJ
cana-3334	114	1	2𝑟	2𝑟	NUM
cana-3334	115	1	)	)	PUNCT
cana-3334	116	1	(	(	PUNCT
cana-3334	116	2	𝑎2−𝑏2	𝑎2−𝑏2	NUM
cana-3334	116	3	𝑎2+𝑏2	𝑎2+𝑏2	PROPN
cana-3334	116	4	)	)	PUNCT
cana-3334	116	5	and	and	CCONJ
cana-3334	116	6	𝑑	𝑑	PROPN
cana-3334	116	7	=	=	X
cana-3334	116	8	(	(	PUNCT
cana-3334	116	9	2𝑛	2𝑛	PROPN
cana-3334	116	10	+	+	CCONJ
cana-3334	116	11	2𝑟	2𝑟	NUM
cana-3334	116	12	)	)	PUNCT
cana-3334	116	13	(	(	PUNCT
cana-3334	116	14	2𝑎𝑏	2𝑎𝑏	PROPN
cana-3334	116	15	𝑎2+𝑏2	𝑎2+𝑏2	PROPN
cana-3334	116	16	)	)	PUNCT
cana-3334	116	17	for	for	ADP
cana-3334	116	18	some	some	DET
cana-3334	116	19	𝑎	𝑎	NOUN
cana-3334	116	20	,	,	PUNCT
cana-3334	116	21	𝑏	𝑏	PROPN
cana-3334	116	22	∈	∈	PROPN
cana-3334	116	23	ℤ	ℤ	PROPN
cana-3334	116	24	and	and	CCONJ
cana-3334	116	25	𝑎	𝑎	ADP
cana-3334	116	26	>	>	X
cana-3334	116	27	𝑏.	𝑏.	NOUN
cana-3334	116	28	to	to	PART
cana-3334	116	29	find	find	VERB
cana-3334	116	30	required	required	ADJ
cana-3334	116	31	𝒏	𝒏	PROPN
cana-3334	116	32	since	since	SCONJ
cana-3334	116	33	the	the	DET
cana-3334	116	34	value	value	NOUN
cana-3334	116	35	𝑑	𝑑	NOUN
cana-3334	116	36	is	be	AUX
cana-3334	116	37	equal	equal	ADJ
cana-3334	116	38	in	in	ADP
cana-3334	116	39	both	both	CCONJ
cana-3334	116	40	the	the	DET
cana-3334	116	41	areas	area	NOUN
cana-3334	116	42	,	,	PUNCT
cana-3334	116	43	we	we	PRON
cana-3334	116	44	can	can	AUX
cana-3334	116	45	equate	equate	VERB
cana-3334	116	46	them	they	PRON
cana-3334	116	47	and	and	CCONJ
cana-3334	116	48	find	find	VERB
cana-3334	116	49	𝑛	𝑛	PRON
cana-3334	116	50	as	as	ADP
cana-3334	116	51	𝑛	𝑛	PROPN
cana-3334	116	52	=	=	SYM
cana-3334	117	1	𝑟𝑎𝑏(𝑚2	𝑟𝑎𝑏(𝑚2	PROPN
cana-3334	117	2	+	+	NUM
cana-3334	117	3	𝑙2	𝑙2	NOUN
cana-3334	117	4	)	)	PUNCT
cana-3334	117	5	𝑚𝑙(𝑎2	𝑚𝑙(𝑎2	NOUN
cana-3334	118	1	+	+	CCONJ
cana-3334	118	2	𝑏2	𝑏2	NOUN
cana-3334	118	3	)	)	PUNCT
cana-3334	118	4	−	−	PROPN
cana-3334	118	5	𝑎𝑏(𝑚2	𝑎𝑏(𝑚2	PROPN
cana-3334	119	1	+	+	CCONJ
cana-3334	119	2	𝑙2	𝑙2	NOUN
cana-3334	119	3	)	)	PUNCT
cana-3334	119	4	5.1	5.1	NUM
cana-3334	119	5	.	.	PUNCT
cana-3334	120	1	python	python	NOUN
cana-3334	120	2	coding	coding	NOUN
cana-3334	120	3	for	for	ADP
cana-3334	120	4	generation	generation	NOUN
cana-3334	120	5	of	of	ADP
cana-3334	120	6	required	require	VERB
cana-3334	120	7	kites	kite	NOUN
cana-3334	120	8	with	with	ADP
cana-3334	120	9	sides	side	NOUN
cana-3334	120	10	𝒏	𝒏	PROPN
cana-3334	120	11	and	and	CCONJ
cana-3334	120	12	𝒏	𝒏	PROPN
cana-3334	120	13	+	+	PROPN
cana-3334	120	14	𝒓	𝒓	PROPN
cana-3334	120	15	in	in	ADP
cana-3334	120	16	this	this	DET
cana-3334	120	17	section	section	NOUN
cana-3334	120	18	we	we	PRON
cana-3334	120	19	display	display	VERB
cana-3334	120	20	python	python	NOUN
cana-3334	120	21	coding	code	VERB
cana-3334	120	22	to	to	PART
cana-3334	120	23	collect	collect	VERB
cana-3334	120	24	kites	kite	NOUN
cana-3334	120	25	with	with	ADP
cana-3334	120	26	sides	side	NOUN
cana-3334	120	27	𝑛	𝑛	PROPN
cana-3334	120	28	,	,	PUNCT
cana-3334	120	29	𝑛	𝑛	PROPN
cana-3334	120	30	+	+	NUM
cana-3334	120	31	𝑟	𝑟	NOUN
cana-3334	120	32	,	,	PUNCT
cana-3334	120	33	rational	rational	ADJ
cana-3334	120	34	diagonals	diagonal	NOUN
cana-3334	120	35	and	and	CCONJ
cana-3334	120	36	integer	integer	NOUN
cana-3334	120	37	area	area	NOUN
cana-3334	120	38	followed	follow	VERB
cana-3334	120	39	by	by	ADP
cana-3334	120	40	its	its	PRON
cana-3334	120	41	output	output	NOUN
cana-3334	120	42	.	.	PUNCT
cana-3334	121	1	communications	communication	NOUN
cana-3334	121	2	on	on	ADP
cana-3334	121	3	applied	apply	VERB
cana-3334	121	4	nonlinear	nonlinear	ADJ
cana-3334	121	5	analysis	analysis	NOUN
cana-3334	121	6	issn	issn	NOUN
cana-3334	121	7	:	:	PUNCT
cana-3334	121	8	1074	1074	NUM
cana-3334	121	9	-	-	PUNCT
cana-3334	121	10	133x	133x	NUM
cana-3334	121	11	vol	vol	NOUN
cana-3334	121	12	32	32	NUM
cana-3334	121	13	no	no	NOUN
cana-3334	121	14	.	.	PUNCT
cana-3334	122	1	7s	7	NOUN
cana-3334	122	2	(	(	PUNCT
cana-3334	122	3	2025	2025	NUM
cana-3334	122	4	)	)	PUNCT
cana-3334	122	5	9	9	NUM
cana-3334	122	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3334	122	7	figure	figure	NOUN
cana-3334	122	8	8	8	NUM
cana-3334	122	9	:	:	PUNCT
cana-3334	122	10	coding	code	VERB
cana-3334	122	11	3	3	NUM
cana-3334	122	12	:	:	PUNCT
cana-3334	122	13	kite	kite	NOUN
cana-3334	122	14	with	with	ADP
cana-3334	122	15	sides	side	NOUN
cana-3334	122	16	𝑛	𝑛	PROPN
cana-3334	122	17	,	,	PUNCT
cana-3334	122	18	𝑛	𝑛	PRON
cana-3334	122	19	+	+	NOUN
cana-3334	122	20	𝑟	𝑟	PRON
cana-3334	122	21	figure	figure	VERB
cana-3334	122	22	9	9	NUM
cana-3334	122	23	:	:	PUNCT
cana-3334	122	24	output	output	NOUN
cana-3334	122	25	3	3	NUM
cana-3334	122	26	:	:	PUNCT
cana-3334	122	27	kite	kite	NOUN
cana-3334	122	28	with	with	ADP
cana-3334	122	29	sides	side	NOUN
cana-3334	122	30	𝑛	𝑛	PROPN
cana-3334	122	31	,	,	PUNCT
cana-3334	122	32	𝑛	𝑛	PROPN
cana-3334	122	33	+	+	NOUN
cana-3334	122	34	𝑟	𝑟	DET
cana-3334	122	35	5.2	5.2	NUM
cana-3334	122	36	.	.	PUNCT
cana-3334	123	1	experimental	experimental	ADJ
cana-3334	123	2	analysis	analysis	NOUN
cana-3334	123	3	by	by	ADP
cana-3334	123	4	an	an	DET
cana-3334	123	5	example	example	NOUN
cana-3334	123	6	in	in	ADP
cana-3334	123	7	figure	figure	NOUN
cana-3334	123	8	1	1	NUM
cana-3334	123	9	,	,	PUNCT
cana-3334	123	10	take	take	VERB
cana-3334	123	11	the	the	DET
cana-3334	123	12	diagonals	diagonal	NOUN
cana-3334	123	13	as	as	ADP
cana-3334	123	14	𝐵𝐷(=	𝐵𝐷(=	NOUN
cana-3334	123	15	𝑑	𝑑	NOUN
cana-3334	123	16	)	)	PUNCT
cana-3334	123	17	,	,	PUNCT
cana-3334	123	18	𝐴𝐶(=	𝐴𝐶(=	CCONJ
cana-3334	123	19	𝑑1	𝑑1	NOUN
cana-3334	123	20	)	)	PUNCT
cana-3334	123	21	and	and	CCONJ
cana-3334	123	22	the	the	DET
cana-3334	123	23	sides	side	NOUN
cana-3334	123	24	as	as	ADP
cana-3334	123	25	𝐴𝐷	𝐴𝐷	PROPN
cana-3334	123	26	=	=	SYM
cana-3334	123	27	𝑛	𝑛	NOUN
cana-3334	123	28	=	=	SYM
cana-3334	123	29	𝐴𝐵	𝐴𝐵	PROPN
cana-3334	123	30	and	and	CCONJ
cana-3334	123	31	𝐵𝐶	𝐵𝐶	PROPN
cana-3334	123	32	=	=	SYM
cana-3334	123	33	𝑛	𝑛	PROPN
cana-3334	123	34	+	+	NUM
cana-3334	123	35	𝑟	𝑟	X
cana-3334	123	36	=	=	SYM
cana-3334	123	37	𝐶𝐷.	𝐶𝐷.	X
cana-3334	123	38	doing	do	VERB
cana-3334	123	39	the	the	DET
cana-3334	123	40	same	same	ADJ
cana-3334	123	41	procedure	procedure	NOUN
cana-3334	123	42	as	as	ADP
cana-3334	123	43	in	in	ADP
cana-3334	123	44	subsection	subsection	NOUN
cana-3334	123	45	3.2	3.2	NUM
cana-3334	123	46	.	.	PUNCT
cana-3334	124	1	,	,	PUNCT
cana-3334	124	2	we	we	PRON
cana-3334	124	3	get	get	VERB
cana-3334	124	4	this	this	PRON
cana-3334	124	5	gives	give	VERB
cana-3334	124	6	𝑑1	𝑑1	NOUN
cana-3334	124	7	=	=	NOUN
cana-3334	124	8	1	1	NUM
cana-3334	124	9	2	2	NUM
cana-3334	124	10	[	[	X
cana-3334	124	11	√4𝑛2	√4𝑛2	NOUN
cana-3334	124	12	−	−	PROPN
cana-3334	124	13	𝑑2	𝑑2	NOUN
cana-3334	124	14	+	+	CCONJ
cana-3334	124	15	√4(𝑛	√4(𝑛	VERB
cana-3334	124	16	+	+	ADJ
cana-3334	124	17	𝑟)2	𝑟)2	NOUN
cana-3334	124	18	−	−	NOUN
cana-3334	124	19	𝑑2	𝑑2	NOUN
cana-3334	124	20	]	]	PUNCT
cana-3334	124	21	.	.	PUNCT
cana-3334	125	1	so	so	ADV
cana-3334	125	2	the	the	DET
cana-3334	125	3	area	area	NOUN
cana-3334	125	4	is	be	AUX
cana-3334	125	5	1	1	NUM
cana-3334	125	6	4	4	NUM
cana-3334	125	7	𝑑	𝑑	NOUN
cana-3334	125	8	[	[	X
cana-3334	125	9	√4𝑛2	√4𝑛2	NOUN
cana-3334	125	10	−	−	PROPN
cana-3334	125	11	𝑑2	𝑑2	NOUN
cana-3334	125	12	+	+	CCONJ
cana-3334	125	13	√4(𝑛	√4(𝑛	VERB
cana-3334	125	14	+	+	ADJ
cana-3334	125	15	𝑟)2	𝑟)2	NOUN
cana-3334	125	16	−	−	NOUN
cana-3334	125	17	𝑑2	𝑑2	NOUN
cana-3334	125	18	]	]	PUNCT
cana-3334	125	19	.	.	PUNCT
cana-3334	126	1	communications	communication	NOUN
cana-3334	126	2	on	on	ADP
cana-3334	126	3	applied	apply	VERB
cana-3334	126	4	nonlinear	nonlinear	ADJ
cana-3334	126	5	analysis	analysis	NOUN
cana-3334	126	6	issn	issn	NOUN
cana-3334	126	7	:	:	PUNCT
cana-3334	126	8	1074	1074	NUM
cana-3334	126	9	-	-	PUNCT
cana-3334	126	10	133x	133x	NUM
cana-3334	126	11	vol	vol	NOUN
cana-3334	126	12	32	32	NUM
cana-3334	126	13	no	no	NOUN
cana-3334	126	14	.	.	PUNCT
cana-3334	127	1	7s	7	NOUN
cana-3334	127	2	(	(	PUNCT
cana-3334	127	3	2025	2025	NUM
cana-3334	127	4	)	)	PUNCT
cana-3334	127	5	10	10	NUM
cana-3334	127	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3334	127	7	now	now	ADV
cana-3334	127	8	,	,	PUNCT
cana-3334	127	9	let	let	VERB
cana-3334	127	10	us	we	PRON
cana-3334	127	11	verify	verify	VERB
cana-3334	127	12	this	this	PRON
cana-3334	127	13	by	by	ADP
cana-3334	127	14	an	an	DET
cana-3334	127	15	example	example	NOUN
cana-3334	127	16	.	.	PUNCT
cana-3334	128	1	take	take	VERB
cana-3334	128	2	𝑛	𝑛	PRON
cana-3334	128	3	=	=	SYM
cana-3334	128	4	50	50	NUM
cana-3334	128	5	,	,	PUNCT
cana-3334	128	6	𝑟	𝑟	NOUN
cana-3334	128	7	=	=	SYM
cana-3334	128	8	10	10	NUM
cana-3334	128	9	and	and	CCONJ
cana-3334	128	10	𝑑	𝑑	X
cana-3334	128	11	=	=	ADJ
cana-3334	128	12	96	96	NUM
cana-3334	128	13	.	.	PUNCT
cana-3334	129	1	then	then	ADV
cana-3334	129	2	we	we	PRON
cana-3334	129	3	obtain	obtain	VERB
cana-3334	129	4	𝑑1	𝑑1	NOUN
cana-3334	129	5	=	=	NOUN
cana-3334	129	6	50	50	NUM
cana-3334	129	7	.	.	PUNCT
cana-3334	130	1	this	this	PRON
cana-3334	130	2	gives	give	VERB
cana-3334	130	3	the	the	DET
cana-3334	130	4	area	area	NOUN
cana-3334	130	5	2400	2400	NUM
cana-3334	130	6	,	,	PUNCT
cana-3334	130	7	is	be	AUX
cana-3334	130	8	same	same	ADJ
cana-3334	130	9	as	as	ADP
cana-3334	130	10	the	the	DET
cana-3334	130	11	one	one	NUM
cana-3334	130	12	found	find	VERB
cana-3334	130	13	from	from	ADP
cana-3334	130	14	the	the	DET
cana-3334	130	15	python	python	NOUN
cana-3334	130	16	coding	coding	NOUN
cana-3334	130	17	.	.	PUNCT
cana-3334	131	1	6	6	X
cana-3334	131	2	.	.	X
cana-3334	131	3	kite	kite	NOUN
cana-3334	131	4	with	with	ADP
cana-3334	131	5	sides	side	NOUN
cana-3334	131	6	𝒏	𝒏	PROPN
cana-3334	131	7	,	,	PUNCT
cana-3334	131	8	𝒏	𝒏	PROPN
cana-3334	131	9	−	−	PROPN
cana-3334	131	10	𝒓	𝒓	PROPN
cana-3334	131	11	in	in	ADP
cana-3334	131	12	this	this	DET
cana-3334	131	13	section	section	NOUN
cana-3334	131	14	,	,	PUNCT
cana-3334	131	15	we	we	PRON
cana-3334	131	16	on	on	ADP
cana-3334	131	17	kites	kite	NOUN
cana-3334	131	18	with	with	ADP
cana-3334	131	19	sides	side	NOUN
cana-3334	131	20	𝑛	𝑛	ADP
cana-3334	131	21	−	−	NOUN
cana-3334	131	22	𝑟	𝑟	NOUN
cana-3334	131	23	,	,	PUNCT
cana-3334	131	24	as	as	ADP
cana-3334	131	25	above	above	ADV
cana-3334	131	26	.	.	PUNCT
cana-3334	132	1	let	let	VERB
cana-3334	132	2	us	we	PRON
cana-3334	132	3	consider	consider	VERB
cana-3334	132	4	a	a	DET
cana-3334	132	5	kite	kite	NOUN
cana-3334	132	6	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	NOUN
cana-3334	132	7	with	with	ADP
cana-3334	132	8	sides	side	NOUN
cana-3334	132	9	𝑛	𝑛	PRON
cana-3334	132	10	and	and	CCONJ
cana-3334	132	11	𝑛	𝑛	DET
cana-3334	132	12	−	−	PROPN
cana-3334	132	13	𝑟.	𝑟.	NOUN
cana-3334	132	14	in	in	ADP
cana-3334	132	15	figure	figure	NOUN
cana-3334	132	16	5	5	NUM
cana-3334	132	17	,	,	PUNCT
cana-3334	132	18	take	take	VERB
cana-3334	132	19	𝐴𝐵	𝐴𝐵	NOUN
cana-3334	132	20	=	=	SYM
cana-3334	132	21	𝑛	𝑛	NOUN
cana-3334	132	22	=	=	SYM
cana-3334	132	23	𝐵𝐶	𝐵𝐶	PROPN
cana-3334	132	24	and	and	CCONJ
cana-3334	132	25	𝐴𝐷	𝐴𝐷	PROPN
cana-3334	132	26	=	=	SYM
cana-3334	132	27	𝑛	𝑛	DET
cana-3334	132	28	−	−	PROPN
cana-3334	132	29	𝑟	𝑟	NOUN
cana-3334	132	30	=	=	X
cana-3334	132	31	𝐷𝐶.	𝐷𝐶.	NOUN
cana-3334	132	32	let	let	VERB
cana-3334	132	33	𝐴𝐶	𝐴𝐶	PROPN
cana-3334	132	34	=	=	SYM
cana-3334	132	35	𝑑.	𝑑.	NOUN
cana-3334	132	36	then	then	ADV
cana-3334	132	37	the	the	DET
cana-3334	132	38	kite	kite	NOUN
cana-3334	132	39	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	132	40	can	can	AUX
cana-3334	132	41	be	be	AUX
cana-3334	132	42	split	split	VERB
cana-3334	132	43	into	into	ADP
cana-3334	132	44	two	two	NUM
cana-3334	132	45	isosceles	isoscele	NOUN
cana-3334	132	46	triangles	triangle	NOUN
cana-3334	132	47	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	132	48	and	and	CCONJ
cana-3334	132	49	𝐴𝐷𝐶.	𝐴𝐷𝐶.	X
cana-3334	132	50	thus	thus	ADV
cana-3334	132	51	,	,	PUNCT
cana-3334	132	52	area	area	NOUN
cana-3334	132	53	of	of	ADP
cana-3334	132	54	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	132	55	=	=	PUNCT
cana-3334	132	56	area	area	NOUN
cana-3334	132	57	of	of	ADP
cana-3334	132	58	δ	δ	PROPN
cana-3334	132	59	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	132	60	+	+	NUM
cana-3334	132	61	area	area	NOUN
cana-3334	132	62	of	of	ADP
cana-3334	132	63	δ	δ	PROPN
cana-3334	132	64	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	132	65	as	as	ADP
cana-3334	132	66	in	in	ADP
cana-3334	132	67	previous	previous	ADJ
cana-3334	132	68	sections	section	NOUN
cana-3334	132	69	,	,	PUNCT
cana-3334	132	70	we	we	PRON
cana-3334	132	71	get	get	VERB
cana-3334	132	72	area	area	NOUN
cana-3334	132	73	of	of	ADP
cana-3334	132	74	δ	δ	PROPN
cana-3334	132	75	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	132	76	=	=	PROPN
cana-3334	132	77	𝑑	𝑑	PROPN
cana-3334	132	78	4	4	NUM
cana-3334	132	79	√4𝑛2	√4𝑛2	NOUN
cana-3334	132	80	−	−	PROPN
cana-3334	132	81	𝑑2	𝑑2	NOUN
cana-3334	132	82	(	(	PUNCT
cana-3334	132	83	7	7	NUM
cana-3334	132	84	)	)	PUNCT
cana-3334	132	85	and	and	CCONJ
cana-3334	132	86	area	area	NOUN
cana-3334	132	87	of	of	ADP
cana-3334	132	88	δ	δ	PROPN
cana-3334	132	89	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	132	90	=	=	PRON
cana-3334	132	91	𝑑	𝑑	PROPN
cana-3334	132	92	4	4	NUM
cana-3334	132	93	√(2𝑛	√(2𝑛	NOUN
cana-3334	133	1	+	+	CCONJ
cana-3334	133	2	2𝑟)2	2𝑟)2	NUM
cana-3334	133	3	−	−	NOUN
cana-3334	133	4	𝑑2	𝑑2	NOUN
cana-3334	133	5	(	(	PUNCT
cana-3334	133	6	8)	8)	NUM
cana-3334	133	7	this	this	PRON
cana-3334	133	8	implies	imply	VERB
cana-3334	133	9	the	the	DET
cana-3334	133	10	fact	fact	NOUN
cana-3334	133	11	that	that	SCONJ
cana-3334	133	12	the	the	DET
cana-3334	133	13	area	area	NOUN
cana-3334	133	14	of	of	ADP
cana-3334	133	15	𝐴𝐵𝐶𝐷	𝐴𝐵𝐶𝐷	PROPN
cana-3334	133	16	∈	∈	PROPN
cana-3334	133	17	ℤ	ℤ	PROPN
cana-3334	133	18	,	,	PUNCT
cana-3334	133	19	if	if	SCONJ
cana-3334	133	20	and	and	CCONJ
cana-3334	133	21	only	only	ADV
cana-3334	133	22	if	if	SCONJ
cana-3334	133	23	the	the	DET
cana-3334	133	24	area	area	NOUN
cana-3334	133	25	of	of	ADP
cana-3334	133	26	δ	δ	PROPN
cana-3334	133	27	𝐴𝐵𝐷	𝐴𝐵𝐷	PROPN
cana-3334	133	28	and	and	CCONJ
cana-3334	133	29	area	area	NOUN
cana-3334	133	30	of	of	ADP
cana-3334	133	31	δ	δ	PROPN
cana-3334	133	32	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	133	33	both	both	PRON
cana-3334	133	34	must	must	AUX
cana-3334	133	35	be	be	AUX
cana-3334	133	36	rational	rational	ADJ
cana-3334	133	37	numbers	number	NOUN
cana-3334	133	38	.	.	PUNCT
cana-3334	134	1	area	area	NOUN
cana-3334	134	2	of	of	ADP
cana-3334	134	3	𝚫	𝚫	PROPN
cana-3334	134	4	𝑨𝑩𝑪	𝑨𝑩𝑪	PROPN
cana-3334	134	5	over	over	ADP
cana-3334	134	6	ℚ	ℚ	PROPN
cana-3334	134	7	`	`	PUNCT
cana-3334	134	8	`	`	PUNCT
cana-3334	134	9	equation	equation	NOUN
cana-3334	134	10	(	(	PUNCT
cana-3334	134	11	7	7	NUM
cana-3334	134	12	)	)	PUNCT
cana-3334	134	13	''	''	PUNCT
cana-3334	134	14	implies	imply	VERB
cana-3334	134	15	that	that	DET
cana-3334	134	16	area	area	NOUN
cana-3334	134	17	of	of	ADP
cana-3334	134	18	δ	δ	PROPN
cana-3334	134	19	𝐴𝐵𝐶	𝐴𝐵𝐶	PROPN
cana-3334	134	20	∈	∈	PROPN
cana-3334	134	21	ℚ	ℚ	PROPN
cana-3334	134	22	if	if	SCONJ
cana-3334	134	23	𝑡1	𝑡1	NOUN
cana-3334	134	24	=	=	SYM
cana-3334	134	25	2𝑛	2𝑛	PROPN
cana-3334	134	26	(	(	PUNCT
cana-3334	134	27	𝑚2−𝑙2	𝑚2−𝑙2	PROPN
cana-3334	134	28	𝑚2+𝑙2	𝑚2+𝑙2	PROPN
cana-3334	134	29	)	)	PUNCT
cana-3334	134	30	and	and	CCONJ
cana-3334	134	31	𝑑	𝑑	PROPN
cana-3334	134	32	=	=	X
cana-3334	134	33	4𝑛	4𝑛	PROPN
cana-3334	134	34	(	(	PUNCT
cana-3334	134	35	𝑚𝑙	𝑚𝑙	NOUN
cana-3334	134	36	𝑚2+𝑙2	𝑚2+𝑙2	PROPN
cana-3334	134	37	)	)	PUNCT
cana-3334	134	38	for	for	ADP
cana-3334	134	39	some	some	DET
cana-3334	134	40	𝑚	𝑚	NOUN
cana-3334	134	41	,	,	PUNCT
cana-3334	134	42	𝑙	𝑙	PROPN
cana-3334	134	43	∈	∈	PROPN
cana-3334	134	44	ℤ	ℤ	PROPN
cana-3334	134	45	and	and	CCONJ
cana-3334	134	46	𝑚	𝑚	X
cana-3334	134	47	>	>	X
cana-3334	134	48	𝑙.	𝑙.	ADJ
cana-3334	134	49	area	area	NOUN
cana-3334	134	50	of	of	ADP
cana-3334	134	51	𝚫	𝚫	PROPN
cana-3334	134	52	𝑨𝑫𝑪	𝑨𝑫𝑪	NOUN
cana-3334	134	53	over	over	ADP
cana-3334	134	54	ℚ	ℚ	PROPN
cana-3334	134	55	`	`	PUNCT
cana-3334	134	56	`	`	PUNCT
cana-3334	134	57	equation	equation	NOUN
cana-3334	134	58	(	(	PUNCT
cana-3334	134	59	8)	8)	NUM
cana-3334	134	60	''	''	PUNCT
cana-3334	134	61	implies	imply	VERB
cana-3334	134	62	that	that	DET
cana-3334	134	63	area	area	NOUN
cana-3334	134	64	of	of	ADP
cana-3334	134	65	δ	δ	PROPN
cana-3334	134	66	𝐴𝐷𝐶	𝐴𝐷𝐶	PROPN
cana-3334	134	67	∈	∈	PROPN
cana-3334	134	68	ℚ	ℚ	PROPN
cana-3334	134	69	if	if	SCONJ
cana-3334	134	70	(	(	PUNCT
cana-3334	134	71	2𝑛	2𝑛	PROPN
cana-3334	134	72	−	−	PROPN
cana-3334	134	73	2𝑟)2	2𝑟)2	NUM
cana-3334	134	74	−	−	ADP
cana-3334	134	75	𝑑2	𝑑2	NOUN
cana-3334	134	76	=	=	SYM
cana-3334	134	77	𝑡2	𝑡2	ADJ
cana-3334	134	78	2	2	NUM
cana-3334	134	79	for	for	ADP
cana-3334	134	80	some	some	DET
cana-3334	134	81	𝑡2	𝑡2	PROPN
cana-3334	134	82	∈	∈	PROPN
cana-3334	134	83	ℚ	ℚ	PROPN
cana-3334	134	84	.	.	PUNCT
cana-3334	135	1	as	as	ADP
cana-3334	135	2	in	in	ADP
cana-3334	135	3	the	the	DET
cana-3334	135	4	above	above	ADJ
cana-3334	135	5	case	case	NOUN
cana-3334	135	6	,	,	PUNCT
cana-3334	135	7	we	we	PRON
cana-3334	135	8	have	have	VERB
cana-3334	135	9	𝑡2	𝑡2	NOUN
cana-3334	135	10	=	=	SYM
cana-3334	135	11	(	(	PUNCT
cana-3334	135	12	2𝑛	2𝑛	PROPN
cana-3334	135	13	−	−	PROPN
cana-3334	135	14	2𝑟	2𝑟	NUM
cana-3334	135	15	)	)	PUNCT
cana-3334	135	16	(	(	PUNCT
cana-3334	135	17	𝑎2−𝑏2	𝑎2−𝑏2	ADV
cana-3334	135	18	)	)	PUNCT
cana-3334	135	19	(	(	PUNCT
cana-3334	135	20	𝑎2+𝑏2	𝑎2+𝑏2	PROPN
cana-3334	135	21	)	)	PUNCT
cana-3334	135	22	and	and	CCONJ
cana-3334	135	23	𝑑	𝑑	PROPN
cana-3334	135	24	=	=	X
cana-3334	135	25	(	(	PUNCT
cana-3334	135	26	2𝑛	2𝑛	PROPN
cana-3334	135	27	−	−	PROPN
cana-3334	135	28	2𝑟	2𝑟	NUM
cana-3334	135	29	)	)	PUNCT
cana-3334	135	30	(	(	PUNCT
cana-3334	135	31	2𝑎𝑏	2𝑎𝑏	PROPN
cana-3334	135	32	𝑎2+𝑏2	𝑎2+𝑏2	PROPN
cana-3334	135	33	)	)	PUNCT
cana-3334	135	34	for	for	ADP
cana-3334	135	35	some	some	DET
cana-3334	135	36	𝑎	𝑎	NOUN
cana-3334	135	37	,	,	PUNCT
cana-3334	135	38	𝑏	𝑏	PROPN
cana-3334	135	39	∈	∈	PROPN
cana-3334	135	40	ℤ	ℤ	PROPN
cana-3334	135	41	and	and	CCONJ
cana-3334	135	42	𝑎	𝑎	ADP
cana-3334	135	43	>	>	X
cana-3334	135	44	𝑏.	𝑏.	NOUN
cana-3334	135	45	to	to	PART
cana-3334	135	46	find	find	VERB
cana-3334	135	47	required	require	VERB
cana-3334	135	48	n	n	NOUN
cana-3334	135	49	since	since	SCONJ
cana-3334	135	50	the	the	DET
cana-3334	135	51	value	value	NOUN
cana-3334	135	52	𝑑	𝑑	NOUN
cana-3334	135	53	is	be	AUX
cana-3334	135	54	equal	equal	ADJ
cana-3334	135	55	in	in	ADP
cana-3334	135	56	both	both	CCONJ
cana-3334	135	57	the	the	DET
cana-3334	135	58	areas	area	NOUN
cana-3334	135	59	,	,	PUNCT
cana-3334	135	60	we	we	PRON
cana-3334	135	61	can	can	AUX
cana-3334	135	62	equate	equate	VERB
cana-3334	135	63	them	they	PRON
cana-3334	135	64	and	and	CCONJ
cana-3334	135	65	find	find	VERB
cana-3334	135	66	𝑛	𝑛	PRON
cana-3334	135	67	as	as	ADP
cana-3334	135	68	𝑛	𝑛	PROPN
cana-3334	135	69	=	=	SYM
cana-3334	135	70	𝑟𝑎𝑏(𝑚2	𝑟𝑎𝑏(𝑚2	PROPN
cana-3334	135	71	+	+	NUM
cana-3334	135	72	𝑙2	𝑙2	NOUN
cana-3334	135	73	)	)	PUNCT
cana-3334	135	74	𝑎𝑏(𝑚2	𝑎𝑏(𝑚2	PROPN
cana-3334	136	1	+	+	CCONJ
cana-3334	136	2	𝑙2	𝑙2	NOUN
cana-3334	136	3	)	)	PUNCT
cana-3334	136	4	−	−	ADP
cana-3334	136	5	𝑚𝑙(𝑎2	𝑚𝑙(𝑎2	NOUN
cana-3334	137	1	+	+	NUM
cana-3334	137	2	𝑏2	𝑏2	NOUN
cana-3334	137	3	)	)	PUNCT
cana-3334	137	4	6.1	6.1	NUM
cana-3334	137	5	.	.	PUNCT
cana-3334	138	1	python	python	NOUN
cana-3334	138	2	coding	coding	NOUN
cana-3334	138	3	for	for	ADP
cana-3334	138	4	generation	generation	NOUN
cana-3334	138	5	of	of	ADP
cana-3334	138	6	required	require	VERB
cana-3334	138	7	kites	kite	NOUN
cana-3334	138	8	with	with	ADP
cana-3334	138	9	sides	side	NOUN
cana-3334	138	10	𝒏	𝒏	PROPN
cana-3334	138	11	and	and	CCONJ
cana-3334	138	12	𝒏	𝒏	PROPN
cana-3334	138	13	−	−	PROPN
cana-3334	138	14	𝒓	𝒓	PROPN
cana-3334	138	15	in	in	ADP
cana-3334	138	16	this	this	DET
cana-3334	138	17	section	section	NOUN
cana-3334	138	18	we	we	PRON
cana-3334	138	19	display	display	VERB
cana-3334	138	20	python	python	NOUN
cana-3334	138	21	coding	code	VERB
cana-3334	138	22	to	to	PART
cana-3334	138	23	collect	collect	VERB
cana-3334	138	24	kites	kite	NOUN
cana-3334	138	25	with	with	ADP
cana-3334	138	26	sides	side	NOUN
cana-3334	138	27	𝑛	𝑛	PROPN
cana-3334	138	28	,	,	PUNCT
cana-3334	138	29	𝑛	𝑛	DET
cana-3334	138	30	−	−	NOUN
cana-3334	138	31	𝑟	𝑟	NOUN
cana-3334	138	32	rational	rational	ADJ
cana-3334	138	33	diagonals	diagonal	NOUN
cana-3334	138	34	and	and	CCONJ
cana-3334	138	35	integer	integer	NOUN
cana-3334	138	36	area	area	NOUN
cana-3334	138	37	followed	follow	VERB
cana-3334	138	38	by	by	ADP
cana-3334	138	39	its	its	PRON
cana-3334	138	40	output	output	NOUN
cana-3334	138	41	.	.	PUNCT
cana-3334	139	1	communications	communication	NOUN
cana-3334	139	2	on	on	ADP
cana-3334	139	3	applied	apply	VERB
cana-3334	139	4	nonlinear	nonlinear	ADJ
cana-3334	139	5	analysis	analysis	NOUN
cana-3334	139	6	issn	issn	NOUN
cana-3334	139	7	:	:	PUNCT
cana-3334	139	8	1074	1074	NUM
cana-3334	139	9	-	-	PUNCT
cana-3334	139	10	133x	133x	NUM
cana-3334	139	11	vol	vol	NOUN
cana-3334	139	12	32	32	NUM
cana-3334	139	13	no	no	NOUN
cana-3334	139	14	.	.	PUNCT
cana-3334	140	1	7s	7	NOUN
cana-3334	140	2	(	(	PUNCT
cana-3334	140	3	2025	2025	NUM
cana-3334	140	4	)	)	PUNCT
cana-3334	140	5	11	11	NUM
cana-3334	140	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3334	140	7	figure	figure	NOUN
cana-3334	140	8	10	10	NUM
cana-3334	140	9	:	:	PUNCT
cana-3334	140	10	coding	code	VERB
cana-3334	140	11	4	4	NUM
cana-3334	140	12	:	:	PUNCT
cana-3334	140	13	kite	kite	NOUN
cana-3334	140	14	with	with	ADP
cana-3334	140	15	sides	side	NOUN
cana-3334	140	16	𝑛	𝑛	PROPN
cana-3334	140	17	,	,	PUNCT
cana-3334	140	18	𝑛	𝑛	DET
cana-3334	140	19	−	−	NOUN
cana-3334	141	1	𝑟	𝑟	PRON
cana-3334	141	2	figure	figure	VERB
cana-3334	141	3	11	11	NUM
cana-3334	141	4	:	:	PUNCT
cana-3334	141	5	output	output	NOUN
cana-3334	141	6	4	4	NUM
cana-3334	141	7	:	:	PUNCT
cana-3334	141	8	kite	kite	NOUN
cana-3334	141	9	with	with	ADP
cana-3334	141	10	sides	side	NOUN
cana-3334	141	11	𝑛	𝑛	PROPN
cana-3334	141	12	,	,	PUNCT
cana-3334	141	13	𝑛	𝑛	PRON
cana-3334	141	14	−	−	NOUN
cana-3334	141	15	𝑟	𝑟	SYM
cana-3334	141	16	6.2	6.2	NUM
cana-3334	141	17	.	.	PUNCT
cana-3334	142	1	experimental	experimental	ADJ
cana-3334	142	2	analysis	analysis	NOUN
cana-3334	142	3	by	by	ADP
cana-3334	142	4	an	an	DET
cana-3334	142	5	example	example	NOUN
cana-3334	142	6	in	in	ADP
cana-3334	142	7	figure	figure	NOUN
cana-3334	142	8	1	1	NUM
cana-3334	142	9	,	,	PUNCT
cana-3334	142	10	take	take	VERB
cana-3334	142	11	the	the	DET
cana-3334	142	12	diagonals	diagonal	NOUN
cana-3334	142	13	as	as	ADP
cana-3334	142	14	𝐵𝐷(=	𝐵𝐷(=	NOUN
cana-3334	142	15	𝑑	𝑑	NOUN
cana-3334	142	16	)	)	PUNCT
cana-3334	142	17	,	,	PUNCT
cana-3334	142	18	𝐴𝐶(=	𝐴𝐶(=	CCONJ
cana-3334	142	19	𝑑1	𝑑1	NOUN
cana-3334	142	20	)	)	PUNCT
cana-3334	142	21	and	and	CCONJ
cana-3334	142	22	the	the	DET
cana-3334	142	23	sides	side	NOUN
cana-3334	142	24	as	as	ADP
cana-3334	142	25	𝐶𝐵	𝐶𝐵	PROPN
cana-3334	142	26	=	=	SYM
cana-3334	142	27	𝑛	𝑛	NOUN
cana-3334	142	28	=	=	PUNCT
cana-3334	142	29	𝐶𝐷	𝐶𝐷	PROPN
cana-3334	142	30	and	and	CCONJ
cana-3334	142	31	ad=	ad=	ADJ
cana-3334	142	32	𝑛	𝑛	DET
cana-3334	142	33	−	−	PROPN
cana-3334	142	34	𝑟	𝑟	NOUN
cana-3334	142	35	=	=	SYM
cana-3334	142	36	𝐴𝐵.	𝐴𝐵.	NOUN
cana-3334	142	37	doing	do	VERB
cana-3334	142	38	the	the	DET
cana-3334	142	39	same	same	ADJ
cana-3334	142	40	procedure	procedure	NOUN
cana-3334	142	41	as	as	ADP
cana-3334	142	42	in	in	ADP
cana-3334	142	43	subsection	subsection	NOUN
cana-3334	142	44	3.2	3.2	NUM
cana-3334	142	45	.	.	PUNCT
cana-3334	143	1	,	,	PUNCT
cana-3334	143	2	we	we	PRON
cana-3334	143	3	get	get	VERB
cana-3334	143	4	this	this	PRON
cana-3334	143	5	gives	give	VERB
cana-3334	143	6	𝑑1	𝑑1	NOUN
cana-3334	143	7	=	=	NOUN
cana-3334	143	8	1	1	NUM
cana-3334	143	9	2	2	NUM
cana-3334	143	10	[	[	X
cana-3334	143	11	√4𝑛2	√4𝑛2	NOUN
cana-3334	143	12	−	−	PROPN
cana-3334	143	13	𝑑2	𝑑2	NOUN
cana-3334	143	14	+	+	CCONJ
cana-3334	143	15	√4(𝑛	√4(𝑛	VERB
cana-3334	143	16	−	−	NOUN
cana-3334	143	17	𝑟)2	𝑟)2	NOUN
cana-3334	143	18	−	−	ADJ
cana-3334	143	19	𝑑2	𝑑2	NOUN
cana-3334	143	20	]	]	PUNCT
cana-3334	143	21	.	.	PUNCT
cana-3334	144	1	communications	communication	NOUN
cana-3334	144	2	on	on	ADP
cana-3334	144	3	applied	apply	VERB
cana-3334	144	4	nonlinear	nonlinear	ADJ
cana-3334	144	5	analysis	analysis	NOUN
cana-3334	144	6	issn	issn	NOUN
cana-3334	144	7	:	:	PUNCT
cana-3334	144	8	1074	1074	NUM
cana-3334	144	9	-	-	PUNCT
cana-3334	144	10	133x	133x	NUM
cana-3334	144	11	vol	vol	NOUN
cana-3334	144	12	32	32	NUM
cana-3334	144	13	no	no	NOUN
cana-3334	144	14	.	.	PUNCT
cana-3334	145	1	7s	7	NOUN
cana-3334	145	2	(	(	PUNCT
cana-3334	145	3	2025	2025	NUM
cana-3334	145	4	)	)	PUNCT
cana-3334	145	5	12	12	NUM
cana-3334	145	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3334	146	1	so	so	ADV
cana-3334	146	2	the	the	DET
cana-3334	146	3	area	area	NOUN
cana-3334	146	4	is	be	AUX
cana-3334	146	5	1	1	NUM
cana-3334	146	6	4	4	NUM
cana-3334	146	7	𝑑	𝑑	NOUN
cana-3334	146	8	[	[	X
cana-3334	146	9	√4𝑛2	√4𝑛2	NOUN
cana-3334	146	10	−	−	PROPN
cana-3334	146	11	𝑑2	𝑑2	NOUN
cana-3334	146	12	+	+	CCONJ
cana-3334	146	13	√4(𝑛	√4(𝑛	VERB
cana-3334	146	14	−	−	NOUN
cana-3334	146	15	𝑟)2	𝑟)2	NOUN
cana-3334	146	16	−	−	ADJ
cana-3334	146	17	𝑑2	𝑑2	NOUN
cana-3334	146	18	]	]	PUNCT
cana-3334	146	19	.	.	PUNCT
cana-3334	147	1	now	now	ADV
cana-3334	147	2	,	,	PUNCT
cana-3334	147	3	let	let	VERB
cana-3334	147	4	us	we	PRON
cana-3334	147	5	verify	verify	VERB
cana-3334	147	6	this	this	PRON
cana-3334	147	7	by	by	ADP
cana-3334	147	8	an	an	DET
cana-3334	147	9	example	example	NOUN
cana-3334	147	10	.	.	PUNCT
cana-3334	148	1	take	take	VERB
cana-3334	148	2	𝑛	𝑛	PRON
cana-3334	148	3	=	=	SYM
cana-3334	148	4	375	375	NUM
cana-3334	148	5	,	,	PUNCT
cana-3334	148	6	𝑟	𝑟	NOUN
cana-3334	148	7	=	=	SYM
cana-3334	148	8	6	6	NUM
cana-3334	148	9	and	and	CCONJ
cana-3334	148	10	𝑑	𝑑	X
cana-3334	148	11	=	=	ADJ
cana-3334	148	12	720	720	X
cana-3334	148	13	.	.	PUNCT
cana-3334	149	1	then	then	ADV
cana-3334	149	2	we	we	PRON
cana-3334	149	3	obtain	obtain	VERB
cana-3334	149	4	𝑑1	𝑑1	NOUN
cana-3334	149	5	=	=	SYM
cana-3334	149	6	186	186	NUM
cana-3334	149	7	.	.	PUNCT
cana-3334	150	1	this	this	PRON
cana-3334	150	2	gives	give	VERB
cana-3334	150	3	the	the	DET
cana-3334	150	4	area	area	NOUN
cana-3334	150	5	66960	66960	NUM
cana-3334	150	6	,	,	PUNCT
cana-3334	150	7	is	be	AUX
cana-3334	150	8	same	same	ADJ
cana-3334	150	9	as	as	ADP
cana-3334	150	10	the	the	DET
cana-3334	150	11	one	one	NUM
cana-3334	150	12	found	find	VERB
cana-3334	150	13	from	from	ADP
cana-3334	150	14	the	the	DET
cana-3334	150	15	python	python	NOUN
cana-3334	150	16	coding	coding	NOUN
cana-3334	150	17	.	.	PUNCT
cana-3334	151	1	7	7	X
cana-3334	151	2	.	.	X
cana-3334	151	3	conclusion	conclusion	NOUN
cana-3334	151	4	in	in	ADP
cana-3334	151	5	this	this	DET
cana-3334	151	6	paper	paper	NOUN
cana-3334	151	7	,	,	PUNCT
cana-3334	151	8	some	some	DET
cana-3334	151	9	particular	particular	ADJ
cana-3334	151	10	choices	choice	NOUN
cana-3334	151	11	of	of	ADP
cana-3334	151	12	kites	kite	NOUN
cana-3334	151	13	with	with	ADP
cana-3334	151	14	sides	side	NOUN
cana-3334	151	15	𝑛	𝑛	PROPN
cana-3334	151	16	,	,	PUNCT
cana-3334	151	17	𝑛	𝑛	DET
cana-3334	151	18	±	±	NUM
cana-3334	151	19	1	1	NUM
cana-3334	151	20	and	and	CCONJ
cana-3334	151	21	𝑛	𝑛	NOUN
cana-3334	151	22	,	,	PUNCT
cana-3334	151	23	𝑛	𝑛	PRON
cana-3334	151	24	±	±	NOUN
cana-3334	151	25	𝑟	𝑟	NOUN
cana-3334	151	26	having	have	VERB
cana-3334	151	27	integer	integer	NOUN
cana-3334	151	28	area	area	NOUN
cana-3334	151	29	and	and	CCONJ
cana-3334	151	30	rational	rational	ADJ
cana-3334	151	31	diagonal	diagonal	NOUN
cana-3334	151	32	are	be	AUX
cana-3334	151	33	collected	collect	VERB
cana-3334	151	34	mathematically	mathematically	ADV
cana-3334	151	35	as	as	ADV
cana-3334	151	36	well	well	ADV
cana-3334	151	37	as	as	ADP
cana-3334	151	38	through	through	ADP
cana-3334	151	39	python	python	NOUN
cana-3334	151	40	programming	programming	NOUN
cana-3334	151	41	.	.	PUNCT
cana-3334	152	1	these	these	DET
cana-3334	152	2	types	type	NOUN
cana-3334	152	3	of	of	ADP
cana-3334	152	4	concepts	concept	NOUN
cana-3334	152	5	may	may	AUX
cana-3334	152	6	be	be	AUX
cana-3334	152	7	applied	apply	VERB
cana-3334	152	8	in	in	ADP
cana-3334	152	9	the	the	DET
cana-3334	152	10	field	field	NOUN
cana-3334	152	11	of	of	ADP
cana-3334	152	12	architecture	architecture	NOUN
cana-3334	152	13	.	.	PUNCT
cana-3334	153	1	in	in	ADP
cana-3334	153	2	future	future	NOUN
cana-3334	153	3	,	,	PUNCT
cana-3334	153	4	this	this	DET
cana-3334	153	5	thought	thought	NOUN
cana-3334	153	6	may	may	AUX
cana-3334	153	7	extend	extend	VERB
cana-3334	153	8	to	to	ADP
cana-3334	153	9	other	other	ADJ
cana-3334	153	10	geometrical	geometrical	ADJ
cana-3334	153	11	shapes	shape	NOUN
cana-3334	153	12	also	also	ADV
cana-3334	153	13	.	.	PUNCT
cana-3334	154	1	references	reference	NOUN
cana-3334	154	2	[	[	X
cana-3334	154	3	1	1	NUM
cana-3334	154	4	]	]	PUNCT
cana-3334	154	5	.	.	PUNCT
cana-3334	155	1	aassila	aassila	PROPN
cana-3334	155	2	,	,	PUNCT
cana-3334	155	3	m.	m.	NOUN
cana-3334	155	4	(	(	PUNCT
cana-3334	155	5	2001	2001	NUM
cana-3334	155	6	)	)	PUNCT
cana-3334	155	7	.	.	PUNCT
cana-3334	156	1	some	some	DET
cana-3334	156	2	results	result	NOUN
cana-3334	156	3	on	on	ADP
cana-3334	156	4	heron	heron	NOUN
cana-3334	156	5	triangles	triangle	NOUN
cana-3334	156	6	.	.	PUNCT
cana-3334	157	1	elemente	elemente	PROPN
cana-3334	157	2	der	der	PROPN
cana-3334	157	3	mathematik	mathematik	PROPN
cana-3334	157	4	,	,	PUNCT
cana-3334	157	5	56(4	56(4	PROPN
cana-3334	157	6	)	)	PUNCT
cana-3334	157	7	,	,	PUNCT
cana-3334	157	8	143	143	NUM
cana-3334	157	9	-	-	SYM
cana-3334	157	10	146	146	NUM
cana-3334	157	11	.	.	PUNCT
cana-3334	158	1	[	[	X
cana-3334	158	2	2	2	NUM
cana-3334	158	3	]	]	PUNCT
cana-3334	158	4	.	.	PUNCT
cana-3334	159	1	burton	burton	PROPN
cana-3334	159	2	,	,	PUNCT
cana-3334	159	3	d.	d.	PROPN
cana-3334	159	4	m.	m.	PROPN
cana-3334	159	5	(	(	PUNCT
cana-3334	159	6	2011	2011	NUM
cana-3334	159	7	)	)	PUNCT
cana-3334	159	8	.	.	PUNCT
cana-3334	160	1	elementary	elementary	ADJ
cana-3334	160	2	number	number	NOUN
cana-3334	160	3	theory	theory	NOUN
cana-3334	160	4	(	(	PUNCT
cana-3334	160	5	7th	7th	ADJ
cana-3334	160	6	ed	ed	NOUN
cana-3334	160	7	.	.	PUNCT
cana-3334	160	8	)	)	PUNCT
cana-3334	160	9	.	.	PUNCT
cana-3334	161	1	the	the	DET
cana-3334	161	2	mcgraw	mcgraw	PROPN
cana-3334	161	3	-	-	PUNCT
cana-3334	161	4	hill	hill	NOUN
cana-3334	161	5	companies	company	NOUN
cana-3334	161	6	,	,	PUNCT
cana-3334	161	7	inc	inc	PROPN
cana-3334	161	8	.	.	PUNCT
cana-3334	162	1	[	[	X
cana-3334	162	2	3	3	NUM
cana-3334	162	3	]	]	PUNCT
cana-3334	162	4	.	.	PUNCT
cana-3334	163	1	dickson	dickson	PROPN
cana-3334	163	2	,	,	PUNCT
cana-3334	163	3	l.	l.	PROPN
cana-3334	163	4	e.	e.	PROPN
cana-3334	163	5	(	(	PUNCT
cana-3334	163	6	2013	2013	NUM
cana-3334	163	7	)	)	PUNCT
cana-3334	163	8	.	.	PUNCT
cana-3334	164	1	history	history	NOUN
cana-3334	164	2	of	of	ADP
cana-3334	164	3	the	the	DET
cana-3334	164	4	theory	theory	NOUN
cana-3334	164	5	of	of	ADP
cana-3334	164	6	numbers	number	NOUN
cana-3334	164	7	(	(	PUNCT
cana-3334	164	8	vol	vol	NOUN
cana-3334	164	9	.	.	PUNCT
cana-3334	164	10	ii	ii	PROPN
cana-3334	164	11	)	)	PUNCT
cana-3334	164	12	.	.	PUNCT
cana-3334	165	1	dover	dover	PROPN
cana-3334	165	2	publications	publication	NOUN
cana-3334	165	3	.	.	PUNCT
cana-3334	166	1	[	[	X
cana-3334	166	2	4	4	NUM
cana-3334	166	3	]	]	PUNCT
cana-3334	166	4	.	.	PUNCT
cana-3334	166	5	gopalan	gopalan	PROPN
cana-3334	166	6	,	,	PUNCT
cana-3334	166	7	m.	m.	NOUN
cana-3334	166	8	,	,	PUNCT
cana-3334	166	9	kannan	kannan	PROPN
cana-3334	166	10	,	,	PUNCT
cana-3334	166	11	j.	j.	PROPN
cana-3334	166	12	,	,	PUNCT
cana-3334	166	13	manju	manju	PROPN
cana-3334	166	14	,	,	PUNCT
cana-3334	166	15	s.	s.	PROPN
cana-3334	166	16	,	,	PUNCT
cana-3334	166	17	&	&	CCONJ
cana-3334	166	18	raja	raja	PROPN
cana-3334	166	19	,	,	PUNCT
cana-3334	166	20	k.	k.	PROPN
cana-3334	166	21	(	(	PUNCT
cana-3334	166	22	2016	2016	NUM
cana-3334	166	23	)	)	PUNCT
cana-3334	166	24	.	.	PUNCT
cana-3334	167	1	integral	integral	ADJ
cana-3334	167	2	solutions	solution	NOUN
cana-3334	167	3	of	of	ADP
cana-3334	167	4	an	an	DET
cana-3334	167	5	infinite	infinite	ADJ
cana-3334	167	6	elliptic	elliptic	ADJ
cana-3334	167	7	cone	cone	NOUN
cana-3334	167	8	𝑋2	𝑋2	VERB
cana-3334	167	9	=	=	SYM
cana-3334	167	10	4𝑌2	4𝑌2	NUM
cana-3334	168	1	+	+	NUM
cana-3334	168	2	5𝑍2	5𝑍2	X
cana-3334	168	3	.	.	PUNCT
cana-3334	168	4	international	international	ADJ
cana-3334	168	5	journal	journal	NOUN
cana-3334	168	6	of	of	ADP
cana-3334	168	7	innovative	innovative	ADJ
cana-3334	168	8	research	research	NOUN
cana-3334	168	9	in	in	ADP
cana-3334	168	10	science	science	NOUN
cana-3334	168	11	,	,	PUNCT
cana-3334	168	12	engineering	engineering	NOUN
cana-3334	168	13	and	and	CCONJ
cana-3334	168	14	technology	technology	NOUN
cana-3334	168	15	,	,	PUNCT
cana-3334	168	16	5(10	5(10	NUM
cana-3334	168	17	)	)	PUNCT
cana-3334	168	18	,	,	PUNCT
cana-3334	168	19	17549	17549	NUM
cana-3334	168	20	-	-	SYM
cana-3334	168	21	17557	17557	NUM
cana-3334	168	22	.	.	PUNCT
cana-3334	169	1	[	[	X
cana-3334	169	2	5	5	NUM
cana-3334	169	3	]	]	PUNCT
cana-3334	169	4	.	.	PUNCT
cana-3334	170	1	hendrik	hendrik	PROPN
cana-3334	170	2	w.	w.	PROPN
cana-3334	170	3	lenstra	lenstra	PROPN
cana-3334	170	4	,	,	PUNCT
cana-3334	170	5	j.	j.	PROPN
cana-3334	170	6	(	(	PUNCT
cana-3334	170	7	2002	2002	NUM
cana-3334	170	8	)	)	PUNCT
cana-3334	170	9	.	.	PUNCT
cana-3334	171	1	solving	solve	VERB
cana-3334	171	2	the	the	DET
cana-3334	171	3	pell	pell	NOUN
cana-3334	171	4	equation	equation	NOUN
cana-3334	171	5	.	.	PUNCT
cana-3334	172	1	notices	notice	NOUN
cana-3334	172	2	of	of	ADP
cana-3334	172	3	the	the	DET
cana-3334	172	4	ams	am	NOUN
cana-3334	172	5	,	,	PUNCT
cana-3334	172	6	44	44	NUM
cana-3334	172	7	,	,	PUNCT
cana-3334	172	8	182	182	NUM
cana-3334	172	9	-	-	SYM
cana-3334	172	10	192	192	NUM
cana-3334	172	11	.	.	PUNCT
cana-3334	173	1	[	[	X
cana-3334	173	2	6	6	NUM
cana-3334	173	3	]	]	PUNCT
cana-3334	173	4	.	.	PUNCT
cana-3334	174	1	kannan	kannan	PROPN
cana-3334	174	2	,	,	PUNCT
cana-3334	174	3	j.	j.	PROPN
cana-3334	174	4	,	,	PUNCT
cana-3334	174	5	&	&	CCONJ
cana-3334	174	6	mahalakshmi	mahalakshmi	PROPN
cana-3334	174	7	,	,	PUNCT
cana-3334	174	8	m.	m.	NOUN
cana-3334	174	9	(	(	PUNCT
cana-3334	174	10	2022	2022	NUM
cana-3334	174	11	)	)	PUNCT
cana-3334	174	12	.	.	PUNCT
cana-3334	175	1	some	some	DET
cana-3334	175	2	annotations	annotation	NOUN
cana-3334	175	3	on	on	ADP
cana-3334	175	4	almost	almost	ADV
cana-3334	175	5	and	and	CCONJ
cana-3334	175	6	pseudo	pseudo	NOUN
cana-3334	175	7	almost	almost	ADV
cana-3334	175	8	equilateral	equilateral	ADJ
cana-3334	175	9	rational	rational	ADJ
cana-3334	175	10	rectangles	rectangle	NOUN
cana-3334	175	11	.	.	PUNCT
cana-3334	176	1	research	research	NOUN
cana-3334	176	2	and	and	CCONJ
cana-3334	176	3	reflections	reflection	NOUN
cana-3334	176	4	on	on	ADP
cana-3334	176	5	education	education	NOUN
cana-3334	176	6	,	,	PUNCT
cana-3334	176	7	20(3a	20(3a	NUM
cana-3334	176	8	)	)	PUNCT
cana-3334	176	9	,	,	PUNCT
cana-3334	176	10	88	88	NUM
cana-3334	176	11	-	-	SYM
cana-3334	176	12	92	92	NUM
cana-3334	176	13	.	.	PUNCT
cana-3334	177	1	[	[	X
cana-3334	177	2	7	7	NUM
cana-3334	177	3	]	]	PUNCT
cana-3334	177	4	.	.	PUNCT
cana-3334	178	1	kannan	kannan	PROPN
cana-3334	178	2	,	,	PUNCT
cana-3334	178	3	j.	j.	PROPN
cana-3334	178	4	,	,	PUNCT
cana-3334	178	5	&	&	CCONJ
cana-3334	178	6	manju	manju	PROPN
cana-3334	178	7	,	,	PUNCT
cana-3334	178	8	s.	s.	PROPN
cana-3334	178	9	(	(	PUNCT
cana-3334	178	10	2023	2023	NUM
cana-3334	178	11	)	)	PUNCT
cana-3334	178	12	.	.	PUNCT
cana-3334	179	1	fundamental	fundamental	ADJ
cana-3334	179	2	perceptions	perception	NOUN
cana-3334	179	3	in	in	ADP
cana-3334	179	4	contemporary	contemporary	ADJ
cana-3334	179	5	number	number	NOUN
cana-3334	179	6	theory	theory	NOUN
cana-3334	179	7	(	(	PUNCT
cana-3334	179	8	1st	1st	ADJ
cana-3334	179	9	ed	ed	NOUN
cana-3334	179	10	.	.	PUNCT
cana-3334	179	11	)	)	PUNCT
cana-3334	179	12	.	.	PUNCT
cana-3334	180	1	new	new	PROPN
cana-3334	180	2	york	york	PROPN
cana-3334	180	3	:	:	PUNCT
cana-3334	180	4	nova	nova	PROPN
cana-3334	180	5	science	science	NOUN
cana-3334	180	6	publisher	publisher	NOUN
cana-3334	180	7	.	.	PUNCT
cana-3334	181	1	[	[	X
cana-3334	181	2	8	8	NUM
cana-3334	181	3	]	]	PUNCT
cana-3334	181	4	.	.	PUNCT
cana-3334	182	1	kannan	kannan	PROPN
cana-3334	182	2	,	,	PUNCT
cana-3334	182	3	j.	j.	PROPN
cana-3334	182	4	,	,	PUNCT
cana-3334	182	5	manju	manju	PROPN
cana-3334	182	6	,	,	PUNCT
cana-3334	182	7	s.	s.	PROPN
cana-3334	182	8	,	,	PUNCT
cana-3334	182	9	mahalakshmi	mahalakshmi	PROPN
cana-3334	182	10	,	,	PUNCT
cana-3334	182	11	m.	m.	NOUN
cana-3334	182	12	,	,	PUNCT
cana-3334	182	13	&	&	CCONJ
cana-3334	182	14	raja	raja	PROPN
cana-3334	182	15	,	,	PUNCT
cana-3334	182	16	k.	k.	PROPN
cana-3334	182	17	(	(	PUNCT
cana-3334	182	18	2022	2022	NUM
cana-3334	182	19	)	)	PUNCT
cana-3334	182	20	.	.	PUNCT
cana-3334	183	1	encryption	encryption	NOUN
cana-3334	183	2	decryption	decryption	NOUN
cana-3334	183	3	algorithm	algorithm	NOUN
cana-3334	183	4	using	use	VERB
cana-3334	183	5	solutions	solution	NOUN
cana-3334	183	6	of	of	ADP
cana-3334	183	7	pell	pell	ADJ
cana-3334	183	8	equation	equation	NOUN
cana-3334	183	9	.	.	PUNCT
cana-3334	184	1	international	international	ADJ
cana-3334	184	2	journal	journal	PROPN
cana-3334	184	3	of	of	ADP
cana-3334	184	4	mathematics	mathematic	NOUN
cana-3334	184	5	and	and	CCONJ
cana-3334	184	6	its	its	PRON
cana-3334	184	7	applications	application	NOUN
cana-3334	184	8	,	,	PUNCT
cana-3334	184	9	10(1	10(1	NUM
cana-3334	184	10	)	)	PUNCT
cana-3334	184	11	,	,	PUNCT
cana-3334	184	12	1	1	NUM
cana-3334	184	13	-	-	SYM
cana-3334	184	14	8	8	NUM
cana-3334	184	15	.	.	PUNCT
cana-3334	185	1	[	[	X
cana-3334	185	2	9	9	NUM
cana-3334	185	3	]	]	PUNCT
cana-3334	185	4	.	.	PUNCT
cana-3334	185	5	mahalakshmi	mahalakshmi	PROPN
cana-3334	185	6	,	,	PUNCT
cana-3334	185	7	m.	m.	NOUN
cana-3334	185	8	,	,	PUNCT
cana-3334	185	9	kannan	kannan	PROPN
cana-3334	185	10	,	,	PUNCT
cana-3334	185	11	j.	j.	PROPN
cana-3334	185	12	,	,	PUNCT
cana-3334	185	13	&	&	CCONJ
cana-3334	185	14	narasimman	narasimman	NOUN
cana-3334	185	15	,	,	PUNCT
cana-3334	185	16	g.	g.	PROPN
cana-3334	185	17	(	(	PUNCT
cana-3334	185	18	2022	2022	NUM
cana-3334	185	19	)	)	PUNCT
cana-3334	185	20	.	.	PUNCT
cana-3334	186	1	certain	certain	ADJ
cana-3334	186	2	sequels	sequel	NOUN
cana-3334	186	3	on	on	ADP
cana-3334	186	4	almost	almost	ADV
cana-3334	186	5	equilateral	equilateral	ADJ
cana-3334	186	6	triangles	triangle	NOUN
cana-3334	186	7	.	.	PUNCT
cana-3334	187	1	advances	advance	NOUN
cana-3334	187	2	and	and	CCONJ
cana-3334	187	3	applications	application	NOUN
cana-3334	187	4	in	in	ADP
cana-3334	187	5	mathematical	mathematical	ADJ
cana-3334	187	6	sciences	science	NOUN
cana-3334	187	7	,	,	PUNCT
cana-3334	187	8	22(1	22(1	NUM
cana-3334	187	9	)	)	PUNCT
cana-3334	187	10	,	,	PUNCT
cana-3334	187	11	149	149	NUM
cana-3334	187	12	-	-	SYM
cana-3334	187	13	157	157	NUM
cana-3334	187	14	.	.	PUNCT
cana-3334	188	1	[	[	X
cana-3334	188	2	10	10	NUM
cana-3334	188	3	]	]	PUNCT
cana-3334	188	4	.	.	PUNCT
cana-3334	189	1	manju	manju	PROPN
cana-3334	189	2	,	,	PUNCT
cana-3334	189	3	s.	s.	PROPN
cana-3334	189	4	,	,	PUNCT
cana-3334	189	5	kannan	kannan	PROPN
cana-3334	189	6	,	,	PUNCT
cana-3334	189	7	j.	j.	PROPN
cana-3334	189	8	,	,	PUNCT
cana-3334	189	9	&	&	CCONJ
cana-3334	189	10	raja	raja	PROPN
cana-3334	189	11	,	,	PUNCT
cana-3334	189	12	k.	k.	PROPN
cana-3334	189	13	(	(	PUNCT
cana-3334	189	14	2017	2017	NUM
cana-3334	189	15	)	)	PUNCT
cana-3334	189	16	.	.	PUNCT
cana-3334	190	1	exponential	exponential	ADJ
cana-3334	190	2	diophantine	diophantine	NOUN
cana-3334	190	3	equation	equation	NOUN
cana-3334	190	4	in	in	ADP
cana-3334	190	5	two	two	NUM
cana-3334	190	6	and	and	CCONJ
cana-3334	190	7	three	three	NUM
cana-3334	190	8	variables	variable	NOUN
cana-3334	190	9	.	.	PUNCT
cana-3334	191	1	global	global	ADJ
cana-3334	191	2	journal	journal	NOUN
cana-3334	191	3	of	of	ADP
cana-3334	191	4	pure	pure	ADJ
cana-3334	191	5	and	and	CCONJ
cana-3334	191	6	applied	applied	ADJ
cana-3334	191	7	mathenmatics	mathenmatic	NOUN
cana-3334	191	8	,	,	PUNCT
cana-3334	191	9	13(5	13(5	NUM
cana-3334	191	10	)	)	PUNCT
cana-3334	191	11	,	,	PUNCT
cana-3334	191	12	128	128	NUM
cana-3334	191	13	-	-	SYM
cana-3334	191	14	132	132	NUM
cana-3334	191	15	.	.	PUNCT
cana-3334	192	1	[	[	X
cana-3334	192	2	11	11	NUM
cana-3334	192	3	]	]	PUNCT
cana-3334	192	4	.	.	PUNCT
cana-3334	193	1	nelsen	nelsen	PROPN
cana-3334	193	2	,	,	PUNCT
cana-3334	193	3	r.	r.	PROPN
cana-3334	193	4	b.	b.	PROPN
cana-3334	193	5	(	(	PUNCT
cana-3334	193	6	2020	2020	NUM
cana-3334	193	7	)	)	PUNCT
cana-3334	193	8	.	.	PUNCT
cana-3334	194	1	almost	almost	ADV
cana-3334	194	2	equilateral	equilateral	ADJ
cana-3334	194	3	heronian	heronian	ADJ
cana-3334	194	4	triangles	triangle	NOUN
cana-3334	194	5	.	.	PUNCT
cana-3334	195	1	mathematics	mathematic	NOUN
cana-3334	195	2	magazine	magazine	NOUN
cana-3334	195	3	,	,	PUNCT
cana-3334	195	4	378	378	NUM
cana-3334	195	5	-	-	SYM
cana-3334	195	6	379	379	NUM
cana-3334	195	7	.	.	PUNCT
cana-3334	196	1	[	[	X
cana-3334	196	2	12	12	NUM
cana-3334	196	3	]	]	PUNCT
cana-3334	196	4	.	.	PUNCT
cana-3334	197	1	robin	robin	PROPN
cana-3334	197	2	mclean	mclean	PROPN
cana-3334	197	3	,	,	PUNCT
cana-3334	197	4	k.	k.	PROPN
cana-3334	197	5	(	(	PUNCT
cana-3334	197	6	1988	1988	NUM
cana-3334	197	7	)	)	PUNCT
cana-3334	197	8	.	.	PUNCT
cana-3334	198	1	heronian	heronian	ADJ
cana-3334	198	2	triangles	triangle	NOUN
cana-3334	198	3	are	be	AUX
cana-3334	198	4	almost	almost	ADV
cana-3334	198	5	everywhere	everywhere	ADV
cana-3334	198	6	.	.	PUNCT
cana-3334	199	1	the	the	DET
cana-3334	199	2	mathematical	mathematical	ADJ
cana-3334	199	3	gazette	gazette	NOUN
cana-3334	199	4	,	,	PUNCT
cana-3334	199	5	72(459	72(459	NOUN
cana-3334	199	6	)	)	PUNCT
cana-3334	199	7	,	,	PUNCT
cana-3334	199	8	49	49	NUM
cana-3334	199	9	-	-	SYM
cana-3334	199	10	51	51	NUM
cana-3334	199	11	.	.	PUNCT
cana-3334	200	1	[	[	X
cana-3334	200	2	13	13	NUM
cana-3334	200	3	]	]	PUNCT
cana-3334	200	4	.	.	PUNCT
cana-3334	201	1	rosen	rosen	PROPN
cana-3334	201	2	,	,	PUNCT
cana-3334	201	3	k.	k.	PROPN
cana-3334	201	4	h.	h.	PROPN
cana-3334	201	5	(	(	PUNCT
cana-3334	201	6	2011	2011	NUM
cana-3334	201	7	)	)	PUNCT
cana-3334	201	8	.	.	PUNCT
cana-3334	202	1	elementary	elementary	ADJ
cana-3334	202	2	number	number	NOUN
cana-3334	202	3	theory	theory	NOUN
cana-3334	202	4	and	and	CCONJ
cana-3334	202	5	its	its	PRON
cana-3334	202	6	applications	application	NOUN
cana-3334	202	7	(	(	PUNCT
cana-3334	202	8	4th	4th	ADJ
cana-3334	202	9	ed	ed	NOUN
cana-3334	202	10	.	.	PUNCT
cana-3334	202	11	)	)	PUNCT
cana-3334	202	12	.	.	PUNCT
cana-3334	203	1	boston	boston	PROPN
cana-3334	203	2	:	:	PUNCT
cana-3334	203	3	pearson	pearson	PROPN
cana-3334	203	4	addison	addison	PROPN
cana-3334	203	5	-	-	PUNCT
cana-3334	203	6	wesley	wesley	PROPN
cana-3334	203	7	.	.	PUNCT
cana-3334	204	1	[	[	X
cana-3334	204	2	14	14	NUM
cana-3334	204	3	]	]	SYM
cana-3334	204	4	.	.	PUNCT
cana-3334	204	5	rusin	rusin	PROPN
cana-3334	204	6	,	,	PUNCT
cana-3334	204	7	d.	d.	PROPN
cana-3334	204	8	j.	j.	PROPN
cana-3334	204	9	(	(	PUNCT
cana-3334	204	10	1998	1998	NUM
cana-3334	204	11	)	)	PUNCT
cana-3334	204	12	.	.	PUNCT
cana-3334	205	1	rational	rational	ADJ
cana-3334	205	2	triangles	triangle	NOUN
cana-3334	205	3	with	with	ADP
cana-3334	205	4	equal	equal	ADJ
cana-3334	205	5	area	area	NOUN
cana-3334	205	6	.	.	PUNCT
cana-3334	206	1	new	new	PROPN
cana-3334	206	2	york	york	PROPN
cana-3334	206	3	journal	journal	PROPN
cana-3334	206	4	of	of	ADP
cana-3334	206	5	mathematics	mathematic	NOUN
cana-3334	206	6	,	,	PUNCT
cana-3334	206	7	1	1	NUM
cana-3334	206	8	-	-	SYM
cana-3334	206	9	15	15	NUM
cana-3334	206	10	.	.	PUNCT
cana-3334	207	1	[	[	X
cana-3334	207	2	15	15	NUM
cana-3334	207	3	]	]	PUNCT
cana-3334	207	4	.	.	PUNCT
cana-3334	208	1	titu	titu	PROPN
cana-3334	208	2	,	,	PUNCT
cana-3334	208	3	a.	a.	PROPN
cana-3334	208	4	,	,	PUNCT
cana-3334	208	5	dorin	dorin	PROPN
cana-3334	208	6	,	,	PUNCT
cana-3334	208	7	a.	a.	PROPN
cana-3334	208	8	,	,	PUNCT
cana-3334	208	9	&	&	CCONJ
cana-3334	208	10	ion	ion	NOUN
cana-3334	208	11	,	,	PUNCT
cana-3334	208	12	c.	c.	NOUN
cana-3334	208	13	(	(	PUNCT
cana-3334	208	14	2010	2010	NUM
cana-3334	208	15	)	)	PUNCT
cana-3334	208	16	.	.	PUNCT
cana-3334	209	1	introduction	introduction	NOUN
cana-3334	209	2	to	to	PART
cana-3334	209	3	diophantine	diophantine	VERB
cana-3334	209	4	equations	equation	NOUN
cana-3334	209	5	:	:	PUNCT
cana-3334	209	6	a	a	DET
cana-3334	209	7	problembased	problembase	VERB
cana-3334	209	8	london	london	PROPN
cana-3334	209	9	:	:	PUNCT
cana-3334	209	10	birkhauser.s	birkhauser.s	X