id	sid	tid	token	lemma	pos
ejpam-1076	1	1	10_filiz.dvi	10_filiz.dvi	NUM
ejpam-1076	1	2	european	european	PROPN
ejpam-1076	1	3	journal	journal	PROPN
ejpam-1076	1	4	of	of	ADP
ejpam-1076	1	5	pure	pure	ADJ
ejpam-1076	1	6	and	and	CCONJ
ejpam-1076	1	7	applied	apply	VERB
ejpam-1076	1	8	mathematics	mathematic	NOUN
ejpam-1076	1	9	vol	vol	NOUN
ejpam-1076	1	10	.	.	PROPN
ejpam-1076	1	11	5	5	NUM
ejpam-1076	1	12	,	,	PUNCT
ejpam-1076	1	13	no	no	INTJ
ejpam-1076	1	14	.	.	NOUN
ejpam-1076	1	15	2	2	NUM
ejpam-1076	1	16	,	,	PUNCT
ejpam-1076	1	17	2012	2012	NUM
ejpam-1076	1	18	,	,	PUNCT
ejpam-1076	1	19	205	205	NUM
ejpam-1076	1	20	-	-	SYM
ejpam-1076	1	21	210	210	NUM
ejpam-1076	1	22	issn	issn	PROPN
ejpam-1076	1	23	1307	1307	NUM
ejpam-1076	1	24	-	-	SYM
ejpam-1076	1	25	5543	5543	NUM
ejpam-1076	1	26	–	–	PUNCT
ejpam-1076	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1076	1	28	on	on	ADP
ejpam-1076	1	29	the	the	DET
ejpam-1076	1	30	pairs	pair	NOUN
ejpam-1076	1	31	of	of	ADP
ejpam-1076	1	32	orthogonal	orthogonal	ADJ
ejpam-1076	1	33	ruled	rule	VERB
ejpam-1076	1	34	surfaces	surface	NOUN
ejpam-1076	1	35	filiz	filiz	NOUN
ejpam-1076	1	36	kanbay	kanbay	PROPN
ejpam-1076	1	37	department	department	PROPN
ejpam-1076	1	38	of	of	ADP
ejpam-1076	1	39	mathematics	mathematic	NOUN
ejpam-1076	1	40	,	,	PUNCT
ejpam-1076	1	41	faculty	faculty	NOUN
ejpam-1076	1	42	of	of	ADP
ejpam-1076	1	43	arts	art	NOUN
ejpam-1076	1	44	and	and	CCONJ
ejpam-1076	1	45	science	science	PROPN
ejpam-1076	1	46	yıldız	yıldız	PROPN
ejpam-1076	1	47	technical	technical	PROPN
ejpam-1076	1	48	university	university	PROPN
ejpam-1076	1	49	,	,	PUNCT
ejpam-1076	1	50	34210	34210	NUM
ejpam-1076	1	51	,	,	PUNCT
ejpam-1076	1	52	davutpas.a	davutpas.a	NUM
ejpam-1076	1	53	,	,	PUNCT
ejpam-1076	1	54	istanbul	istanbul	PROPN
ejpam-1076	1	55	,	,	PUNCT
ejpam-1076	1	56	turkey	turkey	PROPN
ejpam-1076	1	57	abstract	abstract	NOUN
ejpam-1076	1	58	.	.	PUNCT
ejpam-1076	2	1	in	in	ADP
ejpam-1076	2	2	this	this	DET
ejpam-1076	2	3	work	work	NOUN
ejpam-1076	2	4	,	,	PUNCT
ejpam-1076	2	5	in	in	ADP
ejpam-1076	2	6	three	three	NUM
ejpam-1076	2	7	dimensional	dimensional	ADJ
ejpam-1076	2	8	euclidean	euclidean	ADJ
ejpam-1076	2	9	space	space	NOUN
ejpam-1076	2	10	e3	e3	NOUN
ejpam-1076	2	11	,	,	PUNCT
ejpam-1076	2	12	by	by	ADP
ejpam-1076	2	13	using	use	VERB
ejpam-1076	2	14	the	the	DET
ejpam-1076	2	15	ruled	rule	VERB
ejpam-1076	2	16	bonnet	bonnet	NOUN
ejpam-1076	2	17	surfaces	surface	NOUN
ejpam-1076	2	18	which	which	PRON
ejpam-1076	2	19	have	have	AUX
ejpam-1076	2	20	been	be	AUX
ejpam-1076	2	21	known	know	VERB
ejpam-1076	2	22	up	up	ADP
ejpam-1076	2	23	to	to	ADP
ejpam-1076	2	24	now	now	ADV
ejpam-1076	2	25	,	,	PUNCT
ejpam-1076	2	26	the	the	DET
ejpam-1076	2	27	problem	problem	NOUN
ejpam-1076	2	28	of	of	ADP
ejpam-1076	2	29	finding	find	VERB
ejpam-1076	2	30	some	some	DET
ejpam-1076	2	31	pairs	pair	NOUN
ejpam-1076	2	32	of	of	ADP
ejpam-1076	2	33	orthogonal	orthogonal	ADJ
ejpam-1076	2	34	ruled	rule	VERB
ejpam-1076	2	35	surfaces	surface	NOUN
ejpam-1076	2	36	is	be	AUX
ejpam-1076	2	37	examined	examine	VERB
ejpam-1076	2	38	and	and	CCONJ
ejpam-1076	2	39	only	only	ADV
ejpam-1076	2	40	one	one	NUM
ejpam-1076	2	41	pair	pair	NOUN
ejpam-1076	2	42	of	of	ADP
ejpam-1076	2	43	orthogonal	orthogonal	ADJ
ejpam-1076	2	44	ruled	rule	VERB
ejpam-1076	2	45	surfaces	surface	NOUN
ejpam-1076	2	46	can	can	AUX
ejpam-1076	2	47	be	be	AUX
ejpam-1076	2	48	obtained	obtain	VERB
ejpam-1076	2	49	.	.	PUNCT
ejpam-1076	3	1	2010	2010	NUM
ejpam-1076	3	2	mathematics	mathematic	NOUN
ejpam-1076	3	3	subject	subject	NOUN
ejpam-1076	3	4	classifications	classification	NOUN
ejpam-1076	3	5	:	:	PUNCT
ejpam-1076	3	6	53a05	53a05	NUM
ejpam-1076	3	7	key	key	ADJ
ejpam-1076	3	8	words	word	NOUN
ejpam-1076	3	9	and	and	CCONJ
ejpam-1076	3	10	phrases	phrase	NOUN
ejpam-1076	3	11	:	:	PUNCT
ejpam-1076	3	12	orthogonal	orthogonal	ADJ
ejpam-1076	3	13	surface	surface	NOUN
ejpam-1076	3	14	,	,	PUNCT
ejpam-1076	3	15	bonnet	bonnet	NOUN
ejpam-1076	3	16	surface	surface	NOUN
ejpam-1076	3	17	,	,	PUNCT
ejpam-1076	3	18	ruled	rule	VERB
ejpam-1076	3	19	surface	surface	NOUN
ejpam-1076	3	20	,	,	PUNCT
ejpam-1076	3	21	weingarten	weingarten	ADJ
ejpam-1076	3	22	surface	surface	NOUN
ejpam-1076	3	23	,	,	PUNCT
ejpam-1076	3	24	tangential	tangential	ADJ
ejpam-1076	3	25	surface	surface	NOUN
ejpam-1076	3	26	1	1	NUM
ejpam-1076	3	27	.	.	PUNCT
ejpam-1076	4	1	introduction	introduction	NOUN
ejpam-1076	4	2	the	the	DET
ejpam-1076	4	3	orthogonal	orthogonal	ADJ
ejpam-1076	4	4	surfaces	surface	NOUN
ejpam-1076	4	5	are	be	AUX
ejpam-1076	4	6	related	relate	VERB
ejpam-1076	4	7	to	to	ADP
ejpam-1076	4	8	the	the	DET
ejpam-1076	4	9	problem	problem	NOUN
ejpam-1076	4	10	of	of	ADP
ejpam-1076	4	11	isometric	isometric	ADJ
ejpam-1076	4	12	representation	representation	NOUN
ejpam-1076	4	13	.	.	PUNCT
ejpam-1076	5	1	these	these	DET
ejpam-1076	5	2	surfaces	surface	NOUN
ejpam-1076	5	3	also	also	ADV
ejpam-1076	5	4	play	play	VERB
ejpam-1076	5	5	an	an	DET
ejpam-1076	5	6	important	important	ADJ
ejpam-1076	5	7	role	role	NOUN
ejpam-1076	5	8	in	in	ADP
ejpam-1076	5	9	all	all	DET
ejpam-1076	5	10	questions	question	NOUN
ejpam-1076	5	11	connected	connect	VERB
ejpam-1076	5	12	with	with	ADP
ejpam-1076	5	13	the	the	DET
ejpam-1076	5	14	study	study	NOUN
ejpam-1076	5	15	of	of	ADP
ejpam-1076	5	16	the	the	DET
ejpam-1076	5	17	infinitesimal	infinitesimal	ADJ
ejpam-1076	5	18	bending	bending	NOUN
ejpam-1076	5	19	problem	problem	NOUN
ejpam-1076	5	20	.	.	PUNCT
ejpam-1076	6	1	because	because	SCONJ
ejpam-1076	6	2	the	the	DET
ejpam-1076	6	3	infinitesimal	infinitesimal	ADJ
ejpam-1076	6	4	bending	bending	NOUN
ejpam-1076	6	5	problem	problem	NOUN
ejpam-1076	6	6	is	be	AUX
ejpam-1076	6	7	reduced	reduce	VERB
ejpam-1076	6	8	the	the	DET
ejpam-1076	6	9	problem	problem	NOUN
ejpam-1076	6	10	of	of	ADP
ejpam-1076	6	11	finding	find	VERB
ejpam-1076	6	12	the	the	DET
ejpam-1076	6	13	orthogonal	orthogonal	ADJ
ejpam-1076	6	14	surfaces	surface	NOUN
ejpam-1076	6	15	[	[	X
ejpam-1076	6	16	5	5	NUM
ejpam-1076	6	17	,	,	PUNCT
ejpam-1076	6	18	7	7	NUM
ejpam-1076	6	19	,	,	PUNCT
ejpam-1076	6	20	8	8	NUM
ejpam-1076	6	21	]	]	PUNCT
ejpam-1076	6	22	.	.	PUNCT
ejpam-1076	7	1	the	the	DET
ejpam-1076	7	2	orthogonal	orthogonal	ADJ
ejpam-1076	7	3	ruled	rule	VERB
ejpam-1076	7	4	surfaces	surface	NOUN
ejpam-1076	7	5	are	be	AUX
ejpam-1076	7	6	significant	significant	ADJ
ejpam-1076	7	7	to	to	PART
ejpam-1076	7	8	investigate	investigate	VERB
ejpam-1076	7	9	the	the	DET
ejpam-1076	7	10	isometric	isometric	ADJ
ejpam-1076	7	11	representation	representation	NOUN
ejpam-1076	7	12	of	of	ADP
ejpam-1076	7	13	the	the	DET
ejpam-1076	7	14	ruled	rule	VERB
ejpam-1076	7	15	surfaces	surface	NOUN
ejpam-1076	7	16	or	or	CCONJ
ejpam-1076	7	17	the	the	DET
ejpam-1076	7	18	infinitesimal	infinitesimal	ADJ
ejpam-1076	7	19	bending	bending	NOUN
ejpam-1076	7	20	of	of	ADP
ejpam-1076	7	21	ruled	rule	VERB
ejpam-1076	7	22	surfaces	surface	NOUN
ejpam-1076	7	23	.	.	PUNCT
ejpam-1076	8	1	for	for	ADP
ejpam-1076	8	2	this	this	DET
ejpam-1076	8	3	aim	aim	NOUN
ejpam-1076	8	4	,	,	PUNCT
ejpam-1076	8	5	we	we	PRON
ejpam-1076	8	6	can	can	AUX
ejpam-1076	8	7	use	use	VERB
ejpam-1076	8	8	the	the	DET
ejpam-1076	8	9	bonnet	bonnet	NOUN
ejpam-1076	8	10	ruled	rule	VERB
ejpam-1076	8	11	surfaces	surface	NOUN
ejpam-1076	8	12	to	to	PART
ejpam-1076	8	13	examine	examine	VERB
ejpam-1076	8	14	pairs	pair	NOUN
ejpam-1076	8	15	of	of	ADP
ejpam-1076	8	16	orthogonal	orthogonal	ADJ
ejpam-1076	8	17	ruled	rule	VERB
ejpam-1076	8	18	surfaces	surface	NOUN
ejpam-1076	8	19	.	.	PUNCT
ejpam-1076	9	1	generally	generally	ADV
ejpam-1076	9	2	,	,	PUNCT
ejpam-1076	9	3	bonnet	bonnet	NOUN
ejpam-1076	9	4	surfaces	surface	NOUN
ejpam-1076	9	5	have	have	AUX
ejpam-1076	9	6	been	be	AUX
ejpam-1076	9	7	classified	classify	VERB
ejpam-1076	9	8	into	into	ADP
ejpam-1076	9	9	three	three	NUM
ejpam-1076	9	10	categories	category	NOUN
ejpam-1076	9	11	:	:	PUNCT
ejpam-1076	9	12	•	•	ADP
ejpam-1076	9	13	the	the	DET
ejpam-1076	9	14	surfaces	surface	NOUN
ejpam-1076	9	15	of	of	ADP
ejpam-1076	9	16	constant	constant	ADJ
ejpam-1076	9	17	mean	mean	ADJ
ejpam-1076	9	18	curvature	curvature	NOUN
ejpam-1076	9	19	other	other	ADJ
ejpam-1076	9	20	than	than	ADP
ejpam-1076	9	21	the	the	DET
ejpam-1076	9	22	planes	plane	NOUN
ejpam-1076	9	23	and	and	CCONJ
ejpam-1076	9	24	spheres	sphere	NOUN
ejpam-1076	9	25	.	.	PUNCT
ejpam-1076	10	1	•	•	NUM
ejpam-1076	10	2	the	the	DET
ejpam-1076	10	3	isometric	isometric	ADJ
ejpam-1076	10	4	weingarten	weingarten	ADJ
ejpam-1076	10	5	surfaces	surface	NOUN
ejpam-1076	10	6	of	of	ADP
ejpam-1076	10	7	non	non	ADJ
ejpam-1076	10	8	-	-	ADJ
ejpam-1076	10	9	constant	constant	ADJ
ejpam-1076	10	10	mean	mean	NOUN
ejpam-1076	10	11	curvature	curvature	NOUN
ejpam-1076	10	12	which	which	PRON
ejpam-1076	10	13	are	be	AUX
ejpam-1076	10	14	isometric	isometric	ADJ
ejpam-1076	10	15	to	to	ADP
ejpam-1076	10	16	a	a	DET
ejpam-1076	10	17	surface	surface	NOUN
ejpam-1076	10	18	of	of	ADP
ejpam-1076	10	19	revolution	revolution	NOUN
ejpam-1076	10	20	.	.	PUNCT
ejpam-1076	11	1	•	•	NUM
ejpam-1076	11	2	the	the	DET
ejpam-1076	11	3	surfaces	surface	NOUN
ejpam-1076	11	4	of	of	ADP
ejpam-1076	11	5	non	non	ADJ
ejpam-1076	11	6	-	-	ADJ
ejpam-1076	11	7	constant	constant	ADJ
ejpam-1076	11	8	mean	mean	ADJ
ejpam-1076	11	9	curvature	curvature	NOUN
ejpam-1076	11	10	that	that	PRON
ejpam-1076	11	11	admit	admit	VERB
ejpam-1076	11	12	a	a	DET
ejpam-1076	11	13	single	single	ADJ
ejpam-1076	11	14	non	non	ADJ
ejpam-1076	11	15	-	-	ADJ
ejpam-1076	11	16	trivial	trivial	ADJ
ejpam-1076	11	17	isometry	isometry	NOUN
ejpam-1076	11	18	.	.	PUNCT
ejpam-1076	12	1	in	in	ADP
ejpam-1076	12	2	[	[	X
ejpam-1076	12	3	2	2	NUM
ejpam-1076	12	4	]	]	PUNCT
ejpam-1076	12	5	,	,	PUNCT
ejpam-1076	12	6	by	by	ADP
ejpam-1076	12	7	using	use	VERB
ejpam-1076	12	8	the	the	DET
ejpam-1076	12	9	method	method	NOUN
ejpam-1076	12	10	given	give	VERB
ejpam-1076	12	11	in	in	ADP
ejpam-1076	12	12	[	[	PUNCT
ejpam-1076	12	13	4	4	NUM
ejpam-1076	12	14	]	]	PUNCT
ejpam-1076	12	15	,	,	PUNCT
ejpam-1076	12	16	some	some	DET
ejpam-1076	12	17	special	special	ADJ
ejpam-1076	12	18	bonnet	bonnet	NOUN
ejpam-1076	12	19	ruled	rule	VERB
ejpam-1076	12	20	surfaces	surface	NOUN
ejpam-1076	12	21	of	of	ADP
ejpam-1076	12	22	non	non	ADJ
ejpam-1076	12	23	-	-	ADJ
ejpam-1076	12	24	constant	constant	ADJ
ejpam-1076	12	25	mean	mean	NOUN
ejpam-1076	12	26	curvature	curvature	NOUN
ejpam-1076	12	27	are	be	AUX
ejpam-1076	12	28	given	give	VERB
ejpam-1076	12	29	.	.	PUNCT
ejpam-1076	13	1	it	it	PRON
ejpam-1076	13	2	is	be	AUX
ejpam-1076	13	3	shown	show	VERB
ejpam-1076	13	4	that	that	SCONJ
ejpam-1076	13	5	the	the	DET
ejpam-1076	13	6	ruled	rule	VERB
ejpam-1076	13	7	surfaces	surface	NOUN
ejpam-1076	13	8	which	which	PRON
ejpam-1076	13	9	are	be	AUX
ejpam-1076	13	10	formed	form	VERB
ejpam-1076	13	11	by	by	ADP
ejpam-1076	13	12	the	the	DET
ejpam-1076	13	13	binormals	binormal	NOUN
ejpam-1076	13	14	two	two	NUM
ejpam-1076	13	15	curves	curve	NOUN
ejpam-1076	13	16	whose	whose	DET
ejpam-1076	13	17	curvatures	curvature	NOUN
ejpam-1076	13	18	and	and	CCONJ
ejpam-1076	13	19	absolute	absolute	ADJ
ejpam-1076	13	20	value	value	NOUN
ejpam-1076	13	21	of	of	ADP
ejpam-1076	13	22	torsions	torsion	NOUN
ejpam-1076	13	23	are	be	AUX
ejpam-1076	13	24	the	the	DET
ejpam-1076	13	25	same	same	ADJ
ejpam-1076	13	26	are	be	AUX
ejpam-1076	13	27	the	the	DET
ejpam-1076	13	28	bonnet	bonnet	NOUN
ejpam-1076	13	29	pairs	pair	NOUN
ejpam-1076	13	30	.	.	PUNCT
ejpam-1076	14	1	moreover	moreover	ADV
ejpam-1076	14	2	the	the	DET
ejpam-1076	14	3	ruled	rule	VERB
ejpam-1076	14	4	minimal	minimal	ADJ
ejpam-1076	14	5	bonnet	bonnet	NOUN
ejpam-1076	14	6	surfaces	surface	NOUN
ejpam-1076	14	7	and	and	CCONJ
ejpam-1076	14	8	the	the	DET
ejpam-1076	14	9	ruled	rule	VERB
ejpam-1076	14	10	weingarten	weingarten	ADJ
ejpam-1076	14	11	surfaces	surface	NOUN
ejpam-1076	14	12	are	be	AUX
ejpam-1076	14	13	email	email	NOUN
ejpam-1076	14	14	address	address	NOUN
ejpam-1076	14	15	:	:	PUNCT
ejpam-1076	14	16	fkanbay�yildiz.edu.tr	fkanbay�yildiz.edu.tr	PROPN
ejpam-1076	14	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1076	14	18	205	205	NUM
ejpam-1076	14	19	c	c	X
ejpam-1076	14	20	©	©	PROPN
ejpam-1076	14	21	2012	2012	NUM
ejpam-1076	14	22	ejpam	ejpam	VERB
ejpam-1076	14	23	all	all	DET
ejpam-1076	14	24	rights	right	NOUN
ejpam-1076	14	25	reserved	reserve	VERB
ejpam-1076	14	26	.	.	PUNCT
ejpam-1076	15	1	f.	f.	PROPN
ejpam-1076	15	2	kanby	kanby	PROPN
ejpam-1076	15	3	/	/	SYM
ejpam-1076	15	4	eur	eur	PROPN
ejpam-1076	15	5	.	.	PUNCT
ejpam-1076	16	1	j.	j.	PROPN
ejpam-1076	16	2	pure	pure	PROPN
ejpam-1076	16	3	appl	appl	PROPN
ejpam-1076	16	4	.	.	PROPN
ejpam-1076	16	5	math	math	PROPN
ejpam-1076	16	6	,	,	PUNCT
ejpam-1076	16	7	5	5	NUM
ejpam-1076	16	8	(	(	PUNCT
ejpam-1076	16	9	2012	2012	NUM
ejpam-1076	16	10	)	)	PUNCT
ejpam-1076	16	11	,	,	PUNCT
ejpam-1076	16	12	205	205	NUM
ejpam-1076	16	13	-	-	SYM
ejpam-1076	16	14	210	210	NUM
ejpam-1076	16	15	206	206	NUM
ejpam-1076	16	16	indicated	indicate	VERB
ejpam-1076	16	17	(	(	PUNCT
ejpam-1076	16	18	the	the	DET
ejpam-1076	16	19	developable	developable	ADJ
ejpam-1076	16	20	surface	surface	NOUN
ejpam-1076	16	21	are	be	AUX
ejpam-1076	16	22	not	not	PART
ejpam-1076	16	23	investigated	investigate	VERB
ejpam-1076	16	24	)	)	PUNCT
ejpam-1076	16	25	.	.	PUNCT
ejpam-1076	17	1	the	the	DET
ejpam-1076	17	2	tangential	tangential	ADJ
ejpam-1076	17	3	bonnet	bonnet	NOUN
ejpam-1076	17	4	surfaces	surface	NOUN
ejpam-1076	17	5	as	as	ADP
ejpam-1076	17	6	the	the	DET
ejpam-1076	17	7	developable	developable	ADJ
ejpam-1076	17	8	bonnet	bonnet	NOUN
ejpam-1076	17	9	surfaces	surface	NOUN
ejpam-1076	17	10	are	be	AUX
ejpam-1076	17	11	examined	examine	VERB
ejpam-1076	17	12	in	in	ADP
ejpam-1076	17	13	[	[	X
ejpam-1076	17	14	3	3	NUM
ejpam-1076	17	15	]	]	PUNCT
ejpam-1076	17	16	.	.	PUNCT
ejpam-1076	18	1	in	in	ADP
ejpam-1076	18	2	this	this	DET
ejpam-1076	18	3	work	work	NOUN
ejpam-1076	18	4	,	,	PUNCT
ejpam-1076	18	5	the	the	DET
ejpam-1076	18	6	main	main	ADJ
ejpam-1076	18	7	goal	goal	NOUN
ejpam-1076	18	8	is	be	AUX
ejpam-1076	18	9	to	to	PART
ejpam-1076	18	10	find	find	VERB
ejpam-1076	18	11	some	some	DET
ejpam-1076	18	12	ruled	rule	VERB
ejpam-1076	18	13	orthogonal	orthogonal	ADJ
ejpam-1076	18	14	surfaces	surface	NOUN
ejpam-1076	18	15	by	by	ADP
ejpam-1076	18	16	using	use	VERB
ejpam-1076	18	17	the	the	DET
ejpam-1076	18	18	ruled	rule	VERB
ejpam-1076	18	19	bonnet	bonnet	NOUN
ejpam-1076	18	20	surfaces	surface	NOUN
ejpam-1076	18	21	.	.	PUNCT
ejpam-1076	19	1	using	use	VERB
ejpam-1076	19	2	this	this	DET
ejpam-1076	19	3	method	method	NOUN
ejpam-1076	19	4	,	,	PUNCT
ejpam-1076	19	5	it	it	PRON
ejpam-1076	19	6	is	be	AUX
ejpam-1076	19	7	shown	show	VERB
ejpam-1076	19	8	that	that	SCONJ
ejpam-1076	19	9	the	the	DET
ejpam-1076	19	10	pairs	pair	NOUN
ejpam-1076	19	11	of	of	ADP
ejpam-1076	19	12	orthogonal	orthogonal	ADJ
ejpam-1076	19	13	surfaces	surface	NOUN
ejpam-1076	19	14	except	except	SCONJ
ejpam-1076	19	15	one	one	NUM
ejpam-1076	19	16	pair	pair	NOUN
ejpam-1076	19	17	can	can	AUX
ejpam-1076	19	18	not	not	PART
ejpam-1076	19	19	be	be	AUX
ejpam-1076	19	20	obtained	obtain	VERB
ejpam-1076	19	21	.	.	PUNCT
ejpam-1076	20	1	2	2	X
ejpam-1076	20	2	.	.	NUM
ejpam-1076	20	3	ruled	rule	VERB
ejpam-1076	20	4	bonnet	bonnet	NOUN
ejpam-1076	20	5	surfaces	surface	NOUN
ejpam-1076	20	6	and	and	CCONJ
ejpam-1076	20	7	some	some	DET
ejpam-1076	20	8	orthogonal	orthogonal	ADJ
ejpam-1076	20	9	pairs	pair	NOUN
ejpam-1076	20	10	2.1	2.1	NUM
ejpam-1076	20	11	.	.	PUNCT
ejpam-1076	21	1	some	some	DET
ejpam-1076	21	2	ruled	rule	VERB
ejpam-1076	21	3	bonnet	bonnet	NOUN
ejpam-1076	21	4	surfaces	surface	NOUN
ejpam-1076	21	5	a	a	DET
ejpam-1076	21	6	ruled	rule	VERB
ejpam-1076	21	7	surface	surface	NOUN
ejpam-1076	21	8	in	in	ADP
ejpam-1076	21	9	three	three	NUM
ejpam-1076	21	10	dimensional	dimensional	ADJ
ejpam-1076	21	11	euclidean	euclidean	ADJ
ejpam-1076	21	12	space	space	NOUN
ejpam-1076	21	13	e3	e3	NOUN
ejpam-1076	21	14	can	can	AUX
ejpam-1076	21	15	be	be	AUX
ejpam-1076	21	16	given	give	VERB
ejpam-1076	21	17	by	by	ADP
ejpam-1076	21	18	the	the	DET
ejpam-1076	21	19	vectorial	vectorial	ADJ
ejpam-1076	21	20	equation	equation	NOUN
ejpam-1076	21	21	x(u	x(u	PROPN
ejpam-1076	21	22	,	,	PUNCT
ejpam-1076	21	23	v	v	NOUN
ejpam-1076	21	24	)	)	PUNCT
ejpam-1076	21	25	=	=	NOUN
ejpam-1076	21	26	r(v)+	r(v)+	NOUN
ejpam-1076	21	27	ut(v	ut(v	NOUN
ejpam-1076	21	28	)	)	PUNCT
ejpam-1076	21	29	(	(	PUNCT
ejpam-1076	21	30	1	1	X
ejpam-1076	21	31	)	)	PUNCT
ejpam-1076	21	32	where	where	SCONJ
ejpam-1076	21	33	r=	r=	PROPN
ejpam-1076	21	34	r(v	r(v	PROPN
ejpam-1076	21	35	)	)	PUNCT
ejpam-1076	21	36	is	be	AUX
ejpam-1076	21	37	a	a	DET
ejpam-1076	21	38	directrix	directrix	NOUN
ejpam-1076	21	39	curve	curve	NOUN
ejpam-1076	21	40	,	,	PUNCT
ejpam-1076	21	41	t=	t=	ADJ
ejpam-1076	21	42	t(v	t(v	NOUN
ejpam-1076	21	43	)	)	PUNCT
ejpam-1076	21	44	is	be	AUX
ejpam-1076	21	45	a	a	DET
ejpam-1076	21	46	unit	unit	NOUN
ejpam-1076	21	47	vector	vector	NOUN
ejpam-1076	21	48	with	with	ADP
ejpam-1076	21	49	t2(v	t2(v	NOUN
ejpam-1076	21	50	)	)	PUNCT
ejpam-1076	21	51	=	=	SYM
ejpam-1076	21	52	a2(v	a2(v	PROPN
ejpam-1076	21	53	)	)	PUNCT
ejpam-1076	21	54	6=	6=	ADP
ejpam-1076	21	55	0	0	NUM
ejpam-1076	21	56	,	,	PUNCT
ejpam-1076	21	57	t(v	t(v	PROPN
ejpam-1076	21	58	)	)	PUNCT
ejpam-1076	21	59	·	·	PUNCT
ejpam-1076	22	1	r′(v	r′(v	X
ejpam-1076	22	2	)	)	PUNCT
ejpam-1076	22	3	=	=	SYM
ejpam-1076	22	4	cosθ(v	cosθ(v	NOUN
ejpam-1076	22	5	)	)	PUNCT
ejpam-1076	22	6	,	,	PUNCT
ejpam-1076	22	7	t′(v	t′(v	PROPN
ejpam-1076	22	8	)	)	PUNCT
ejpam-1076	22	9	·	·	PUNCT
ejpam-1076	23	1	r′(v	r′(v	X
ejpam-1076	23	2	)	)	PUNCT
ejpam-1076	23	3	=	=	SYM
ejpam-1076	23	4	b(v	b(v	NOUN
ejpam-1076	23	5	)	)	PUNCT
ejpam-1076	23	6	,	,	PUNCT
ejpam-1076	23	7	(	(	PUNCT
ejpam-1076	23	8	0≤	0≤	NUM
ejpam-1076	23	9	θ	θ	NOUN
ejpam-1076	23	10	≤	≤	NUM
ejpam-1076	23	11	π	π	X
ejpam-1076	23	12	)	)	PUNCT
ejpam-1076	23	13	,	,	PUNCT
ejpam-1076	23	14	where	where	SCONJ
ejpam-1076	23	15	f	f	X
ejpam-1076	23	16	′	′	NOUN
ejpam-1076	24	1	=	=	PUNCT
ejpam-1076	25	1	d	d	X
ejpam-1076	25	2	f	f	PROPN
ejpam-1076	25	3	dv	dv	PROPN
ejpam-1076	25	4	)	)	PUNCT
ejpam-1076	25	5	(	(	PUNCT
ejpam-1076	25	6	2	2	X
ejpam-1076	25	7	)	)	PUNCT
ejpam-1076	25	8	the	the	DET
ejpam-1076	25	9	first	first	ADJ
ejpam-1076	25	10	fundamental	fundamental	ADJ
ejpam-1076	25	11	form	form	NOUN
ejpam-1076	25	12	of	of	ADP
ejpam-1076	25	13	the	the	DET
ejpam-1076	25	14	ruled	rule	VERB
ejpam-1076	25	15	surface	surface	NOUN
ejpam-1076	25	16	(	(	PUNCT
ejpam-1076	25	17	1	1	X
ejpam-1076	25	18	)	)	PUNCT
ejpam-1076	25	19	is	be	AUX
ejpam-1076	25	20	ds2	ds2	PROPN
ejpam-1076	25	21	=	=	SYM
ejpam-1076	25	22	du2	du2	PROPN
ejpam-1076	25	23	+	+	NOUN
ejpam-1076	25	24	2	2	NUM
ejpam-1076	25	25	cosθdudv+	cosθdudv+	NOUN
ejpam-1076	25	26	(	(	PUNCT
ejpam-1076	25	27	a2u2	a2u2	PROPN
ejpam-1076	25	28	+	+	NUM
ejpam-1076	25	29	2bu+	2bu+	NUM
ejpam-1076	25	30	1)dv2	1)dv2	NUM
ejpam-1076	25	31	(	(	PUNCT
ejpam-1076	25	32	3	3	NUM
ejpam-1076	25	33	)	)	PUNCT
ejpam-1076	25	34	tthe	tthe	PRON
ejpam-1076	25	35	value	value	NOUN
ejpam-1076	25	36	of	of	ADP
ejpam-1076	25	37	u	u	NOUN
ejpam-1076	25	38	for	for	ADP
ejpam-1076	25	39	the	the	DET
ejpam-1076	25	40	central	central	ADJ
ejpam-1076	25	41	point	point	NOUN
ejpam-1076	25	42	;	;	PUNCT
ejpam-1076	25	43	the	the	DET
ejpam-1076	25	44	parameter	parameter	NOUN
ejpam-1076	25	45	of	of	ADP
ejpam-1076	25	46	the	the	DET
ejpam-1076	25	47	distribution	distribution	NOUN
ejpam-1076	25	48	β	β	NOUN
ejpam-1076	25	49	are	be	AUX
ejpam-1076	25	50	expressed	express	VERB
ejpam-1076	25	51	as	as	ADP
ejpam-1076	25	52	u	u	NOUN
ejpam-1076	25	53	=	=	NOUN
ejpam-1076	25	54	α(v	α(v	X
ejpam-1076	25	55	)	)	PUNCT
ejpam-1076	26	1	=	=	SYM
ejpam-1076	26	2	−	−	PROPN
ejpam-1076	26	3	b(v	b(v	NOUN
ejpam-1076	26	4	)	)	PUNCT
ejpam-1076	26	5	a2(v	a2(v	X
ejpam-1076	26	6	)	)	PUNCT
ejpam-1076	26	7	,	,	PUNCT
ejpam-1076	26	8	β	β	NOUN
ejpam-1076	26	9	=	=	SYM
ejpam-1076	26	10	1	1	NUM
ejpam-1076	26	11	a2	a2	PROPN
ejpam-1076	26	12	(	(	PUNCT
ejpam-1076	26	13	t	t	PROPN
ejpam-1076	26	14	,	,	PUNCT
ejpam-1076	26	15	t	t	PROPN
ejpam-1076	26	16	,	,	PUNCT
ejpam-1076	26	17	t′	t′	NUM
ejpam-1076	26	18	)	)	PUNCT
ejpam-1076	26	19	(	(	PUNCT
ejpam-1076	26	20	4	4	X
ejpam-1076	26	21	)	)	PUNCT
ejpam-1076	26	22	here	here	ADV
ejpam-1076	26	23	the	the	DET
ejpam-1076	26	24	central	central	ADJ
ejpam-1076	26	25	point	point	NOUN
ejpam-1076	26	26	is	be	AUX
ejpam-1076	26	27	the	the	DET
ejpam-1076	26	28	limit	limit	NOUN
ejpam-1076	26	29	of	of	ADP
ejpam-1076	26	30	the	the	DET
ejpam-1076	26	31	point	point	NOUN
ejpam-1076	26	32	in	in	ADP
ejpam-1076	26	33	which	which	PRON
ejpam-1076	26	34	a	a	DET
ejpam-1076	26	35	generator	generator	NOUN
ejpam-1076	26	36	g1	g1	PROPN
ejpam-1076	26	37	is	be	AUX
ejpam-1076	26	38	met	meet	VERB
ejpam-1076	26	39	by	by	ADP
ejpam-1076	26	40	the	the	DET
ejpam-1076	26	41	common	common	ADJ
ejpam-1076	26	42	perpendicular	perpendicular	NOUN
ejpam-1076	26	43	of	of	ADP
ejpam-1076	26	44	g1and	g1and	PROPN
ejpam-1076	26	45	a	a	DET
ejpam-1076	26	46	neighboring	neighboring	NOUN
ejpam-1076	26	47	generator	generator	NOUN
ejpam-1076	26	48	g2	g2	PROPN
ejpam-1076	26	49	as	as	SCONJ
ejpam-1076	26	50	g2	g2	PROPN
ejpam-1076	26	51	approaches	approach	VERB
ejpam-1076	26	52	g1	g1	PROPN
ejpam-1076	26	53	over	over	ADP
ejpam-1076	26	54	a	a	DET
ejpam-1076	26	55	ruled	rule	VERB
ejpam-1076	26	56	surface	surface	NOUN
ejpam-1076	26	57	;	;	PUNCT
ejpam-1076	26	58	the	the	DET
ejpam-1076	26	59	parameter	parameter	NOUN
ejpam-1076	26	60	of	of	ADP
ejpam-1076	26	61	distribution	distribution	NOUN
ejpam-1076	26	62	is	be	AUX
ejpam-1076	26	63	the	the	DET
ejpam-1076	26	64	limit	limit	NOUN
ejpam-1076	26	65	of	of	ADP
ejpam-1076	26	66	the	the	DET
ejpam-1076	26	67	ratio	ratio	NOUN
ejpam-1076	26	68	of	of	ADP
ejpam-1076	26	69	the	the	DET
ejpam-1076	26	70	shortest	short	ADJ
ejpam-1076	26	71	distance	distance	NOUN
ejpam-1076	26	72	between	between	ADP
ejpam-1076	26	73	two	two	NUM
ejpam-1076	26	74	generators	generator	NOUN
ejpam-1076	26	75	and	and	CCONJ
ejpam-1076	26	76	their	their	PRON
ejpam-1076	26	77	included	include	VERB
ejpam-1076	26	78	angle	angle	NOUN
ejpam-1076	26	79	.	.	PUNCT
ejpam-1076	27	1	now	now	ADV
ejpam-1076	27	2	let	let	VERB
ejpam-1076	27	3	an	an	DET
ejpam-1076	27	4	orthogonal	orthogonal	ADJ
ejpam-1076	27	5	trajectory	trajectory	NOUN
ejpam-1076	27	6	to	to	ADP
ejpam-1076	27	7	the	the	DET
ejpam-1076	27	8	generators	generator	NOUN
ejpam-1076	27	9	be	be	AUX
ejpam-1076	27	10	taken	take	VERB
ejpam-1076	27	11	as	as	ADP
ejpam-1076	27	12	a	a	DET
ejpam-1076	27	13	directrix	directrix	NOUN
ejpam-1076	27	14	and	and	CCONJ
ejpam-1076	27	15	t2(v	t2(v	NOUN
ejpam-1076	28	1	)	)	PUNCT
ejpam-1076	28	2	=	=	SYM
ejpam-1076	28	3	1	1	NUM
ejpam-1076	28	4	,	,	PUNCT
ejpam-1076	28	5	t′	t′	NUM
ejpam-1076	28	6	2	2	NUM
ejpam-1076	28	7	(	(	PUNCT
ejpam-1076	28	8	v	v	NOUN
ejpam-1076	28	9	)	)	PUNCT
ejpam-1076	28	10	=	=	SYM
ejpam-1076	28	11	1	1	NUM
ejpam-1076	28	12	.	.	PUNCT
ejpam-1076	29	1	such	such	DET
ejpam-1076	29	2	a	a	DET
ejpam-1076	29	3	ruled	rule	VERB
ejpam-1076	29	4	surface	surface	NOUN
ejpam-1076	29	5	can	can	AUX
ejpam-1076	29	6	be	be	AUX
ejpam-1076	29	7	obtained	obtain	VERB
ejpam-1076	29	8	from	from	ADP
ejpam-1076	29	9	(	(	PUNCT
ejpam-1076	29	10	1	1	NUM
ejpam-1076	29	11	)	)	PUNCT
ejpam-1076	29	12	under	under	ADP
ejpam-1076	29	13	the	the	DET
ejpam-1076	29	14	conditions	condition	NOUN
ejpam-1076	29	15	[	[	X
ejpam-1076	29	16	6	6	NUM
ejpam-1076	29	17	,	,	PUNCT
ejpam-1076	29	18	1	1	NUM
ejpam-1076	29	19	]	]	PUNCT
ejpam-1076	29	20	:	:	PUNCT
ejpam-1076	30	1	t	t	X
ejpam-1076	30	2	=	=	SYM
ejpam-1076	30	3	1	1	NUM
ejpam-1076	30	4	β	β	X
ejpam-1076	30	5	(	(	PUNCT
ejpam-1076	30	6	t′	t′	NUM
ejpam-1076	30	7	∧	∧	PROPN
ejpam-1076	30	8	r′),t′	r′),t′	NOUN
ejpam-1076	30	9	=	=	SYM
ejpam-1076	30	10	−	−	PROPN
ejpam-1076	30	11	α	α	PROPN
ejpam-1076	30	12	β2+α2	β2+α2	PROPN
ejpam-1076	30	13	r′+	r′+	NOUN
ejpam-1076	30	14	β	β	NOUN
ejpam-1076	30	15	β2+α2	β2+α2	NUM
ejpam-1076	30	16	r′	r′	PROPN
ejpam-1076	30	17	∧	∧	PROPN
ejpam-1076	30	18	t	t	PROPN
ejpam-1076	30	19	r′	r′	NOUN
ejpam-1076	30	20	=	=	SYM
ejpam-1076	30	21	−αt′+	−αt′+	PROPN
ejpam-1076	30	22	βt∧	βt∧	NOUN
ejpam-1076	30	23	t′	t′	NUM
ejpam-1076	30	24	(	(	PUNCT
ejpam-1076	30	25	5	5	NUM
ejpam-1076	30	26	)	)	PUNCT
ejpam-1076	30	27	n	n	NOUN
ejpam-1076	30	28	=	=	SYM
ejpam-1076	30	29	−1	−1	NOUN
ejpam-1076	30	30	βw	βw	ADP
ejpam-1076	30	31	[	[	X
ejpam-1076	30	32	(	(	PUNCT
ejpam-1076	30	33	β2+α2	β2+α2	INTJ
ejpam-1076	30	34	−	−	NOUN
ejpam-1076	30	35	uα)t′	uα)t′	NUM
ejpam-1076	30	36	+	+	CCONJ
ejpam-1076	30	37	(	(	PUNCT
ejpam-1076	30	38	α−	α−	ADP
ejpam-1076	30	39	u)r′	u)r′	PROPN
ejpam-1076	30	40	]	]	PUNCT
ejpam-1076	30	41	,	,	PUNCT
ejpam-1076	30	42	w	w	PROPN
ejpam-1076	30	43	=	=	SYM
ejpam-1076	30	44	p	p	X
ejpam-1076	30	45	(	(	PUNCT
ejpam-1076	30	46	u−α)2	u−α)2	ADV
ejpam-1076	30	47	+	+	CCONJ
ejpam-1076	30	48	β2	β2	VERB
ejpam-1076	30	49	,	,	PUNCT
ejpam-1076	30	50	(	(	PUNCT
ejpam-1076	30	51	β	β	X
ejpam-1076	30	52	6=	6=	ADP
ejpam-1076	30	53	0	0	NUM
ejpam-1076	30	54	)	)	PUNCT
ejpam-1076	30	55	we	we	PRON
ejpam-1076	30	56	recall	recall	VERB
ejpam-1076	30	57	that	that	SCONJ
ejpam-1076	30	58	the	the	DET
ejpam-1076	30	59	director	director	NOUN
ejpam-1076	30	60	-	-	PUNCT
ejpam-1076	30	61	cone	cone	NOUN
ejpam-1076	30	62	is	be	AUX
ejpam-1076	30	63	the	the	DET
ejpam-1076	30	64	cone	cone	NOUN
ejpam-1076	30	65	formed	form	VERB
ejpam-1076	30	66	by	by	ADP
ejpam-1076	30	67	drawing	draw	VERB
ejpam-1076	30	68	through	through	ADP
ejpam-1076	30	69	a	a	DET
ejpam-1076	30	70	point	point	NOUN
ejpam-1076	30	71	lines	line	NOUN
ejpam-1076	30	72	parallel	parallel	ADJ
ejpam-1076	30	73	to	to	ADP
ejpam-1076	30	74	the	the	DET
ejpam-1076	30	75	generators	generator	NOUN
ejpam-1076	30	76	and	and	CCONJ
ejpam-1076	30	77	it	it	PRON
ejpam-1076	30	78	is	be	AUX
ejpam-1076	30	79	determined	determine	VERB
ejpam-1076	30	80	by	by	ADP
ejpam-1076	30	81	the	the	DET
ejpam-1076	30	82	function	function	NOUN
ejpam-1076	30	83	d(v	d(v	PROPN
ejpam-1076	30	84	)	)	PUNCT
ejpam-1076	31	1	=	=	SYM
ejpam-1076	31	2	r′	r′	PRON
ejpam-1076	31	3	·	·	PUNCT
ejpam-1076	31	4	t′′	t′′	VERB
ejpam-1076	31	5	β	β	X
ejpam-1076	31	6	=	=	SYM
ejpam-1076	31	7	(	(	PUNCT
ejpam-1076	31	8	t	t	PROPN
ejpam-1076	31	9	,	,	PUNCT
ejpam-1076	31	10	t′,t′′	t′,t′′	NOUN
ejpam-1076	31	11	)	)	PUNCT
ejpam-1076	31	12	(	(	PUNCT
ejpam-1076	31	13	6	6	NUM
ejpam-1076	31	14	)	)	PUNCT
ejpam-1076	31	15	f.	f.	PROPN
ejpam-1076	31	16	kanby	kanby	PROPN
ejpam-1076	31	17	/	/	SYM
ejpam-1076	31	18	eur	eur	PROPN
ejpam-1076	31	19	.	.	PUNCT
ejpam-1076	32	1	j.	j.	PROPN
ejpam-1076	32	2	pure	pure	PROPN
ejpam-1076	32	3	appl	appl	PROPN
ejpam-1076	32	4	.	.	PROPN
ejpam-1076	32	5	math	math	PROPN
ejpam-1076	32	6	,	,	PUNCT
ejpam-1076	32	7	5	5	NUM
ejpam-1076	32	8	(	(	PUNCT
ejpam-1076	32	9	2012	2012	NUM
ejpam-1076	32	10	)	)	PUNCT
ejpam-1076	32	11	,	,	PUNCT
ejpam-1076	32	12	205	205	NUM
ejpam-1076	32	13	-	-	SYM
ejpam-1076	32	14	210	210	NUM
ejpam-1076	32	15	207	207	NUM
ejpam-1076	32	16	because	because	SCONJ
ejpam-1076	32	17	κ2	κ2	NOUN
ejpam-1076	32	18	=	=	SYM
ejpam-1076	32	19	1+d2	1+d2	NUM
ejpam-1076	32	20	and	and	CCONJ
ejpam-1076	32	21	τ	τ	X
ejpam-1076	32	22	=	=	SYM
ejpam-1076	32	23	d′	d′	NUM
ejpam-1076	32	24	1+d2	1+d2	NUM
ejpam-1076	32	25	are	be	AUX
ejpam-1076	32	26	the	the	DET
ejpam-1076	32	27	curvature	curvature	NOUN
ejpam-1076	32	28	and	and	CCONJ
ejpam-1076	32	29	the	the	DET
ejpam-1076	32	30	torsion	torsion	NOUN
ejpam-1076	32	31	of	of	ADP
ejpam-1076	32	32	the	the	DET
ejpam-1076	32	33	unit	unit	NOUN
ejpam-1076	32	34	spherical	spherical	ADJ
ejpam-1076	32	35	curve	curve	NOUN
ejpam-1076	32	36	x	x	PUNCT
ejpam-1076	32	37	=	=	SYM
ejpam-1076	32	38	t(v	t(v	PROPN
ejpam-1076	32	39	)	)	PUNCT
ejpam-1076	32	40	which	which	PRON
ejpam-1076	32	41	determines	determine	VERB
ejpam-1076	32	42	the	the	DET
ejpam-1076	32	43	director	director	NOUN
ejpam-1076	32	44	-	-	PUNCT
ejpam-1076	32	45	cone	cone	NOUN
ejpam-1076	33	1	[	[	X
ejpam-1076	33	2	2	2	NUM
ejpam-1076	33	3	]	]	PUNCT
ejpam-1076	33	4	.	.	PUNCT
ejpam-1076	34	1	the	the	DET
ejpam-1076	34	2	minimal	minimal	ADJ
ejpam-1076	34	3	surfaces	surface	NOUN
ejpam-1076	34	4	and	and	CCONJ
ejpam-1076	34	5	the	the	DET
ejpam-1076	34	6	isothermic	isothermic	ADJ
ejpam-1076	34	7	weingarten	weingarten	PROPN
ejpam-1076	34	8	ruled	rule	VERB
ejpam-1076	34	9	surfaces	surface	NOUN
ejpam-1076	34	10	are	be	AUX
ejpam-1076	34	11	given	give	VERB
ejpam-1076	34	12	by	by	ADP
ejpam-1076	34	13	the	the	DET
ejpam-1076	34	14	equations	equation	NOUN
ejpam-1076	34	15	α′	α′	NUM
ejpam-1076	34	16	=	=	PUNCT
ejpam-1076	34	17	β	β	X
ejpam-1076	34	18	′	′	NUM
ejpam-1076	35	1	=	=	PUNCT
ejpam-1076	35	2	d	d	NOUN
ejpam-1076	35	3	=	=	SYM
ejpam-1076	35	4	0	0	NUM
ejpam-1076	35	5	and	and	CCONJ
ejpam-1076	35	6	α′′	α′′	NOUN
ejpam-1076	35	7	=	=	SYM
ejpam-1076	35	8	β	β	X
ejpam-1076	35	9	′	′	NUM
ejpam-1076	35	10	=	=	PUNCT
ejpam-1076	36	1	d′	d′	X
ejpam-1076	36	2	=	=	SYM
ejpam-1076	36	3	0	0	PUNCT
ejpam-1076	36	4	respectively	respectively	ADV
ejpam-1076	36	5	[	[	X
ejpam-1076	36	6	2	2	NUM
ejpam-1076	36	7	,	,	PUNCT
ejpam-1076	36	8	6	6	NUM
ejpam-1076	36	9	]	]	PUNCT
ejpam-1076	36	10	.	.	PUNCT
ejpam-1076	37	1	if	if	SCONJ
ejpam-1076	37	2	a	a	DET
ejpam-1076	37	3	isometric	isometric	ADJ
ejpam-1076	37	4	representation	representation	NOUN
ejpam-1076	37	5	between	between	ADP
ejpam-1076	37	6	two	two	NUM
ejpam-1076	37	7	surfaces	surface	NOUN
ejpam-1076	37	8	preserves	preserve	VERB
ejpam-1076	37	9	the	the	DET
ejpam-1076	37	10	principal	principal	ADJ
ejpam-1076	37	11	curvatures	curvature	NOUN
ejpam-1076	37	12	of	of	ADP
ejpam-1076	37	13	these	these	DET
ejpam-1076	37	14	surface	surface	NOUN
ejpam-1076	37	15	,	,	PUNCT
ejpam-1076	37	16	these	these	DET
ejpam-1076	37	17	surfaces	surface	NOUN
ejpam-1076	37	18	are	be	AUX
ejpam-1076	37	19	said	say	VERB
ejpam-1076	37	20	to	to	PART
ejpam-1076	37	21	be	be	AUX
ejpam-1076	37	22	bonnet	bonnet	NOUN
ejpam-1076	37	23	surfaces	surface	NOUN
ejpam-1076	37	24	.	.	PUNCT
ejpam-1076	38	1	in	in	ADP
ejpam-1076	38	2	[	[	X
ejpam-1076	38	3	4	4	NUM
ejpam-1076	38	4	]	]	PUNCT
ejpam-1076	38	5	,	,	PUNCT
ejpam-1076	38	6	in	in	ADP
ejpam-1076	38	7	order	order	NOUN
ejpam-1076	38	8	to	to	PART
ejpam-1076	38	9	find	find	VERB
ejpam-1076	38	10	a	a	DET
ejpam-1076	38	11	bonnet	bonnet	NOUN
ejpam-1076	38	12	surface	surface	NOUN
ejpam-1076	38	13	a	a	DET
ejpam-1076	38	14	method	method	NOUN
ejpam-1076	38	15	is	be	AUX
ejpam-1076	38	16	given	give	VERB
ejpam-1076	38	17	.	.	PUNCT
ejpam-1076	39	1	in	in	ADP
ejpam-1076	39	2	according	accord	VERB
ejpam-1076	39	3	to	to	ADP
ejpam-1076	39	4	this	this	PRON
ejpam-1076	39	5	,	,	PUNCT
ejpam-1076	39	6	a	a	DET
ejpam-1076	39	7	-	-	PUNCT
ejpam-1076	39	8	net	net	NOUN
ejpam-1076	39	9	on	on	ADP
ejpam-1076	39	10	a	a	DET
ejpam-1076	39	11	surface	surface	NOUN
ejpam-1076	39	12	such	such	ADJ
ejpam-1076	39	13	that	that	SCONJ
ejpam-1076	39	14	,	,	PUNCT
ejpam-1076	39	15	when	when	SCONJ
ejpam-1076	39	16	this	this	DET
ejpam-1076	39	17	net	net	NOUN
ejpam-1076	39	18	is	be	AUX
ejpam-1076	39	19	parametrized	parametrize	VERB
ejpam-1076	39	20	,	,	PUNCT
ejpam-1076	39	21	the	the	DET
ejpam-1076	39	22	conditions	condition	NOUN
ejpam-1076	39	23	e	e	NOUN
ejpam-1076	39	24	=	=	SYM
ejpam-1076	39	25	g	g	PROPN
ejpam-1076	39	26	,	,	PUNCT
ejpam-1076	39	27	f	f	PROPN
ejpam-1076	39	28	=	=	SYM
ejpam-1076	39	29	0	0	PROPN
ejpam-1076	39	30	,	,	PUNCT
ejpam-1076	39	31	m	m	VERB
ejpam-1076	39	32	=	=	NOUN
ejpam-1076	39	33	c	c	NOUN
ejpam-1076	39	34	=	=	SYM
ejpam-1076	39	35	const	const	PROPN
ejpam-1076	39	36	.	.	PUNCT
ejpam-1076	40	1	6=	6=	NOUN
ejpam-1076	40	2	0	0	NUM
ejpam-1076	40	3	are	be	AUX
ejpam-1076	40	4	satisfied	satisfied	ADJ
ejpam-1076	40	5	,	,	PUNCT
ejpam-1076	40	6	is	be	AUX
ejpam-1076	40	7	called	call	VERB
ejpam-1076	40	8	an	an	DET
ejpam-1076	40	9	a	a	DET
ejpam-1076	40	10	-	-	PUNCT
ejpam-1076	40	11	net	net	NOUN
ejpam-1076	40	12	,	,	PUNCT
ejpam-1076	40	13	where	where	SCONJ
ejpam-1076	40	14	e	e	NOUN
ejpam-1076	40	15	,	,	PUNCT
ejpam-1076	40	16	f	f	PROPN
ejpam-1076	40	17	,	,	PUNCT
ejpam-1076	40	18	g	g	PROPN
ejpam-1076	40	19	are	be	AUX
ejpam-1076	40	20	the	the	DET
ejpam-1076	40	21	coefficients	coefficient	NOUN
ejpam-1076	40	22	of	of	ADP
ejpam-1076	40	23	the	the	DET
ejpam-1076	40	24	first	first	ADJ
ejpam-1076	40	25	fundamental	fundamental	ADJ
ejpam-1076	40	26	form	form	NOUN
ejpam-1076	40	27	of	of	ADP
ejpam-1076	40	28	the	the	DET
ejpam-1076	40	29	surface	surface	NOUN
ejpam-1076	40	30	and	and	CCONJ
ejpam-1076	40	31	l	l	NOUN
ejpam-1076	40	32	,	,	PUNCT
ejpam-1076	40	33	m	m	VERB
ejpam-1076	40	34	,	,	PUNCT
ejpam-1076	40	35	n	n	PRON
ejpam-1076	40	36	are	be	AUX
ejpam-1076	40	37	the	the	DET
ejpam-1076	40	38	coefficients	coefficient	NOUN
ejpam-1076	40	39	of	of	ADP
ejpam-1076	40	40	the	the	DET
ejpam-1076	40	41	second	second	ADJ
ejpam-1076	40	42	fundamental	fundamental	ADJ
ejpam-1076	40	43	form	form	NOUN
ejpam-1076	40	44	.	.	PUNCT
ejpam-1076	41	1	and	and	CCONJ
ejpam-1076	41	2	necessary	necessary	ADJ
ejpam-1076	41	3	and	and	CCONJ
ejpam-1076	41	4	sufficient	sufficient	ADJ
ejpam-1076	41	5	condition	condition	NOUN
ejpam-1076	41	6	for	for	SCONJ
ejpam-1076	41	7	a	a	DET
ejpam-1076	41	8	surface	surface	NOUN
ejpam-1076	41	9	to	to	PART
ejpam-1076	41	10	be	be	AUX
ejpam-1076	41	11	a	a	DET
ejpam-1076	41	12	bonnet	bonnet	NOUN
ejpam-1076	41	13	surface	surface	NOUN
ejpam-1076	41	14	is	be	AUX
ejpam-1076	41	15	that	that	SCONJ
ejpam-1076	41	16	the	the	DET
ejpam-1076	41	17	surface	surface	NOUN
ejpam-1076	41	18	can	can	AUX
ejpam-1076	41	19	have	have	VERB
ejpam-1076	41	20	an	an	DET
ejpam-1076	41	21	a	a	DET
ejpam-1076	41	22	-	-	PUNCT
ejpam-1076	41	23	net	net	NOUN
ejpam-1076	41	24	.	.	PUNCT
ejpam-1076	42	1	in	in	ADP
ejpam-1076	42	2	[	[	X
ejpam-1076	42	3	2	2	NUM
ejpam-1076	42	4	]	]	PUNCT
ejpam-1076	42	5	,	,	PUNCT
ejpam-1076	42	6	on	on	ADP
ejpam-1076	42	7	the	the	DET
ejpam-1076	42	8	ruled	rule	VERB
ejpam-1076	42	9	surface	surface	NOUN
ejpam-1076	42	10	,	,	PUNCT
ejpam-1076	42	11	the	the	DET
ejpam-1076	42	12	generators	generator	NOUN
ejpam-1076	42	13	and	and	CCONJ
ejpam-1076	42	14	orthogonal	orthogonal	ADJ
ejpam-1076	42	15	trajectories	trajectory	NOUN
ejpam-1076	42	16	form	form	VERB
ejpam-1076	42	17	an	an	DET
ejpam-1076	42	18	a	a	DET
ejpam-1076	42	19	-	-	PUNCT
ejpam-1076	42	20	net	net	NOUN
ejpam-1076	42	21	if	if	SCONJ
ejpam-1076	42	22	and	and	CCONJ
ejpam-1076	42	23	only	only	ADV
ejpam-1076	42	24	if	if	SCONJ
ejpam-1076	42	25	the	the	DET
ejpam-1076	42	26	parameter	parameter	NOUN
ejpam-1076	42	27	of	of	ADP
ejpam-1076	42	28	the	the	DET
ejpam-1076	42	29	distribution	distribution	NOUN
ejpam-1076	42	30	β	β	NOUN
ejpam-1076	42	31	and	and	CCONJ
ejpam-1076	42	32	the	the	DET
ejpam-1076	42	33	abscissa	abscissa	NOUN
ejpam-1076	42	34	of	of	ADP
ejpam-1076	42	35	the	the	DET
ejpam-1076	42	36	central	central	ADJ
ejpam-1076	42	37	point	point	NOUN
ejpam-1076	42	38	α	α	NOUN
ejpam-1076	42	39	are	be	AUX
ejpam-1076	42	40	constants	constant	NOUN
ejpam-1076	42	41	.	.	PUNCT
ejpam-1076	43	1	and	and	CCONJ
ejpam-1076	43	2	the	the	DET
ejpam-1076	43	3	parameter	parameter	NOUN
ejpam-1076	43	4	of	of	ADP
ejpam-1076	43	5	distribution	distribution	NOUN
ejpam-1076	43	6	and	and	CCONJ
ejpam-1076	43	7	the	the	DET
ejpam-1076	43	8	abscissa	abscissa	NOUN
ejpam-1076	43	9	of	of	ADP
ejpam-1076	43	10	the	the	DET
ejpam-1076	43	11	central	central	ADJ
ejpam-1076	43	12	point	point	NOUN
ejpam-1076	43	13	of	of	ADP
ejpam-1076	43	14	a	a	DET
ejpam-1076	43	15	surface	surface	NOUN
ejpam-1076	43	16	are	be	AUX
ejpam-1076	43	17	constant	constant	ADJ
ejpam-1076	43	18	,	,	PUNCT
ejpam-1076	43	19	then	then	ADV
ejpam-1076	43	20	the	the	DET
ejpam-1076	43	21	surface	surface	NOUN
ejpam-1076	43	22	is	be	AUX
ejpam-1076	43	23	a	a	DET
ejpam-1076	43	24	bonnet	bonnet	NOUN
ejpam-1076	43	25	surface	surface	NOUN
ejpam-1076	43	26	.	.	PUNCT
ejpam-1076	44	1	the	the	DET
ejpam-1076	44	2	torsion	torsion	NOUN
ejpam-1076	44	3	of	of	ADP
ejpam-1076	44	4	the	the	DET
ejpam-1076	44	5	striction	striction	NOUN
ejpam-1076	44	6	line	line	NOUN
ejpam-1076	44	7	of	of	ADP
ejpam-1076	44	8	such	such	DET
ejpam-1076	44	9	a	a	DET
ejpam-1076	44	10	bonnet	bonnet	NOUN
ejpam-1076	44	11	surface	surface	NOUN
ejpam-1076	44	12	is	be	AUX
ejpam-1076	44	13	constant	constant	ADJ
ejpam-1076	44	14	and	and	CCONJ
ejpam-1076	44	15	is	be	AUX
ejpam-1076	44	16	equal	equal	ADJ
ejpam-1076	44	17	to	to	ADP
ejpam-1076	44	18	the	the	DET
ejpam-1076	44	19	reciprocal	reciprocal	NOUN
ejpam-1076	44	20	of	of	ADP
ejpam-1076	44	21	the	the	DET
ejpam-1076	44	22	parameter	parameter	NOUN
ejpam-1076	44	23	of	of	ADP
ejpam-1076	44	24	distribution	distribution	NOUN
ejpam-1076	44	25	.	.	PUNCT
ejpam-1076	45	1	and	and	CCONJ
ejpam-1076	45	2	the	the	DET
ejpam-1076	45	3	ruled	rule	VERB
ejpam-1076	45	4	surfaces	surface	NOUN
ejpam-1076	45	5	which	which	PRON
ejpam-1076	45	6	are	be	AUX
ejpam-1076	45	7	formed	form	VERB
ejpam-1076	45	8	by	by	ADP
ejpam-1076	45	9	the	the	DET
ejpam-1076	45	10	binormals	binormal	NOUN
ejpam-1076	45	11	two	two	NUM
ejpam-1076	45	12	curves	curve	NOUN
ejpam-1076	45	13	whose	whose	DET
ejpam-1076	45	14	curvatures	curvature	NOUN
ejpam-1076	45	15	and	and	CCONJ
ejpam-1076	45	16	absolute	absolute	ADJ
ejpam-1076	45	17	value	value	NOUN
ejpam-1076	45	18	of	of	ADP
ejpam-1076	45	19	torsions	torsion	NOUN
ejpam-1076	45	20	are	be	AUX
ejpam-1076	45	21	the	the	DET
ejpam-1076	45	22	same	same	ADJ
ejpam-1076	45	23	are	be	AUX
ejpam-1076	45	24	the	the	DET
ejpam-1076	45	25	bonnet	bonnet	NOUN
ejpam-1076	45	26	pairs	pair	NOUN
ejpam-1076	45	27	.	.	PUNCT
ejpam-1076	46	1	this	this	PRON
ejpam-1076	46	2	means	mean	VERB
ejpam-1076	46	3	that	that	SCONJ
ejpam-1076	46	4	the	the	DET
ejpam-1076	46	5	ruled	rule	VERB
ejpam-1076	46	6	surfaces	surface	NOUN
ejpam-1076	46	7	given	give	VERB
ejpam-1076	46	8	by	by	ADP
ejpam-1076	46	9	the	the	DET
ejpam-1076	46	10	equations	equation	NOUN
ejpam-1076	46	11	x(u	x(u	PROPN
ejpam-1076	46	12	,	,	PUNCT
ejpam-1076	46	13	v	v	NOUN
ejpam-1076	46	14	)	)	PUNCT
ejpam-1076	46	15	=	=	SYM
ejpam-1076	46	16	r(v)+	r(v)+	NOUN
ejpam-1076	46	17	|β	|β	VERB
ejpam-1076	46	18	|	|	ADV
ejpam-1076	46	19	sinhut(v	sinhut(v	NOUN
ejpam-1076	46	20	)	)	PUNCT
ejpam-1076	46	21	y(u	y(u	PROPN
ejpam-1076	46	22	,	,	PUNCT
ejpam-1076	46	23	v	v	NOUN
ejpam-1076	46	24	)	)	PUNCT
ejpam-1076	46	25	=	=	SYM
ejpam-1076	47	1	−r(v)+	−r(v)+	PROPN
ejpam-1076	47	2	|β	|β	VERB
ejpam-1076	47	3	|	|	ADV
ejpam-1076	47	4	sinhut(v	sinhut(v	NOUN
ejpam-1076	47	5	)	)	PUNCT
ejpam-1076	47	6	(	(	PUNCT
ejpam-1076	47	7	7	7	X
ejpam-1076	47	8	)	)	PUNCT
ejpam-1076	47	9	respectively	respectively	ADV
ejpam-1076	47	10	are	be	AUX
ejpam-1076	47	11	bonnet	bonnet	NOUN
ejpam-1076	47	12	pairs	pair	NOUN
ejpam-1076	47	13	.	.	PUNCT
ejpam-1076	48	1	here	here	ADV
ejpam-1076	48	2	β	β	X
ejpam-1076	48	3	6=	6=	ADP
ejpam-1076	48	4	0	0	NUM
ejpam-1076	48	5	and	and	CCONJ
ejpam-1076	48	6	d(v	d(v	PROPN
ejpam-1076	48	7	)	)	PUNCT
ejpam-1076	48	8	is	be	AUX
ejpam-1076	48	9	an	an	DET
ejpam-1076	48	10	arbitrary	arbitrary	ADJ
ejpam-1076	48	11	function	function	NOUN
ejpam-1076	48	12	.	.	PUNCT
ejpam-1076	49	1	in	in	ADP
ejpam-1076	49	2	[	[	X
ejpam-1076	49	3	4	4	NUM
ejpam-1076	49	4	]	]	PUNCT
ejpam-1076	49	5	,	,	PUNCT
ejpam-1076	49	6	the	the	DET
ejpam-1076	49	7	cases	case	NOUN
ejpam-1076	49	8	d(v	d(v	ADJ
ejpam-1076	49	9	)	)	PUNCT
ejpam-1076	49	10	=	=	SYM
ejpam-1076	50	1	const	const	ADJ
ejpam-1076	50	2	.	.	PUNCT
ejpam-1076	51	1	and	and	CCONJ
ejpam-1076	51	2	d(v	d(v	PROPN
ejpam-1076	51	3	)	)	PUNCT
ejpam-1076	52	1	=	=	SYM
ejpam-1076	52	2	0	0	NUM
ejpam-1076	52	3	are	be	AUX
ejpam-1076	52	4	indicated	indicate	VERB
ejpam-1076	52	5	.	.	PUNCT
ejpam-1076	53	1	in	in	ADP
ejpam-1076	53	2	the	the	DET
ejpam-1076	53	3	case	case	NOUN
ejpam-1076	53	4	d(v	d(v	PROPN
ejpam-1076	53	5	)	)	PUNCT
ejpam-1076	53	6	=	=	SYM
ejpam-1076	53	7	const	const	ADJ
ejpam-1076	53	8	.	.	PUNCT
ejpam-1076	54	1	the	the	DET
ejpam-1076	54	2	bonnet	bonnet	NOUN
ejpam-1076	54	3	pairs	pair	NOUN
ejpam-1076	54	4	are	be	AUX
ejpam-1076	54	5	obtained	obtain	VERB
ejpam-1076	54	6	that	that	SCONJ
ejpam-1076	54	7	x(u	x(u	PROPN
ejpam-1076	54	8	,	,	PUNCT
ejpam-1076	54	9	v	v	NOUN
ejpam-1076	54	10	)	)	PUNCT
ejpam-1076	54	11	=	=	SYM
ejpam-1076	54	12	�	�	PROPN
ejpam-1076	54	13	a	a	DET
ejpam-1076	54	14	cos	cos	PROPN
ejpam-1076	54	15	v	v	PROPN
ejpam-1076	54	16	p	p	X
ejpam-1076	54	17	|b|	|b|	PROPN
ejpam-1076	54	18	+	+	CCONJ
ejpam-1076	54	19	ǫ	ǫ	PROPN
ejpam-1076	54	20	a2	a2	NOUN
ejpam-1076	54	21	+	+	CCONJ
ejpam-1076	54	22	b2	b2	PROPN
ejpam-1076	54	23	b	b	NOUN
ejpam-1076	54	24	p	p	X
ejpam-1076	54	25	|b|	|b|	PROPN
ejpam-1076	54	26	sinhu	sinhu	NOUN
ejpam-1076	54	27	sin	sin	VERB
ejpam-1076	54	28	v	v	ADP
ejpam-1076	54	29	p	p	X
ejpam-1076	54	30	|b|	|b|	PROPN
ejpam-1076	54	31	,	,	PUNCT
ejpam-1076	54	32	a	a	DET
ejpam-1076	54	33	sin	sin	NOUN
ejpam-1076	54	34	v	v	ADP
ejpam-1076	54	35	p	p	X
ejpam-1076	54	36	|b|	|b|	PRON
ejpam-1076	54	37	−	−	PROPN
ejpam-1076	54	38	ǫ	ǫ	PROPN
ejpam-1076	54	39	a2	a2	PROPN
ejpam-1076	54	40	+	+	CCONJ
ejpam-1076	54	41	b2	b2	PROPN
ejpam-1076	54	42	b	b	NOUN
ejpam-1076	55	1	p	p	X
ejpam-1076	56	1	|b|	|b|	PROPN
ejpam-1076	56	2	sinhu	sinhu	PROPN
ejpam-1076	56	3	cos	cos	PROPN
ejpam-1076	57	1	v	v	ADP
ejpam-1076	57	2	p	p	X
ejpam-1076	57	3	|b|	|b|	PROPN
ejpam-1076	57	4	,	,	PUNCT
ejpam-1076	58	1	ǫ	ǫ	PRON
ejpam-1076	58	2	p	p	PROPN
ejpam-1076	58	3	|b|v	|b|v	PROPN
ejpam-1076	58	4	+	+	NUM
ejpam-1076	58	5	a(a2	a(a2	NOUN
ejpam-1076	58	6	+	+	NUM
ejpam-1076	58	7	b2	b2	NOUN
ejpam-1076	58	8	)	)	PUNCT
ejpam-1076	58	9	b	b	NOUN
ejpam-1076	59	1	p	p	X
ejpam-1076	59	2	|b|	|b|	PROPN
ejpam-1076	59	3	sinhu	sinhu	PROPN
ejpam-1076	59	4	�	�	PROPN
ejpam-1076	59	5	(	(	PUNCT
ejpam-1076	59	6	8)	8)	NUM
ejpam-1076	59	7	y(u	y(u	PROPN
ejpam-1076	59	8	,	,	PUNCT
ejpam-1076	59	9	v	v	NOUN
ejpam-1076	59	10	)	)	PUNCT
ejpam-1076	59	11	=	=	SYM
ejpam-1076	59	12	�	�	PROPN
ejpam-1076	59	13	−a	−a	NOUN
ejpam-1076	60	1	cos	cos	PROPN
ejpam-1076	60	2	v	v	PROPN
ejpam-1076	60	3	p	p	X
ejpam-1076	60	4	|b|	|b|	PROPN
ejpam-1076	61	1	+	+	CCONJ
ejpam-1076	61	2	ǫ	ǫ	PROPN
ejpam-1076	61	3	a2	a2	NOUN
ejpam-1076	61	4	+	+	CCONJ
ejpam-1076	61	5	b2	b2	NOUN
ejpam-1076	61	6	b	b	NOUN
ejpam-1076	61	7	p	p	X
ejpam-1076	61	8	|b|	|b|	PROPN
ejpam-1076	61	9	sinh	sinh	NOUN
ejpam-1076	61	10	u	u	PROPN
ejpam-1076	61	11	sin	sin	NOUN
ejpam-1076	61	12	v	v	ADP
ejpam-1076	61	13	p	p	X
ejpam-1076	61	14	|b|	|b|	PROPN
ejpam-1076	61	15	,	,	PUNCT
ejpam-1076	61	16	−a	−a	VERB
ejpam-1076	61	17	sin	sin	NOUN
ejpam-1076	61	18	v	v	ADP
ejpam-1076	61	19	p	p	X
ejpam-1076	61	20	|b|	|b|	PRON
ejpam-1076	61	21	−	−	PROPN
ejpam-1076	61	22	ǫ	ǫ	PROPN
ejpam-1076	61	23	a2	a2	PROPN
ejpam-1076	61	24	+	+	CCONJ
ejpam-1076	61	25	b2	b2	NOUN
ejpam-1076	61	26	b	b	NOUN
ejpam-1076	61	27	p	p	X
ejpam-1076	61	28	|b|	|b|	PROPN
ejpam-1076	61	29	sinh	sinh	NOUN
ejpam-1076	61	30	u	u	PROPN
ejpam-1076	61	31	cos	cos	PROPN
ejpam-1076	61	32	v	v	PROPN
ejpam-1076	61	33	p	p	X
ejpam-1076	61	34	|b|	|b|	PROPN
ejpam-1076	61	35	,	,	PUNCT
ejpam-1076	61	36	−ǫ	−ǫ	NOUN
ejpam-1076	61	37	p	p	PROPN
ejpam-1076	61	38	|b|v	|b|v	PROPN
ejpam-1076	61	39	+	+	NUM
ejpam-1076	61	40	a(a2	a(a2	NOUN
ejpam-1076	61	41	+	+	NUM
ejpam-1076	61	42	b2	b2	NOUN
ejpam-1076	61	43	)	)	PUNCT
ejpam-1076	61	44	b	b	NOUN
ejpam-1076	62	1	p	p	X
ejpam-1076	62	2	|b|	|b|	PROPN
ejpam-1076	62	3	sinh	sinh	NOUN
ejpam-1076	62	4	u	u	PROPN
ejpam-1076	62	5	�	�	PROPN
ejpam-1076	62	6	f.	f.	PROPN
ejpam-1076	62	7	kanby	kanby	PROPN
ejpam-1076	62	8	/	/	SYM
ejpam-1076	62	9	eur	eur	PROPN
ejpam-1076	62	10	.	.	PUNCT
ejpam-1076	63	1	j.	j.	PROPN
ejpam-1076	63	2	pure	pure	PROPN
ejpam-1076	63	3	appl	appl	PROPN
ejpam-1076	63	4	.	.	PROPN
ejpam-1076	63	5	math	math	PROPN
ejpam-1076	63	6	,	,	PUNCT
ejpam-1076	63	7	5	5	NUM
ejpam-1076	63	8	(	(	PUNCT
ejpam-1076	63	9	2012	2012	NUM
ejpam-1076	63	10	)	)	PUNCT
ejpam-1076	63	11	,	,	PUNCT
ejpam-1076	63	12	205	205	NUM
ejpam-1076	63	13	-	-	SYM
ejpam-1076	63	14	210	210	NUM
ejpam-1076	63	15	208	208	NUM
ejpam-1076	63	16	where	where	SCONJ
ejpam-1076	63	17	ǫ	ǫ	NOUN
ejpam-1076	63	18	=	=	SYM
ejpam-1076	63	19	sgn(b	sgn(b	PROPN
ejpam-1076	63	20	)	)	PUNCT
ejpam-1076	63	21	=	=	SYM
ejpam-1076	63	22	sgn(β	sgn(β	PROPN
ejpam-1076	63	23	)	)	PUNCT
ejpam-1076	63	24	.	.	PUNCT
ejpam-1076	64	1	in	in	ADP
ejpam-1076	64	2	the	the	DET
ejpam-1076	64	3	case	case	NOUN
ejpam-1076	64	4	d(v	d(v	PROPN
ejpam-1076	64	5	)	)	PUNCT
ejpam-1076	64	6	=	=	SYM
ejpam-1076	64	7	0	0	NUM
ejpam-1076	64	8	,	,	PUNCT
ejpam-1076	64	9	x(u	x(u	PROPN
ejpam-1076	64	10	,	,	PUNCT
ejpam-1076	64	11	v	v	NOUN
ejpam-1076	64	12	)	)	PUNCT
ejpam-1076	64	13	=	=	SYM
ejpam-1076	64	14	�	�	PROPN
ejpam-1076	64	15	|β	|β	VERB
ejpam-1076	64	16	|	|	ADV
ejpam-1076	64	17	sinhu	sinhu	PROPN
ejpam-1076	64	18	cos	cos	PROPN
ejpam-1076	64	19	v	v	PROPN
ejpam-1076	64	20	,	,	PUNCT
ejpam-1076	64	21	|β	|β	VERB
ejpam-1076	64	22	|	|	ADV
ejpam-1076	64	23	sinhu	sinhu	NOUN
ejpam-1076	64	24	sin	sin	NOUN
ejpam-1076	64	25	v	v	PROPN
ejpam-1076	64	26	,	,	PUNCT
ejpam-1076	64	27	β	β	PROPN
ejpam-1076	64	28	v	v	NUM
ejpam-1076	64	29	�	�	PROPN
ejpam-1076	64	30	y(u	y(u	PROPN
ejpam-1076	64	31	,	,	PUNCT
ejpam-1076	64	32	v	v	NOUN
ejpam-1076	64	33	)	)	PUNCT
ejpam-1076	64	34	=	=	SYM
ejpam-1076	64	35	�	�	PROPN
ejpam-1076	64	36	|β	|β	VERB
ejpam-1076	64	37	|	|	ADV
ejpam-1076	64	38	sinhu	sinhu	PROPN
ejpam-1076	64	39	cos	cos	PROPN
ejpam-1076	64	40	v	v	PROPN
ejpam-1076	64	41	,	,	PUNCT
ejpam-1076	64	42	|β	|β	VERB
ejpam-1076	64	43	|	|	ADV
ejpam-1076	64	44	sinhu	sinhu	NOUN
ejpam-1076	64	45	sin	sin	NOUN
ejpam-1076	64	46	v,−β	v,−β	PROPN
ejpam-1076	64	47	v	v	PROPN
ejpam-1076	64	48	�	�	PROPN
ejpam-1076	64	49	(	(	PUNCT
ejpam-1076	64	50	9	9	NUM
ejpam-1076	64	51	)	)	PUNCT
ejpam-1076	64	52	are	be	AUX
ejpam-1076	64	53	found	find	VERB
ejpam-1076	64	54	.	.	PUNCT
ejpam-1076	65	1	these	these	DET
ejpam-1076	65	2	solutions	solution	NOUN
ejpam-1076	65	3	are	be	AUX
ejpam-1076	65	4	valid	valid	ADJ
ejpam-1076	65	5	for	for	ADP
ejpam-1076	65	6	the	the	DET
ejpam-1076	65	7	non	non	ADJ
ejpam-1076	65	8	-	-	ADJ
ejpam-1076	65	9	developable	developable	ADJ
ejpam-1076	65	10	surfaces	surface	NOUN
ejpam-1076	65	11	(	(	PUNCT
ejpam-1076	65	12	β	β	X
ejpam-1076	65	13	6=	6=	ADP
ejpam-1076	65	14	0	0	NUM
ejpam-1076	65	15	)	)	PUNCT
ejpam-1076	66	1	[	[	X
ejpam-1076	66	2	2	2	NUM
ejpam-1076	66	3	]	]	PUNCT
ejpam-1076	66	4	.	.	PUNCT
ejpam-1076	67	1	in	in	ADP
ejpam-1076	67	2	[	[	X
ejpam-1076	67	3	3	3	NUM
ejpam-1076	67	4	]	]	PUNCT
ejpam-1076	67	5	,	,	PUNCT
ejpam-1076	67	6	the	the	DET
ejpam-1076	67	7	tangential	tangential	ADJ
ejpam-1076	67	8	developable	developable	ADJ
ejpam-1076	67	9	surfaces	surface	NOUN
ejpam-1076	67	10	of	of	ADP
ejpam-1076	67	11	the	the	DET
ejpam-1076	67	12	circular	circular	ADJ
ejpam-1076	67	13	helices	helix	NOUN
ejpam-1076	67	14	(	(	PUNCT
ejpam-1076	67	15	β	β	X
ejpam-1076	67	16	=	=	SYM
ejpam-1076	67	17	0	0	NUM
ejpam-1076	67	18	)	)	PUNCT
ejpam-1076	67	19	are	be	AUX
ejpam-1076	67	20	given	give	VERB
ejpam-1076	67	21	as	as	ADP
ejpam-1076	67	22	an	an	DET
ejpam-1076	67	23	example	example	NOUN
ejpam-1076	67	24	of	of	ADP
ejpam-1076	67	25	the	the	DET
ejpam-1076	67	26	ruled	rule	VERB
ejpam-1076	67	27	bonnet	bonnet	NOUN
ejpam-1076	67	28	pairs	pair	NOUN
ejpam-1076	67	29	.	.	PUNCT
ejpam-1076	68	1	these	these	DET
ejpam-1076	68	2	surfaces	surface	NOUN
ejpam-1076	68	3	are	be	AUX
ejpam-1076	68	4	calculated	calculate	VERB
ejpam-1076	68	5	as	as	ADP
ejpam-1076	68	6	x(u	x(u	PROPN
ejpam-1076	68	7	,	,	PUNCT
ejpam-1076	68	8	v	v	NOUN
ejpam-1076	68	9	)	)	PUNCT
ejpam-1076	68	10	=	=	SYM
ejpam-1076	68	11	�	�	PROPN
ejpam-1076	68	12	a	a	DET
ejpam-1076	68	13	cos	cos	PROPN
ejpam-1076	68	14	v	v	PROPN
ejpam-1076	68	15	p	p	PROPN
ejpam-1076	68	16	a2	a2	PROPN
ejpam-1076	68	17	+	+	CCONJ
ejpam-1076	68	18	b2	b2	NOUN
ejpam-1076	68	19	−	−	PROPN
ejpam-1076	68	20	au	au	PROPN
ejpam-1076	68	21	p	p	PROPN
ejpam-1076	68	22	a2	a2	PROPN
ejpam-1076	68	23	+	+	CCONJ
ejpam-1076	68	24	b2	b2	NOUN
ejpam-1076	68	25	sin	sin	NOUN
ejpam-1076	68	26	v	v	ADP
ejpam-1076	68	27	p	p	PROPN
ejpam-1076	68	28	a2	a2	PROPN
ejpam-1076	68	29	+	+	CCONJ
ejpam-1076	68	30	b2	b2	NOUN
ejpam-1076	68	31	,	,	PUNCT
ejpam-1076	68	32	a	a	DET
ejpam-1076	68	33	sin	sin	NOUN
ejpam-1076	68	34	v	v	ADP
ejpam-1076	68	35	p	p	PROPN
ejpam-1076	68	36	a2	a2	PROPN
ejpam-1076	68	37	+	+	CCONJ
ejpam-1076	68	38	b2	b2	NOUN
ejpam-1076	68	39	+	+	CCONJ
ejpam-1076	68	40	au	au	PROPN
ejpam-1076	68	41	p	p	PROPN
ejpam-1076	68	42	a2	a2	PROPN
ejpam-1076	68	43	+	+	CCONJ
ejpam-1076	68	44	b2	b2	NOUN
ejpam-1076	68	45	cos	cos	PROPN
ejpam-1076	68	46	v	v	PROPN
ejpam-1076	68	47	p	p	PROPN
ejpam-1076	68	48	a2	a2	PROPN
ejpam-1076	68	49	+	+	CCONJ
ejpam-1076	68	50	b2	b2	NOUN
ejpam-1076	68	51	,	,	PUNCT
ejpam-1076	68	52	bv	bv	PROPN
ejpam-1076	68	53	p	p	PROPN
ejpam-1076	68	54	a2	a2	PROPN
ejpam-1076	68	55	+	+	CCONJ
ejpam-1076	68	56	b2	b2	NOUN
ejpam-1076	68	57	+	+	CCONJ
ejpam-1076	68	58	bu	bu	PROPN
ejpam-1076	68	59	p	p	PROPN
ejpam-1076	68	60	a2	a2	PROPN
ejpam-1076	68	61	+	+	CCONJ
ejpam-1076	68	62	b2	b2	NOUN
ejpam-1076	68	63	�	�	PROPN
ejpam-1076	68	64	(	(	PUNCT
ejpam-1076	68	65	10	10	NUM
ejpam-1076	68	66	)	)	PUNCT
ejpam-1076	68	67	y(u	y(u	PROPN
ejpam-1076	68	68	,	,	PUNCT
ejpam-1076	68	69	v	v	NOUN
ejpam-1076	68	70	)	)	PUNCT
ejpam-1076	68	71	=	=	SYM
ejpam-1076	68	72	�	�	PROPN
ejpam-1076	68	73	a	a	DET
ejpam-1076	68	74	cos	cos	PROPN
ejpam-1076	68	75	�	�	PROPN
ejpam-1076	68	76	v	v	ADP
ejpam-1076	68	77	+	+	NOUN
ejpam-1076	68	78	2(a2+b2	2(a2+b2	NUM
ejpam-1076	68	79	)	)	PUNCT
ejpam-1076	68	80	3	3	NUM
ejpam-1076	68	81	2	2	NUM
ejpam-1076	68	82	a	a	DET
ejpam-1076	68	83	arctan	arctan	PROPN
ejpam-1076	68	84	(	(	PUNCT
ejpam-1076	68	85	au	au	ADV
ejpam-1076	68	86	a2+b2	a2+b2	PROPN
ejpam-1076	68	87	)	)	PUNCT
ejpam-1076	68	88	p	p	PROPN
ejpam-1076	68	89	a2	a2	PROPN
ejpam-1076	68	90	+	+	CCONJ
ejpam-1076	68	91	b2	b2	NOUN
ejpam-1076	68	92	�	�	NOUN
ejpam-1076	68	93	+	+	CCONJ
ejpam-1076	68	94	au	au	PROPN
ejpam-1076	68	95	a2	a2	PROPN
ejpam-1076	68	96	+	+	CCONJ
ejpam-1076	68	97	b2	b2	NOUN
ejpam-1076	68	98	sin	sin	NOUN
ejpam-1076	68	99	�	�	PROPN
ejpam-1076	68	100	v+	v+	ADP
ejpam-1076	68	101	2(a2+b2	2(a2+b2	NUM
ejpam-1076	68	102	)	)	PUNCT
ejpam-1076	68	103	3	3	NUM
ejpam-1076	68	104	2	2	NUM
ejpam-1076	68	105	a	a	DET
ejpam-1076	68	106	arctan	arctan	PROPN
ejpam-1076	68	107	(	(	PUNCT
ejpam-1076	68	108	au	au	ADV
ejpam-1076	68	109	a2+b2	a2+b2	PROPN
ejpam-1076	68	110	)	)	PUNCT
ejpam-1076	68	111	p	p	PROPN
ejpam-1076	68	112	a2	a2	PROPN
ejpam-1076	68	113	+	+	CCONJ
ejpam-1076	68	114	b2	b2	NOUN
ejpam-1076	68	115	�	�	PROPN
ejpam-1076	68	116	,	,	PUNCT
ejpam-1076	68	117	−a	−a	VERB
ejpam-1076	68	118	sin	sin	PROPN
ejpam-1076	68	119	�	�	PROPN
ejpam-1076	68	120	v	v	ADP
ejpam-1076	68	121	+	+	NOUN
ejpam-1076	68	122	2(a2+b2	2(a2+b2	NUM
ejpam-1076	68	123	)	)	PUNCT
ejpam-1076	68	124	3	3	NUM
ejpam-1076	68	125	2	2	NUM
ejpam-1076	68	126	a	a	DET
ejpam-1076	68	127	arctan	arctan	PROPN
ejpam-1076	68	128	(	(	PUNCT
ejpam-1076	68	129	au	au	ADV
ejpam-1076	68	130	a2+b2	a2+b2	PROPN
ejpam-1076	68	131	)	)	PUNCT
ejpam-1076	68	132	p	p	PROPN
ejpam-1076	68	133	a2	a2	PROPN
ejpam-1076	68	134	+	+	CCONJ
ejpam-1076	68	135	b2	b2	NOUN
ejpam-1076	68	136	�	�	NOUN
ejpam-1076	68	137	+	+	CCONJ
ejpam-1076	68	138	au	au	PROPN
ejpam-1076	68	139	a2	a2	PROPN
ejpam-1076	68	140	+	+	CCONJ
ejpam-1076	68	141	b2	b2	PROPN
ejpam-1076	68	142	cos	cos	PROPN
ejpam-1076	68	143	�	�	PROPN
ejpam-1076	68	144	v+	v+	ADP
ejpam-1076	68	145	2(a2+b2	2(a2+b2	NUM
ejpam-1076	68	146	)	)	PUNCT
ejpam-1076	68	147	3	3	NUM
ejpam-1076	68	148	2	2	NUM
ejpam-1076	68	149	a	a	DET
ejpam-1076	68	150	arctan	arctan	PROPN
ejpam-1076	68	151	(	(	PUNCT
ejpam-1076	68	152	au	au	ADV
ejpam-1076	68	153	a2+b2	a2+b2	PROPN
ejpam-1076	68	154	)	)	PUNCT
ejpam-1076	68	155	p	p	PROPN
ejpam-1076	68	156	a2	a2	PROPN
ejpam-1076	68	157	+	+	CCONJ
ejpam-1076	68	158	b2	b2	NOUN
ejpam-1076	68	159	�	�	PROPN
ejpam-1076	68	160	,	,	PUNCT
ejpam-1076	68	161	−b(v+	−b(v+	NUM
ejpam-1076	68	162	2(a2+b2	2(a2+b2	NUM
ejpam-1076	68	163	)	)	PUNCT
ejpam-1076	68	164	3	3	NUM
ejpam-1076	68	165	2	2	NUM
ejpam-1076	68	166	a	a	DET
ejpam-1076	68	167	arctan	arctan	PROPN
ejpam-1076	68	168	(	(	PUNCT
ejpam-1076	68	169	au	au	ADV
ejpam-1076	68	170	a2+b2	a2+b2	PROPN
ejpam-1076	68	171	)	)	PUNCT
ejpam-1076	68	172	)	)	PUNCT
ejpam-1076	69	1	p	p	PROPN
ejpam-1076	69	2	a2	a2	PROPN
ejpam-1076	69	3	+	+	CCONJ
ejpam-1076	69	4	b2	b2	NOUN
ejpam-1076	69	5	+	+	CCONJ
ejpam-1076	69	6	bu	bu	PROPN
ejpam-1076	69	7	p	p	PROPN
ejpam-1076	69	8	a2	a2	PROPN
ejpam-1076	69	9	+	+	CCONJ
ejpam-1076	69	10	b2	b2	NOUN
ejpam-1076	69	11	�	�	PROPN
ejpam-1076	69	12	all	all	PRON
ejpam-1076	69	13	ruled	rule	VERB
ejpam-1076	69	14	bonnet	bonnet	NOUN
ejpam-1076	69	15	pairs	pair	NOUN
ejpam-1076	69	16	which	which	PRON
ejpam-1076	69	17	have	have	AUX
ejpam-1076	69	18	been	be	AUX
ejpam-1076	69	19	known	know	VERB
ejpam-1076	69	20	up	up	ADP
ejpam-1076	69	21	to	to	ADP
ejpam-1076	69	22	now	now	ADV
ejpam-1076	69	23	,	,	PUNCT
ejpam-1076	69	24	can	can	AUX
ejpam-1076	69	25	be	be	AUX
ejpam-1076	69	26	taken	take	VERB
ejpam-1076	69	27	the	the	DET
ejpam-1076	69	28	equations	equation	NOUN
ejpam-1076	69	29	(	(	PUNCT
ejpam-1076	69	30	7	7	NUM
ejpam-1076	69	31	)	)	PUNCT
ejpam-1076	69	32	,	,	PUNCT
ejpam-1076	69	33	(	(	PUNCT
ejpam-1076	69	34	8)	8)	NUM
ejpam-1076	69	35	,	,	PUNCT
ejpam-1076	69	36	(	(	PUNCT
ejpam-1076	69	37	9	9	NUM
ejpam-1076	69	38	)	)	PUNCT
ejpam-1076	69	39	,	,	PUNCT
ejpam-1076	69	40	(	(	PUNCT
ejpam-1076	69	41	10	10	NUM
ejpam-1076	69	42	)	)	PUNCT
ejpam-1076	69	43	.	.	PUNCT
ejpam-1076	70	1	2.2	2.2	NUM
ejpam-1076	70	2	.	.	PUNCT
ejpam-1076	71	1	some	some	DET
ejpam-1076	71	2	orthogonal	orthogonal	ADJ
ejpam-1076	71	3	ruled	rule	VERB
ejpam-1076	71	4	surfaces	surface	NOUN
ejpam-1076	71	5	if	if	SCONJ
ejpam-1076	71	6	two	two	NUM
ejpam-1076	71	7	surfaces	surface	NOUN
ejpam-1076	71	8	s(a	s(a	PROPN
ejpam-1076	71	9	)	)	PUNCT
ejpam-1076	71	10	and	and	CCONJ
ejpam-1076	71	11	s(b	s(b	NOUN
ejpam-1076	71	12	)	)	PUNCT
ejpam-1076	71	13	given	give	VERB
ejpam-1076	71	14	by	by	ADP
ejpam-1076	71	15	the	the	DET
ejpam-1076	71	16	equations	equation	NOUN
ejpam-1076	71	17	a	a	DET
ejpam-1076	71	18	=	=	SYM
ejpam-1076	71	19	a(u	a(u	X
ejpam-1076	71	20	,	,	PUNCT
ejpam-1076	71	21	v	v	NOUN
ejpam-1076	71	22	)	)	PUNCT
ejpam-1076	71	23	and	and	CCONJ
ejpam-1076	71	24	b	b	X
ejpam-1076	71	25	=	=	SYM
ejpam-1076	71	26	b(u	b(u	PROPN
ejpam-1076	71	27	,	,	PUNCT
ejpam-1076	71	28	v	v	NOUN
ejpam-1076	71	29	)	)	PUNCT
ejpam-1076	71	30	map	map	NOUN
ejpam-1076	71	31	upon	upon	SCONJ
ejpam-1076	71	32	each	each	DET
ejpam-1076	71	33	other	other	ADJ
ejpam-1076	71	34	such	such	ADJ
ejpam-1076	71	35	that	that	SCONJ
ejpam-1076	71	36	their	their	PRON
ejpam-1076	71	37	linear	linear	ADJ
ejpam-1076	71	38	elements	element	NOUN
ejpam-1076	71	39	are	be	AUX
ejpam-1076	71	40	orthogonal	orthogonal	ADJ
ejpam-1076	71	41	at	at	ADP
ejpam-1076	71	42	corresponding	correspond	VERB
ejpam-1076	71	43	points	point	NOUN
ejpam-1076	71	44	,	,	PUNCT
ejpam-1076	71	45	da	da	X
ejpam-1076	71	46	·	·	PUNCT
ejpam-1076	71	47	db	db	PROPN
ejpam-1076	72	1	=	=	SYM
ejpam-1076	72	2	0	0	PROPN
ejpam-1076	72	3	,	,	PUNCT
ejpam-1076	72	4	then	then	ADV
ejpam-1076	72	5	,	,	PUNCT
ejpam-1076	72	6	these	these	DET
ejpam-1076	72	7	surfaces	surface	NOUN
ejpam-1076	72	8	are	be	AUX
ejpam-1076	72	9	called	call	VERB
ejpam-1076	72	10	to	to	PART
ejpam-1076	72	11	be	be	AUX
ejpam-1076	72	12	orthogonal	orthogonal	ADJ
ejpam-1076	72	13	surfaces	surface	NOUN
ejpam-1076	72	14	.	.	PUNCT
ejpam-1076	73	1	now	now	ADV
ejpam-1076	73	2	,	,	PUNCT
ejpam-1076	73	3	we	we	PRON
ejpam-1076	73	4	recall	recall	VERB
ejpam-1076	73	5	the	the	DET
ejpam-1076	73	6	relationship	relationship	NOUN
ejpam-1076	73	7	between	between	ADP
ejpam-1076	73	8	the	the	DET
ejpam-1076	73	9	orthogonal	orthogonal	ADJ
ejpam-1076	73	10	surfaces	surface	NOUN
ejpam-1076	73	11	and	and	CCONJ
ejpam-1076	73	12	the	the	DET
ejpam-1076	73	13	isometric	isometric	ADJ
ejpam-1076	73	14	surfaces	surface	NOUN
ejpam-1076	73	15	:	:	PUNCT
ejpam-1076	73	16	if	if	SCONJ
ejpam-1076	73	17	two	two	NUM
ejpam-1076	73	18	surfaces	surface	NOUN
ejpam-1076	73	19	s(x	s(x	NOUN
ejpam-1076	73	20	)	)	PUNCT
ejpam-1076	73	21	and	and	CCONJ
ejpam-1076	73	22	s(y	s(y	NOUN
ejpam-1076	73	23	)	)	PUNCT
ejpam-1076	73	24	given	give	VERB
ejpam-1076	73	25	by	by	ADP
ejpam-1076	73	26	the	the	DET
ejpam-1076	73	27	equations	equation	NOUN
ejpam-1076	73	28	x	x	PUNCT
ejpam-1076	73	29	=	=	SYM
ejpam-1076	73	30	x(u	x(u	PROPN
ejpam-1076	73	31	,	,	PUNCT
ejpam-1076	73	32	v	v	NOUN
ejpam-1076	73	33	)	)	PUNCT
ejpam-1076	73	34	and	and	CCONJ
ejpam-1076	73	35	y	y	PROPN
ejpam-1076	73	36	=	=	SYM
ejpam-1076	73	37	y(u	y(u	PROPN
ejpam-1076	73	38	,	,	PUNCT
ejpam-1076	73	39	v	v	NOUN
ejpam-1076	73	40	)	)	PUNCT
ejpam-1076	73	41	are	be	AUX
ejpam-1076	73	42	isometric	isometric	ADJ
ejpam-1076	73	43	(	(	PUNCT
ejpam-1076	73	44	dx2	dx2	PROPN
ejpam-1076	73	45	=	=	PROPN
ejpam-1076	73	46	dy2	dy2	PROPN
ejpam-1076	73	47	)	)	PUNCT
ejpam-1076	73	48	,	,	PUNCT
ejpam-1076	73	49	two	two	NUM
ejpam-1076	73	50	surfaces	surface	NOUN
ejpam-1076	73	51	written	write	VERB
ejpam-1076	73	52	as	as	ADP
ejpam-1076	73	53	s(x+	s(x+	NOUN
ejpam-1076	73	54	y	y	NOUN
ejpam-1076	73	55	)	)	PUNCT
ejpam-1076	73	56	and	and	CCONJ
ejpam-1076	73	57	s(x−	s(x−	PRON
ejpam-1076	73	58	y	y	PROPN
ejpam-1076	73	59	)	)	PUNCT
ejpam-1076	73	60	are	be	AUX
ejpam-1076	73	61	orthogonal	orthogonal	ADJ
ejpam-1076	73	62	surfaces	surface	NOUN
ejpam-1076	73	63	d(x+	d(x+	PROPN
ejpam-1076	73	64	y	y	NOUN
ejpam-1076	73	65	)	)	PUNCT
ejpam-1076	73	66	·	·	PUNCT
ejpam-1076	74	1	d(x−	d(x−	X
ejpam-1076	74	2	y	y	NOUN
ejpam-1076	74	3	)	)	PUNCT
ejpam-1076	74	4	=	=	SYM
ejpam-1076	74	5	0	0	X
ejpam-1076	74	6	.	.	PUNCT
ejpam-1076	75	1	by	by	ADP
ejpam-1076	75	2	using	use	VERB
ejpam-1076	75	3	two	two	NUM
ejpam-1076	75	4	surfaces	surface	NOUN
ejpam-1076	75	5	s(x	s(x	NOUN
ejpam-1076	75	6	)	)	PUNCT
ejpam-1076	75	7	and	and	CCONJ
ejpam-1076	75	8	s(y	s(y	PROPN
ejpam-1076	75	9	)	)	PUNCT
ejpam-1076	75	10	which	which	PRON
ejpam-1076	75	11	can	can	AUX
ejpam-1076	75	12	be	be	AUX
ejpam-1076	75	13	map	map	VERB
ejpam-1076	75	14	isometrically	isometrically	ADV
ejpam-1076	75	15	on	on	ADP
ejpam-1076	75	16	the	the	DET
ejpam-1076	75	17	each	each	DET
ejpam-1076	75	18	other	other	ADJ
ejpam-1076	75	19	,	,	PUNCT
ejpam-1076	75	20	the	the	DET
ejpam-1076	75	21	orthogonal	orthogonal	ADJ
ejpam-1076	75	22	surfaces	surface	NOUN
ejpam-1076	75	23	s(a	s(a	PROPN
ejpam-1076	75	24	)	)	PUNCT
ejpam-1076	75	25	and	and	CCONJ
ejpam-1076	75	26	s(b	s(b	NOUN
ejpam-1076	75	27	)	)	PUNCT
ejpam-1076	75	28	given	give	VERB
ejpam-1076	75	29	by	by	ADP
ejpam-1076	75	30	the	the	DET
ejpam-1076	75	31	equations	equation	NOUN
ejpam-1076	75	32	a=	a=	VERB
ejpam-1076	75	33	x+	x+	PROPN
ejpam-1076	76	1	y	y	PROPN
ejpam-1076	76	2	,	,	PUNCT
ejpam-1076	76	3	b	b	PROPN
ejpam-1076	76	4	=	=	SYM
ejpam-1076	76	5	x−	x−	PROPN
ejpam-1076	76	6	y	y	PROPN
ejpam-1076	76	7	(	(	PUNCT
ejpam-1076	76	8	11	11	NUM
ejpam-1076	76	9	)	)	PUNCT
ejpam-1076	76	10	can	can	AUX
ejpam-1076	76	11	be	be	AUX
ejpam-1076	76	12	written	write	VERB
ejpam-1076	76	13	.	.	PUNCT
ejpam-1076	77	1	by	by	ADP
ejpam-1076	77	2	using	use	VERB
ejpam-1076	77	3	this	this	DET
ejpam-1076	77	4	method	method	NOUN
ejpam-1076	77	5	,	,	PUNCT
ejpam-1076	77	6	we	we	PRON
ejpam-1076	77	7	can	can	AUX
ejpam-1076	77	8	get	get	VERB
ejpam-1076	77	9	the	the	DET
ejpam-1076	77	10	orthogonal	orthogonal	ADJ
ejpam-1076	77	11	surfaces	surface	NOUN
ejpam-1076	77	12	easily	easily	ADV
ejpam-1076	77	13	.	.	PUNCT
ejpam-1076	78	1	for	for	ADP
ejpam-1076	78	2	this	this	DET
ejpam-1076	78	3	aim	aim	NOUN
ejpam-1076	78	4	,	,	PUNCT
ejpam-1076	78	5	we	we	PRON
ejpam-1076	78	6	can	can	AUX
ejpam-1076	78	7	use	use	VERB
ejpam-1076	78	8	the	the	DET
ejpam-1076	78	9	ruled	rule	VERB
ejpam-1076	78	10	surfaces	surface	NOUN
ejpam-1076	78	11	given	give	VERB
ejpam-1076	78	12	by	by	ADP
ejpam-1076	78	13	the	the	DET
ejpam-1076	78	14	equations	equation	NOUN
ejpam-1076	78	15	(	(	PUNCT
ejpam-1076	78	16	7	7	NUM
ejpam-1076	78	17	)	)	PUNCT
ejpam-1076	78	18	,	,	PUNCT
ejpam-1076	78	19	(	(	PUNCT
ejpam-1076	78	20	8)	8)	NUM
ejpam-1076	78	21	,	,	PUNCT
ejpam-1076	78	22	(	(	PUNCT
ejpam-1076	78	23	9	9	NUM
ejpam-1076	78	24	)	)	PUNCT
ejpam-1076	78	25	,	,	PUNCT
ejpam-1076	78	26	(	(	PUNCT
ejpam-1076	78	27	10	10	NUM
ejpam-1076	78	28	)	)	PUNCT
ejpam-1076	78	29	to	to	PART
ejpam-1076	78	30	find	find	VERB
ejpam-1076	78	31	orthogonal	orthogonal	ADJ
ejpam-1076	78	32	f.	f.	PROPN
ejpam-1076	78	33	kanby	kanby	PROPN
ejpam-1076	78	34	/	/	SYM
ejpam-1076	78	35	eur	eur	PROPN
ejpam-1076	78	36	.	.	PUNCT
ejpam-1076	79	1	j.	j.	PROPN
ejpam-1076	79	2	pure	pure	PROPN
ejpam-1076	79	3	appl	appl	PROPN
ejpam-1076	79	4	.	.	PROPN
ejpam-1076	79	5	math	math	PROPN
ejpam-1076	79	6	,	,	PUNCT
ejpam-1076	79	7	5	5	NUM
ejpam-1076	79	8	(	(	PUNCT
ejpam-1076	79	9	2012	2012	NUM
ejpam-1076	79	10	)	)	PUNCT
ejpam-1076	79	11	,	,	PUNCT
ejpam-1076	79	12	205	205	NUM
ejpam-1076	79	13	-	-	SYM
ejpam-1076	79	14	210	210	NUM
ejpam-1076	79	15	209	209	NUM
ejpam-1076	79	16	ruled	rule	VERB
ejpam-1076	79	17	surfaces	surface	NOUN
ejpam-1076	79	18	.	.	PUNCT
ejpam-1076	80	1	but	but	CCONJ
ejpam-1076	80	2	the	the	DET
ejpam-1076	80	3	process	process	NOUN
ejpam-1076	80	4	of	of	ADP
ejpam-1076	80	5	using	use	VERB
ejpam-1076	80	6	the	the	DET
ejpam-1076	80	7	ruled	rule	VERB
ejpam-1076	80	8	surfaces	surface	NOUN
ejpam-1076	80	9	is	be	AUX
ejpam-1076	80	10	not	not	PART
ejpam-1076	80	11	as	as	ADV
ejpam-1076	80	12	easy	easy	ADJ
ejpam-1076	80	13	as	as	ADP
ejpam-1076	80	14	the	the	DET
ejpam-1076	80	15	general	general	ADJ
ejpam-1076	80	16	process	process	NOUN
ejpam-1076	80	17	.	.	PUNCT
ejpam-1076	81	1	since	since	SCONJ
ejpam-1076	81	2	the	the	DET
ejpam-1076	81	3	equation	equation	NOUN
ejpam-1076	81	4	of	of	ADP
ejpam-1076	81	5	a	a	DET
ejpam-1076	81	6	ruled	rule	VERB
ejpam-1076	81	7	surface	surface	NOUN
ejpam-1076	81	8	consists	consist	VERB
ejpam-1076	81	9	of	of	ADP
ejpam-1076	81	10	two	two	NUM
ejpam-1076	81	11	parts	part	NOUN
ejpam-1076	81	12	(	(	PUNCT
ejpam-1076	81	13	x(u	x(u	PROPN
ejpam-1076	81	14	,	,	PUNCT
ejpam-1076	81	15	v	v	NOUN
ejpam-1076	81	16	)	)	PUNCT
ejpam-1076	81	17	=	=	SYM
ejpam-1076	81	18	r(v)+ut(v	r(v)+ut(v	NUM
ejpam-1076	81	19	)	)	PUNCT
ejpam-1076	81	20	)	)	PUNCT
ejpam-1076	81	21	,	,	PUNCT
ejpam-1076	81	22	mostly	mostly	ADV
ejpam-1076	81	23	,	,	PUNCT
ejpam-1076	81	24	one	one	NUM
ejpam-1076	81	25	of	of	ADP
ejpam-1076	81	26	the	the	DET
ejpam-1076	81	27	first	first	ADJ
ejpam-1076	81	28	(	(	PUNCT
ejpam-1076	81	29	r(v	r(v	PROPN
ejpam-1076	81	30	)	)	PUNCT
ejpam-1076	81	31	)	)	PUNCT
ejpam-1076	81	32	or	or	CCONJ
ejpam-1076	81	33	second	second	ADJ
ejpam-1076	81	34	(	(	PUNCT
ejpam-1076	81	35	t(v	t(v	NOUN
ejpam-1076	81	36	)	)	PUNCT
ejpam-1076	81	37	)	)	PUNCT
ejpam-1076	81	38	part	part	NOUN
ejpam-1076	81	39	can	can	AUX
ejpam-1076	81	40	vanish	vanish	VERB
ejpam-1076	81	41	and	and	CCONJ
ejpam-1076	81	42	the	the	DET
ejpam-1076	81	43	surface	surface	NOUN
ejpam-1076	81	44	becomes	become	VERB
ejpam-1076	81	45	a	a	DET
ejpam-1076	81	46	curve	curve	NOUN
ejpam-1076	81	47	.	.	PUNCT
ejpam-1076	82	1	because	because	SCONJ
ejpam-1076	82	2	of	of	ADP
ejpam-1076	82	3	this	this	PRON
ejpam-1076	82	4	,	,	PUNCT
ejpam-1076	82	5	only	only	ADV
ejpam-1076	82	6	one	one	NUM
ejpam-1076	82	7	pairs	pair	NOUN
ejpam-1076	82	8	of	of	ADP
ejpam-1076	82	9	orthogonal	orthogonal	ADJ
ejpam-1076	82	10	surfaces	surface	NOUN
ejpam-1076	82	11	given	give	VERB
ejpam-1076	82	12	by	by	ADP
ejpam-1076	82	13	x	x	X
ejpam-1076	82	14	=	=	VERB
ejpam-1076	82	15	a	a	DET
ejpam-1076	82	16	�	�	PROPN
ejpam-1076	82	17	cos	cos	PROPN
ejpam-1076	82	18	v	v	PROPN
ejpam-1076	82	19	p	p	PROPN
ejpam-1076	82	20	a2	a2	PROPN
ejpam-1076	82	21	+	+	CCONJ
ejpam-1076	82	22	b2	b2	NOUN
ejpam-1076	82	23	+	+	CCONJ
ejpam-1076	82	24	cos	cos	PROPN
ejpam-1076	82	25	v+	v+	ADP
ejpam-1076	82	26	2(a2+b2	2(a2+b2	NUM
ejpam-1076	82	27	)	)	PUNCT
ejpam-1076	82	28	3	3	NUM
ejpam-1076	82	29	2	2	NUM
ejpam-1076	82	30	a	a	DET
ejpam-1076	82	31	arctan	arctan	PROPN
ejpam-1076	82	32	(	(	PUNCT
ejpam-1076	82	33	au	au	ADV
ejpam-1076	82	34	a2+b2	a2+b2	NOUN
ejpam-1076	82	35	)	)	PUNCT
ejpam-1076	82	36	p	p	PROPN
ejpam-1076	82	37	a2	a2	PROPN
ejpam-1076	82	38	+	+	CCONJ
ejpam-1076	82	39	b2	b2	NOUN
ejpam-1076	82	40	�	�	NOUN
ejpam-1076	82	41	+	+	CCONJ
ejpam-1076	82	42	+	+	NUM
ejpam-1076	82	43	au	au	PROPN
ejpam-1076	82	44	p	p	PROPN
ejpam-1076	82	45	a2	a2	PROPN
ejpam-1076	82	46	+	+	CCONJ
ejpam-1076	82	47	b2	b2	NOUN
ejpam-1076	82	48	�	�	PROPN
ejpam-1076	82	49	−	−	PROPN
ejpam-1076	82	50	sin	sin	NOUN
ejpam-1076	82	51	v	v	ADP
ejpam-1076	82	52	p	p	PROPN
ejpam-1076	82	53	a2	a2	PROPN
ejpam-1076	82	54	+	+	CCONJ
ejpam-1076	82	55	b2	b2	NOUN
ejpam-1076	82	56	+	+	CCONJ
ejpam-1076	82	57	sin	sin	NOUN
ejpam-1076	82	58	v+	v+	X
ejpam-1076	82	59	2(a2+b2	2(a2+b2	NUM
ejpam-1076	82	60	)	)	PUNCT
ejpam-1076	82	61	3	3	NUM
ejpam-1076	82	62	2	2	NUM
ejpam-1076	82	63	a	a	DET
ejpam-1076	82	64	arctan	arctan	PROPN
ejpam-1076	82	65	(	(	PUNCT
ejpam-1076	82	66	au	au	ADV
ejpam-1076	82	67	a2+b2	a2+b2	NOUN
ejpam-1076	82	68	)	)	PUNCT
ejpam-1076	82	69	p	p	PROPN
ejpam-1076	82	70	a2	a2	PROPN
ejpam-1076	82	71	+	+	CCONJ
ejpam-1076	82	72	b2	b2	NOUN
ejpam-1076	82	73	�	�	PROPN
ejpam-1076	82	74	y	y	PROPN
ejpam-1076	82	75	=	=	PROPN
ejpam-1076	82	76	a	a	DET
ejpam-1076	82	77	�	�	PROPN
ejpam-1076	82	78	sin	sin	VERB
ejpam-1076	82	79	v	v	ADP
ejpam-1076	82	80	p	p	PROPN
ejpam-1076	82	81	a2	a2	PROPN
ejpam-1076	82	82	+	+	CCONJ
ejpam-1076	82	83	b2	b2	NOUN
ejpam-1076	82	84	−	−	NOUN
ejpam-1076	82	85	sin	sin	NOUN
ejpam-1076	82	86	v+	v+	X
ejpam-1076	82	87	2(a2+b2	2(a2+b2	NUM
ejpam-1076	82	88	)	)	PUNCT
ejpam-1076	82	89	3	3	NUM
ejpam-1076	82	90	2	2	NUM
ejpam-1076	82	91	a	a	DET
ejpam-1076	82	92	arctan	arctan	PROPN
ejpam-1076	82	93	(	(	PUNCT
ejpam-1076	82	94	au	au	ADV
ejpam-1076	82	95	a2+b2	a2+b2	NOUN
ejpam-1076	82	96	)	)	PUNCT
ejpam-1076	82	97	p	p	PROPN
ejpam-1076	82	98	a2	a2	PROPN
ejpam-1076	82	99	+	+	CCONJ
ejpam-1076	82	100	b2	b2	NOUN
ejpam-1076	82	101	�	�	NOUN
ejpam-1076	82	102	+	+	CCONJ
ejpam-1076	82	103	+	+	NUM
ejpam-1076	82	104	au	au	PROPN
ejpam-1076	82	105	p	p	PROPN
ejpam-1076	82	106	a2	a2	PROPN
ejpam-1076	82	107	+	+	CCONJ
ejpam-1076	82	108	b2	b2	PROPN
ejpam-1076	82	109	�	�	PROPN
ejpam-1076	82	110	cos	cos	PROPN
ejpam-1076	82	111	v	v	PROPN
ejpam-1076	82	112	p	p	PROPN
ejpam-1076	82	113	a2	a2	PROPN
ejpam-1076	82	114	+	+	CCONJ
ejpam-1076	82	115	b2	b2	NOUN
ejpam-1076	82	116	+	+	CCONJ
ejpam-1076	82	117	cos	cos	PROPN
ejpam-1076	82	118	v	v	NOUN
ejpam-1076	82	119	+	+	NOUN
ejpam-1076	82	120	2(a2+b2	2(a2+b2	NUM
ejpam-1076	82	121	)	)	PUNCT
ejpam-1076	82	122	3	3	NUM
ejpam-1076	82	123	2	2	NUM
ejpam-1076	82	124	a	a	DET
ejpam-1076	82	125	arctan	arctan	PROPN
ejpam-1076	82	126	(	(	PUNCT
ejpam-1076	82	127	au	au	ADV
ejpam-1076	82	128	a2+b2	a2+b2	NOUN
ejpam-1076	82	129	)	)	PUNCT
ejpam-1076	82	130	p	p	PROPN
ejpam-1076	82	131	a2	a2	PROPN
ejpam-1076	82	132	+	+	CCONJ
ejpam-1076	82	133	b2	b2	NOUN
ejpam-1076	82	134	�	�	PROPN
ejpam-1076	82	135	z	z	PROPN
ejpam-1076	82	136	=	=	SYM
ejpam-1076	83	1	−	−	PROPN
ejpam-1076	84	1	2b(a2+b2	2b(a2+b2	PROPN
ejpam-1076	84	2	)	)	PUNCT
ejpam-1076	84	3	3	3	NUM
ejpam-1076	84	4	2	2	NUM
ejpam-1076	84	5	a	a	DET
ejpam-1076	84	6	arctan	arctan	PROPN
ejpam-1076	84	7	(	(	PUNCT
ejpam-1076	84	8	au	au	ADV
ejpam-1076	84	9	a2+b2	a2+b2	NOUN
ejpam-1076	84	10	)	)	PUNCT
ejpam-1076	84	11	p	p	PROPN
ejpam-1076	84	12	a2	a2	PROPN
ejpam-1076	84	13	+	+	CCONJ
ejpam-1076	84	14	b2	b2	NOUN
ejpam-1076	84	15	+	+	CCONJ
ejpam-1076	84	16	2bu	2bu	ADJ
ejpam-1076	84	17	p	p	PROPN
ejpam-1076	84	18	a2	a2	PROPN
ejpam-1076	84	19	+	+	CCONJ
ejpam-1076	84	20	b2	b2	NOUN
ejpam-1076	84	21	(	(	PUNCT
ejpam-1076	84	22	12	12	NUM
ejpam-1076	84	23	)	)	PUNCT
ejpam-1076	84	24	x	x	X
ejpam-1076	85	1	=	=	PUNCT
ejpam-1076	85	2	a	a	DET
ejpam-1076	85	3	�	�	PROPN
ejpam-1076	85	4	cos	cos	PROPN
ejpam-1076	85	5	v	v	PROPN
ejpam-1076	85	6	p	p	PROPN
ejpam-1076	85	7	a2	a2	PROPN
ejpam-1076	85	8	+	+	CCONJ
ejpam-1076	85	9	b2	b2	NOUN
ejpam-1076	85	10	−	−	PROPN
ejpam-1076	85	11	cos	cos	PROPN
ejpam-1076	85	12	v	v	PROPN
ejpam-1076	85	13	+	+	NOUN
ejpam-1076	85	14	2(a2+b2	2(a2+b2	NUM
ejpam-1076	85	15	)	)	PUNCT
ejpam-1076	85	16	3	3	NUM
ejpam-1076	85	17	2	2	NUM
ejpam-1076	85	18	a	a	DET
ejpam-1076	85	19	arctan	arctan	PROPN
ejpam-1076	85	20	(	(	PUNCT
ejpam-1076	85	21	au	au	ADV
ejpam-1076	85	22	a2+b2	a2+b2	NOUN
ejpam-1076	85	23	)	)	PUNCT
ejpam-1076	85	24	p	p	PROPN
ejpam-1076	85	25	a2	a2	PROPN
ejpam-1076	85	26	+	+	CCONJ
ejpam-1076	85	27	b2	b2	NOUN
ejpam-1076	85	28	�	�	NOUN
ejpam-1076	85	29	−	−	PROPN
ejpam-1076	85	30	−	−	PROPN
ejpam-1076	85	31	au	au	PROPN
ejpam-1076	85	32	p	p	PROPN
ejpam-1076	85	33	a2	a2	PROPN
ejpam-1076	85	34	+	+	CCONJ
ejpam-1076	85	35	b2	b2	NOUN
ejpam-1076	85	36	�	�	PROPN
ejpam-1076	85	37	sin	sin	NOUN
ejpam-1076	85	38	v	v	ADP
ejpam-1076	85	39	p	p	PROPN
ejpam-1076	85	40	a2	a2	PROPN
ejpam-1076	85	41	+	+	CCONJ
ejpam-1076	85	42	b2	b2	NOUN
ejpam-1076	85	43	+	+	CCONJ
ejpam-1076	85	44	sin	sin	NOUN
ejpam-1076	85	45	v+	v+	X
ejpam-1076	85	46	2(a2+b2	2(a2+b2	NUM
ejpam-1076	85	47	)	)	PUNCT
ejpam-1076	85	48	3	3	NUM
ejpam-1076	85	49	2	2	NUM
ejpam-1076	85	50	a	a	DET
ejpam-1076	85	51	arctan	arctan	PROPN
ejpam-1076	85	52	(	(	PUNCT
ejpam-1076	85	53	au	au	ADV
ejpam-1076	85	54	a2+b2	a2+b2	NOUN
ejpam-1076	85	55	)	)	PUNCT
ejpam-1076	85	56	p	p	PROPN
ejpam-1076	85	57	a2	a2	PROPN
ejpam-1076	85	58	+	+	CCONJ
ejpam-1076	85	59	b2	b2	NOUN
ejpam-1076	85	60	�	�	PROPN
ejpam-1076	85	61	y	y	PROPN
ejpam-1076	85	62	=	=	PROPN
ejpam-1076	85	63	a	a	DET
ejpam-1076	85	64	�	�	PROPN
ejpam-1076	85	65	sin	sin	VERB
ejpam-1076	85	66	v	v	ADP
ejpam-1076	85	67	p	p	PROPN
ejpam-1076	85	68	a2	a2	PROPN
ejpam-1076	85	69	+	+	CCONJ
ejpam-1076	85	70	b2	b2	NOUN
ejpam-1076	85	71	+	+	CCONJ
ejpam-1076	85	72	sin	sin	NOUN
ejpam-1076	85	73	v	v	ADP
ejpam-1076	85	74	+	+	NOUN
ejpam-1076	85	75	2(a2+b2	2(a2+b2	NUM
ejpam-1076	85	76	)	)	PUNCT
ejpam-1076	85	77	3	3	NUM
ejpam-1076	85	78	2	2	NUM
ejpam-1076	85	79	a	a	DET
ejpam-1076	85	80	arctan	arctan	PROPN
ejpam-1076	85	81	(	(	PUNCT
ejpam-1076	85	82	au	au	ADV
ejpam-1076	85	83	a2+b2	a2+b2	NOUN
ejpam-1076	85	84	)	)	PUNCT
ejpam-1076	85	85	p	p	PROPN
ejpam-1076	85	86	a2	a2	PROPN
ejpam-1076	85	87	+	+	CCONJ
ejpam-1076	85	88	b2	b2	NOUN
ejpam-1076	85	89	�	�	NOUN
ejpam-1076	85	90	+	+	CCONJ
ejpam-1076	85	91	+	+	NUM
ejpam-1076	85	92	au	au	PROPN
ejpam-1076	85	93	p	p	PROPN
ejpam-1076	85	94	a2	a2	PROPN
ejpam-1076	85	95	+	+	CCONJ
ejpam-1076	85	96	b2	b2	PROPN
ejpam-1076	85	97	�	�	PROPN
ejpam-1076	85	98	cos	cos	PROPN
ejpam-1076	85	99	v	v	PROPN
ejpam-1076	85	100	p	p	PROPN
ejpam-1076	85	101	a2	a2	PROPN
ejpam-1076	85	102	+	+	CCONJ
ejpam-1076	85	103	b2	b2	NOUN
ejpam-1076	85	104	−	−	PROPN
ejpam-1076	85	105	cos	cos	PROPN
ejpam-1076	85	106	v	v	PROPN
ejpam-1076	85	107	+	+	NOUN
ejpam-1076	85	108	2(a2+b2	2(a2+b2	NUM
ejpam-1076	85	109	)	)	PUNCT
ejpam-1076	85	110	3	3	NUM
ejpam-1076	85	111	2	2	NUM
ejpam-1076	85	112	a	a	DET
ejpam-1076	85	113	arctan	arctan	PROPN
ejpam-1076	85	114	(	(	PUNCT
ejpam-1076	85	115	au	au	ADV
ejpam-1076	85	116	a2+b2	a2+b2	NOUN
ejpam-1076	85	117	)	)	PUNCT
ejpam-1076	86	1	p	p	PROPN
ejpam-1076	86	2	a2	a2	PROPN
ejpam-1076	86	3	+	+	CCONJ
ejpam-1076	86	4	b2	b2	NOUN
ejpam-1076	86	5	�	�	PROPN
ejpam-1076	86	6	z	z	PROPN
ejpam-1076	86	7	=	=	SYM
ejpam-1076	86	8	2bv+	2bv+	NUM
ejpam-1076	86	9	2b(a2+b2	2b(a2+b2	PROPN
ejpam-1076	86	10	)	)	PUNCT
ejpam-1076	86	11	3	3	NUM
ejpam-1076	86	12	2	2	NUM
ejpam-1076	86	13	a	a	DET
ejpam-1076	86	14	arctan	arctan	PROPN
ejpam-1076	86	15	(	(	PUNCT
ejpam-1076	86	16	au	au	ADV
ejpam-1076	86	17	a2+b2	a2+b2	NOUN
ejpam-1076	86	18	)	)	PUNCT
ejpam-1076	86	19	p	p	PROPN
ejpam-1076	86	20	a2	a2	PROPN
ejpam-1076	86	21	+	+	CCONJ
ejpam-1076	86	22	b2	b2	NOUN
ejpam-1076	86	23	can	can	AUX
ejpam-1076	86	24	be	be	AUX
ejpam-1076	86	25	found	find	VERB
ejpam-1076	86	26	.	.	PUNCT
ejpam-1076	87	1	theorem	theorem	NOUN
ejpam-1076	87	2	1	1	NUM
ejpam-1076	87	3	.	.	PUNCT
ejpam-1076	87	4	by	by	ADP
ejpam-1076	87	5	using	use	VERB
ejpam-1076	87	6	the	the	DET
ejpam-1076	87	7	bonnet	bonnet	NOUN
ejpam-1076	87	8	ruled	rule	VERB
ejpam-1076	87	9	surfaces	surface	NOUN
ejpam-1076	87	10	;	;	PUNCT
ejpam-1076	87	11	only	only	ADV
ejpam-1076	87	12	one	one	NUM
ejpam-1076	87	13	pair	pair	NOUN
ejpam-1076	87	14	of	of	ADP
ejpam-1076	87	15	orthogonal	orthogonal	ADJ
ejpam-1076	87	16	surfaces	surface	NOUN
ejpam-1076	87	17	can	can	AUX
ejpam-1076	87	18	be	be	AUX
ejpam-1076	87	19	found	find	VERB
ejpam-1076	87	20	.	.	PUNCT
ejpam-1076	88	1	this	this	DET
ejpam-1076	88	2	surfaces	surface	NOUN
ejpam-1076	88	3	are	be	AUX
ejpam-1076	88	4	generated	generate	VERB
ejpam-1076	88	5	by	by	ADP
ejpam-1076	88	6	the	the	DET
ejpam-1076	88	7	tangential	tangential	ADJ
ejpam-1076	88	8	developable	developable	ADJ
ejpam-1076	88	9	surfaces	surface	NOUN
ejpam-1076	88	10	of	of	ADP
ejpam-1076	88	11	the	the	DET
ejpam-1076	88	12	circular	circular	ADJ
ejpam-1076	88	13	helices	helix	NOUN
ejpam-1076	88	14	.	.	PUNCT
ejpam-1076	89	1	references	reference	NOUN
ejpam-1076	89	2	210	210	NUM
ejpam-1076	89	3	the	the	DET
ejpam-1076	89	4	infinitesimal	infinitesimal	ADJ
ejpam-1076	89	5	bending	bending	NOUN
ejpam-1076	89	6	problem	problem	NOUN
ejpam-1076	89	7	is	be	AUX
ejpam-1076	89	8	reduced	reduce	VERB
ejpam-1076	89	9	the	the	DET
ejpam-1076	89	10	finding	find	VERB
ejpam-1076	89	11	them	they	PRON
ejpam-1076	90	1	[	[	X
ejpam-1076	90	2	5	5	NUM
ejpam-1076	90	3	,	,	PUNCT
ejpam-1076	90	4	7	7	NUM
ejpam-1076	90	5	,	,	PUNCT
ejpam-1076	90	6	8	8	NUM
ejpam-1076	90	7	]	]	PUNCT
ejpam-1076	90	8	:	:	PUNCT
ejpam-1076	90	9	the	the	DET
ejpam-1076	90	10	equation	equation	NOUN
ejpam-1076	90	11	xt(u	xt(u	NUM
ejpam-1076	90	12	,	,	PUNCT
ejpam-1076	90	13	v	v	PROPN
ejpam-1076	90	14	,	,	PUNCT
ejpam-1076	90	15	t	t	PROPN
ejpam-1076	90	16	)	)	PUNCT
ejpam-1076	90	17	=	=	SYM
ejpam-1076	90	18	x(u	x(u	PROPN
ejpam-1076	90	19	,	,	PUNCT
ejpam-1076	90	20	v	v	NOUN
ejpam-1076	90	21	)	)	PUNCT
ejpam-1076	90	22	+	+	NUM
ejpam-1076	90	23	ty(u	ty(u	NUM
ejpam-1076	90	24	,	,	PUNCT
ejpam-1076	90	25	v	v	NOUN
ejpam-1076	90	26	)	)	PUNCT
ejpam-1076	90	27	(	(	PUNCT
ejpam-1076	90	28	13	13	NUM
ejpam-1076	90	29	)	)	PUNCT
ejpam-1076	90	30	gives	give	VERB
ejpam-1076	90	31	the	the	DET
ejpam-1076	90	32	infinitesimal	infinitesimal	ADJ
ejpam-1076	90	33	bending	bend	VERB
ejpam-1076	90	34	surfaces	surface	NOUN
ejpam-1076	90	35	of	of	ADP
ejpam-1076	90	36	the	the	DET
ejpam-1076	90	37	surface	surface	NOUN
ejpam-1076	90	38	s(x	s(x	PROPN
ejpam-1076	90	39	)	)	PUNCT
ejpam-1076	90	40	under	under	ADP
ejpam-1076	90	41	the	the	DET
ejpam-1076	90	42	condition	condition	NOUN
ejpam-1076	90	43	dxt	dxt	PROPN
ejpam-1076	90	44	2(u	2(u	NUM
ejpam-1076	90	45	,	,	PUNCT
ejpam-1076	90	46	v	v	NOUN
ejpam-1076	90	47	,	,	PUNCT
ejpam-1076	90	48	t	t	PROPN
ejpam-1076	90	49	)	)	PUNCT
ejpam-1076	91	1	=	=	PUNCT
ejpam-1076	92	1	(	(	PUNCT
ejpam-1076	92	2	dx(u	dx(u	X
ejpam-1076	92	3	,	,	PUNCT
ejpam-1076	92	4	v)+	v)+	NOUN
ejpam-1076	92	5	tdy(u	tdy(u	NUM
ejpam-1076	92	6	,	,	PUNCT
ejpam-1076	92	7	v))2	v))2	X
ejpam-1076	92	8	(	(	PUNCT
ejpam-1076	92	9	14	14	NUM
ejpam-1076	92	10	)	)	PUNCT
ejpam-1076	92	11	where	where	SCONJ
ejpam-1076	92	12	t	t	PROPN
ejpam-1076	92	13	is	be	AUX
ejpam-1076	92	14	a	a	DET
ejpam-1076	92	15	real	real	ADJ
ejpam-1076	92	16	infinitesimal	infinitesimal	ADJ
ejpam-1076	92	17	parameter	parameter	NOUN
ejpam-1076	92	18	.	.	PUNCT
ejpam-1076	93	1	here	here	ADV
ejpam-1076	93	2	the	the	DET
ejpam-1076	93	3	condition	condition	NOUN
ejpam-1076	93	4	(	(	PUNCT
ejpam-1076	93	5	14	14	NUM
ejpam-1076	93	6	)	)	PUNCT
ejpam-1076	93	7	is	be	AUX
ejpam-1076	93	8	equivalent	equivalent	ADJ
ejpam-1076	93	9	to	to	ADP
ejpam-1076	93	10	the	the	DET
ejpam-1076	93	11	condition	condition	NOUN
ejpam-1076	93	12	dx	dx	PROPN
ejpam-1076	93	13	·	·	PUNCT
ejpam-1076	94	1	dy=	dy=	NOUN
ejpam-1076	94	2	0	0	NUM
ejpam-1076	94	3	.	.	PUNCT
ejpam-1076	95	1	consequently	consequently	ADV
ejpam-1076	95	2	,	,	PUNCT
ejpam-1076	95	3	we	we	PRON
ejpam-1076	95	4	give	give	VERB
ejpam-1076	95	5	the	the	DET
ejpam-1076	95	6	following	follow	VERB
ejpam-1076	95	7	corollary	corollary	ADJ
ejpam-1076	95	8	:	:	PUNCT
ejpam-1076	95	9	corollary	corollary	ADJ
ejpam-1076	95	10	1	1	NUM
ejpam-1076	95	11	.	.	PUNCT
ejpam-1076	95	12	one	one	NUM
ejpam-1076	95	13	of	of	ADP
ejpam-1076	95	14	the	the	DET
ejpam-1076	95	15	surfaces	surface	NOUN
ejpam-1076	95	16	given	give	VERB
ejpam-1076	95	17	by	by	ADP
ejpam-1076	95	18	the	the	DET
ejpam-1076	95	19	equation	equation	NOUN
ejpam-1076	95	20	(	(	PUNCT
ejpam-1076	95	21	12	12	NUM
ejpam-1076	95	22	)	)	PUNCT
ejpam-1076	95	23	can	can	AUX
ejpam-1076	95	24	be	be	AUX
ejpam-1076	95	25	infinitesimal	infinitesimal	ADJ
ejpam-1076	95	26	deformation	deformation	NOUN
ejpam-1076	95	27	by	by	ADP
ejpam-1076	95	28	using	use	VERB
ejpam-1076	95	29	the	the	DET
ejpam-1076	95	30	other	other	ADJ
ejpam-1076	95	31	one	one	NUM
ejpam-1076	95	32	.	.	PUNCT
ejpam-1076	96	1	references	reference	NOUN
ejpam-1076	96	2	[	[	X
ejpam-1076	96	3	1	1	NUM
ejpam-1076	96	4	]	]	PUNCT
ejpam-1076	96	5	l	l	NOUN
ejpam-1076	96	6	eisenhart	eisenhart	NOUN
ejpam-1076	96	7	.	.	PUNCT
ejpam-1076	97	1	"	"	PUNCT
ejpam-1076	97	2	a	a	DET
ejpam-1076	97	3	treatise	treatise	NOUN
ejpam-1076	97	4	on	on	ADP
ejpam-1076	97	5	the	the	DET
ejpam-1076	97	6	differantial	differantial	ADJ
ejpam-1076	97	7	geometry	geometry	NOUN
ejpam-1076	97	8	of	of	ADP
ejpam-1076	97	9	curves	curve	NOUN
ejpam-1076	97	10	and	and	CCONJ
ejpam-1076	97	11	surfaces	surface	NOUN
ejpam-1076	97	12	"	"	PUNCT
ejpam-1076	97	13	dover	dover	PROPN
ejpam-1076	97	14	publications	publications	PROPN
ejpam-1076	97	15	,	,	PUNCT
ejpam-1076	97	16	inc	inc	PROPN
ejpam-1076	97	17	.	.	PROPN
ejpam-1076	97	18	,	,	PUNCT
ejpam-1076	97	19	new	new	PROPN
ejpam-1076	97	20	york	york	PROPN
ejpam-1076	97	21	,	,	PUNCT
ejpam-1076	97	22	p.260	p.260	PROPN
ejpam-1076	97	23	-	-	PUNCT
ejpam-1076	97	24	263	263	NUM
ejpam-1076	97	25	.	.	PUNCT
ejpam-1076	97	26	1960	1960	NUM
ejpam-1076	97	27	.	.	PUNCT
ejpam-1076	98	1	[	[	X
ejpam-1076	98	2	2	2	NUM
ejpam-1076	98	3	]	]	SYM
ejpam-1076	98	4	f	f	PROPN
ejpam-1076	98	5	kanbay	kanbay	NOUN
ejpam-1076	98	6	.	.	PUNCT
ejpam-1076	99	1	"	"	PUNCT
ejpam-1076	99	2	bonnet	bonnet	NOUN
ejpam-1076	99	3	ruled	rule	VERB
ejpam-1076	99	4	surfaces	surface	NOUN
ejpam-1076	99	5	"	"	PUNCT
ejpam-1076	99	6	,	,	PUNCT
ejpam-1076	99	7	acta	acta	PROPN
ejpam-1076	99	8	mathematica	mathematica	PROPN
ejpam-1076	99	9	sinica	sinica	PROPN
ejpam-1076	99	10	,	,	PUNCT
ejpam-1076	99	11	english	english	ADJ
ejpam-1076	99	12	series	series	NOUN
ejpam-1076	99	13	,	,	PUNCT
ejpam-1076	99	14	vol	vol	NOUN
ejpam-1076	99	15	21	21	NUM
ejpam-1076	99	16	no:3	no:3	PROPN
ejpam-1076	99	17	,	,	PUNCT
ejpam-1076	99	18	623	623	NUM
ejpam-1076	99	19	-	-	SYM
ejpam-1076	99	20	630	630	NUM
ejpam-1076	99	21	.	.	PUNCT
ejpam-1076	99	22	2005	2005	NUM
ejpam-1076	99	23	.	.	PUNCT
ejpam-1076	100	1	[	[	X
ejpam-1076	100	2	3	3	X
ejpam-1076	100	3	]	]	X
ejpam-1076	100	4	i	i	PRON
ejpam-1076	100	5	raussos	rausso	VERB
ejpam-1076	100	6	.	.	PUNCT
ejpam-1076	101	1	"	"	PUNCT
ejpam-1076	101	2	tangential	tangential	ADJ
ejpam-1076	101	3	developable	developable	ADJ
ejpam-1076	101	4	surfaces	surface	NOUN
ejpam-1076	101	5	as	as	ADP
ejpam-1076	101	6	bonnet	bonnet	NOUN
ejpam-1076	101	7	surfaces	surface	NOUN
ejpam-1076	101	8	"	"	PUNCT
ejpam-1076	101	9	.	.	PUNCT
ejpam-1076	102	1	acta	acta	PROPN
ejpam-1076	102	2	mathematica	mathematica	PROPN
ejpam-1076	102	3	sinica	sinica	PROPN
ejpam-1076	102	4	,	,	PUNCT
ejpam-1076	102	5	english	english	ADJ
ejpam-1076	102	6	series	series	NOUN
ejpam-1076	102	7	,	,	PUNCT
ejpam-1076	102	8	15(2	15(2	NUM
ejpam-1076	102	9	)	)	PUNCT
ejpam-1076	102	10	,	,	PUNCT
ejpam-1076	102	11	269	269	NUM
ejpam-1076	102	12	-	-	SYM
ejpam-1076	102	13	276	276	NUM
ejpam-1076	102	14	.	.	PUNCT
ejpam-1076	102	15	1999	1999	NUM
ejpam-1076	102	16	.	.	PUNCT
ejpam-1076	103	1	[	[	X
ejpam-1076	103	2	4	4	X
ejpam-1076	103	3	]	]	X
ejpam-1076	103	4	z	z	PROPN
ejpam-1076	103	5	soyuc.ok	soyuc.ok	PROPN
ejpam-1076	103	6	.	.	PUNCT
ejpam-1076	104	1	"	"	PUNCT
ejpam-1076	104	2	the	the	DET
ejpam-1076	104	3	problem	problem	NOUN
ejpam-1076	104	4	of	of	ADP
ejpam-1076	104	5	non	non	ADJ
ejpam-1076	104	6	-	-	ADJ
ejpam-1076	104	7	trivial	trivial	ADJ
ejpam-1076	104	8	isometries	isometry	NOUN
ejpam-1076	104	9	of	of	ADP
ejpam-1076	104	10	surfaces	surface	NOUN
ejpam-1076	104	11	preserving	preserve	VERB
ejpam-1076	104	12	principal	principal	ADJ
ejpam-1076	104	13	curvatures	curvature	NOUN
ejpam-1076	104	14	"	"	PUNCT
ejpam-1076	104	15	,	,	PUNCT
ejpam-1076	104	16	journal	journal	NOUN
ejpam-1076	104	17	of	of	ADP
ejpam-1076	104	18	geometry	geometry	NOUN
ejpam-1076	104	19	vol	vol	NOUN
ejpam-1076	104	20	.	.	PROPN
ejpam-1076	104	21	52	52	NUM
ejpam-1076	104	22	,	,	PUNCT
ejpam-1076	104	23	173	173	NUM
ejpam-1076	104	24	-	-	SYM
ejpam-1076	104	25	188	188	NUM
ejpam-1076	104	26	.	.	PUNCT
ejpam-1076	104	27	1995	1995	NUM
ejpam-1076	104	28	.	.	PUNCT
ejpam-1076	105	1	[	[	X
ejpam-1076	105	2	5	5	NUM
ejpam-1076	105	3	]	]	PUNCT
ejpam-1076	105	4	z	z	PROPN
ejpam-1076	105	5	soyuc.ok	soyuc.ok	PROPN
ejpam-1076	105	6	.	.	PUNCT
ejpam-1076	106	1	"	"	PUNCT
ejpam-1076	106	2	infinitesimal	infinitesimal	ADJ
ejpam-1076	106	3	deformations	deformation	NOUN
ejpam-1076	106	4	of	of	ADP
ejpam-1076	106	5	surfaces	surface	NOUN
ejpam-1076	106	6	and	and	CCONJ
ejpam-1076	106	7	the	the	DET
ejpam-1076	106	8	stress	stress	NOUN
ejpam-1076	106	9	distribution	distribution	NOUN
ejpam-1076	106	10	on	on	ADP
ejpam-1076	106	11	some	some	DET
ejpam-1076	106	12	membranes	membrane	NOUN
ejpam-1076	106	13	under	under	ADP
ejpam-1076	106	14	constant	constant	ADJ
ejpam-1076	106	15	inner	inner	ADJ
ejpam-1076	106	16	pressure	pressure	NOUN
ejpam-1076	106	17	"	"	PUNCT
ejpam-1076	106	18	,	,	PUNCT
ejpam-1076	106	19	int	int	PROPN
ejpam-1076	106	20	.	.	PUNCT
ejpam-1076	107	1	j.	j.	PROPN
ejpam-1076	107	2	engng	engng	PROPN
ejpam-1076	107	3	sci	sci	PROPN
ejpam-1076	107	4	.	.	PUNCT
ejpam-1076	107	5	vol	vol	NOUN
ejpam-1076	107	6	34	34	NUM
ejpam-1076	107	7	,	,	PUNCT
ejpam-1076	107	8	n0	n0	X
ejpam-1076	107	9	9	9	NUM
ejpam-1076	107	10	,	,	PUNCT
ejpam-1076	107	11	pp	pp	ADV
ejpam-1076	107	12	993	993	NUM
ejpam-1076	107	13	-	-	SYM
ejpam-1076	107	14	1004	1004	NUM
ejpam-1076	107	15	.	.	PUNCT
ejpam-1076	107	16	1996	1996	NUM
ejpam-1076	107	17	.	.	PUNCT
ejpam-1076	108	1	[	[	X
ejpam-1076	108	2	6	6	NUM
ejpam-1076	108	3	]	]	X
ejpam-1076	108	4	f	f	X
ejpam-1076	108	5	uras	uras	PROPN
ejpam-1076	108	6	.	.	PUNCT
ejpam-1076	109	1	"	"	PUNCT
ejpam-1076	109	2	diferensiyel	diferensiyel	PROPN
ejpam-1076	109	3	geometri	geometri	PROPN
ejpam-1076	109	4	ii	ii	PROPN
ejpam-1076	109	5	dersleri	dersleri	PROPN
ejpam-1076	109	6	"	"	PUNCT
ejpam-1076	109	7	yıldız	yıldız	PROPN
ejpam-1076	109	8	teknik	teknik	PROPN
ejpam-1076	109	9	üniversitesi	üniversitesi	PROPN
ejpam-1076	109	10	fen	fen	PROPN
ejpam-1076	109	11	-	-	PUNCT
ejpam-1076	109	12	edebiyat	edebiyat	PROPN
ejpam-1076	109	13	fakultesi	fakultesi	PROPN
ejpam-1076	109	14	matematik	matematik	PROPN
ejpam-1076	109	15	bölümü	bölümü	PROPN
ejpam-1076	109	16	sayı:261	sayı:261	PROPN
ejpam-1076	109	17	.	.	PROPN
ejpam-1076	109	18	istanbul	istanbul	PROPN
ejpam-1076	109	19	.	.	PUNCT
ejpam-1076	110	1	1992	1992	NUM
ejpam-1076	110	2	.	.	PUNCT
ejpam-1076	111	1	[	[	X
ejpam-1076	111	2	7	7	X
ejpam-1076	111	3	]	]	X
ejpam-1076	111	4	f	f	X
ejpam-1076	111	5	uras	uras	PROPN
ejpam-1076	111	6	.	.	PUNCT
ejpam-1076	112	1	"	"	PUNCT
ejpam-1076	112	2	on	on	ADP
ejpam-1076	112	3	the	the	DET
ejpam-1076	112	4	net	net	NOUN
ejpam-1076	112	5	of	of	ADP
ejpam-1076	112	6	the	the	DET
ejpam-1076	112	7	principal	principal	NOUN
ejpam-1076	112	8	stresses	stress	NOUN
ejpam-1076	112	9	related	relate	VERB
ejpam-1076	112	10	with	with	ADP
ejpam-1076	112	11	the	the	DET
ejpam-1076	112	12	infinitesimal	infinitesimal	ADJ
ejpam-1076	112	13	bending	bending	NOUN
ejpam-1076	112	14	of	of	ADP
ejpam-1076	112	15	surfaces	surface	NOUN
ejpam-1076	112	16	"	"	PUNCT
ejpam-1076	112	17	,	,	PUNCT
ejpam-1076	112	18	bulletin	bulletin	NOUN
ejpam-1076	112	19	of	of	ADP
ejpam-1076	112	20	the	the	DET
ejpam-1076	112	21	technical	technical	ADJ
ejpam-1076	112	22	university	university	PROPN
ejpam-1076	112	23	of	of	ADP
ejpam-1076	112	24	istanbul	istanbul	PROPN
ejpam-1076	112	25	vol	vol	NOUN
ejpam-1076	112	26	49	49	NUM
ejpam-1076	112	27	,	,	PUNCT
ejpam-1076	112	28	no:3	no:3	NOUN
ejpam-1076	112	29	-	-	PUNCT
ejpam-1076	112	30	4	4	NUM
ejpam-1076	112	31	.	.	NOUN
ejpam-1076	112	32	1996	1996	NUM
ejpam-1076	112	33	.	.	PUNCT
ejpam-1076	113	1	[	[	X
ejpam-1076	113	2	8	8	NUM
ejpam-1076	113	3	]	]	X
ejpam-1076	113	4	i	i	PRON
ejpam-1076	113	5	vekua	vekua	NOUN
ejpam-1076	113	6	.	.	PUNCT
ejpam-1076	114	1	"	"	PUNCT
ejpam-1076	114	2	generalized	generalize	VERB
ejpam-1076	114	3	analiytic	analiytic	ADJ
ejpam-1076	114	4	functions	function	NOUN
ejpam-1076	114	5	.	.	PUNCT
ejpam-1076	115	1	pergamon	pergamon	PROPN
ejpam-1076	115	2	pres	pres	PROPN
ejpam-1076	115	3	,	,	PUNCT
ejpam-1076	115	4	oxford	oxford	PROPN
ejpam-1076	115	5	.	.	PUNCT
ejpam-1076	116	1	1962	1962	NUM
ejpam-1076	116	2	.	.	PUNCT