Equable shape - Revision history

en>Jason Quinn: cleanup and modernization of refs

2014-12-30T23:58:23Z

cleanup and modernization of refs

← Older revision		Revision as of 01:58, 31 December 2014
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	~~{{too technical\|date=November 2012}}~~		Her title is Felicidad Ahmad. Bookkeeping has been his day job for a whilst. Some time ago he selected to reside in Kansas. Playing crochet is some thing that I've carried out for many years.<br><br>Here is my page [http://bjjoutlet.com/UserProfile/tabid/43/userId/20679/Default.aspx auto warranty]
	~~In [[geometry]], '''anti-parallel lines''' can be defined with respect to either lines or angles.~~

	~~==Definitions==~~

	[[File:anti1.svg\|thumb\|right\|Given two lines <math>m_1 \,</math> and <math>m_2 \,</math>, lines <math>l_1 \,</math> and <math>l_2 \,</math> are anti-parallel with respect to <math>m_1 \,</math> and <math>m_2 \,</math> if <math>\angle 1 = \angle 2 \,</math>. ]]
	Given two lines <math>m_1 \,</math> and <math>m_2 \,</math>, lines <math>l_1 \,</math> and <math>l_2 \,</math> are anti-parallel with respect to <math>m_1 \,</math> and <math>m_2 \,</math> if <math>\angle 1 = \angle 2 \,</math>. If <math>l_1 \,</math> and <math>l_2 \,</math> are anti-parallel with respect to <math>m_1 \,</math> and <math>m_2 \,</math>, then <math>m_1 \,</math> and <math>m_2 \,</math> are also anti-parallel with respect to <math>l_1 \,</math> and <math>l_2 \,</math>.

	~~In any [[quadrilateral]] inscribed in~~ a ~~circle, any two opposite sides are anti-parallel with respect to the other two sides~~.
	~~[[File:anti5.svg\|thumb\|right\|In any quadrilateral inscribed in a circle, any two opposite sides are anti-parallel with respect~~ to ~~the other two sides. ]]~~

	~~Two lines <math>l_1 \,</math> and <math>l_2 \, </math>are said to be antiparallel with respect to the sides of an angle if they make the same angle <math>\angle APC</math>~~ in ~~the opposite senses with the [[bisector]] of that angle~~.

	[[File:anti2.svg\|thumb\|right\|Two lines <math>l_1 \,</math> and <math>l_2 \, </math> are said to be antiparallel with respect to the sides of an angle if they make the same angle <math>\angle APC</math> in the opposite senses with the bisector of that ~~angle. Notice that our previous angles 1 and 2 are still equivalent~~. ]]

	~~[[File:anti3.svg\|thumb\|right\|If the lines~~ <~~math~~>~~m_1 \,~~<~~/math~~> ~~and <math>m_2 \,</math> coincide, <math>l_1 \,</math> and <math>l_2 \, </math> are said to be anti-parallel with respect to a straight line.]]~~

	~~===Antiparallel vectors===~~
	~~In a [[vector space]] over <math> \mathbb{R} </math> (or some other [~~[~~ordered field]]),~~
	~~two nonzero vectors are called antiparallel if they are parallel but have opposite directions.<ref>{{cite book~~
	~~\|title=Handbook of mathematics and computational science~~
	~~\|first1=John~~
	~~\|last1=Harris~~
	~~\|first2=John W.~~
	~~\|last2=Harris~~
	~~\|first3=Horst~~
	~~\|last3=Stöcker~~
	~~\|publisher=Birkhäuser~~
	~~\|year=1998~~
	~~\|isbn=0-387-94746-9~~
	~~\|page=332~~
	~~\|url=~~http://~~books.google~~.com/~~books?id=DnKLkOb_YfIC}}, [http:~~//~~books.google.com~~/~~books?id=DnKLkOb_YfIC&pg=PA332 Chapter 6, p. 332]~~
	</~~ref>~~
	~~In that case, one is a [[negative number\|negative]] [[scalar (mathematics)\|scalar]] times the other.~~

	~~==Relations==~~
	~~# The line joining the feet to two altitudes of a triangle is antiparallel to the third side.(any cevians which 'see' the third side with the same angle create antiparallel lines)~~
	~~# The tangent to a triangle's [[circumcircle]] at a vertex is antiparallel to the opposite side.~~
	~~# The radius of the circumcircle at a vertex is perpendicular to all lines antiparallel to the opposite sides.~~

	~~==References==~~
	~~{{reflist}}~~
	*A.B. Ivanov, Encyclopaedia of Mathematics - ISBN 1-4020-0609-8
	*Weisstein, Eric W. "Antiparallel." From MathWorld--A Wolfram Web Resource. [http:/~~/mathworld.wolfram.com/Antiparallel~~.~~html]~~

	~~[[Category:Elementary geometry]~~]

en>Duoduoduo: /* Cyclic polygons */ correcting section title

2013-08-19T17:25:54Z

Cyclic polygons: correcting section title

← Older revision		Revision as of 19:25, 19 August 2013
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	~~Hello buddy~~. ~~Allow me introduce myself~~. ~~I am Luther Aubrey~~. ~~Kansas is our beginning location~~ and ~~my mothers~~ and ~~fathers reside close by~~. ~~I am~~ a ~~cashier~~ and ~~I'll~~ be ~~promoted quickly~~. ~~What she loves doing is~~ to ~~play croquet but she hasn't made~~ a ~~dime with it~~.<br><br>~~My blog post: car warranty~~ ([http://~~Pcresourcesllc~~.com/~~UserProfile~~/~~tabid~~/61/~~userId~~/~~94025~~/~~Default~~.~~aspx just click the next article~~])		{{too technical\|date=November 2012}}
			In [[geometry]], '''anti-parallel lines''' can be defined with respect to either lines or angles.

			==Definitions==

			[[File:anti1.svg\|thumb\|right\|Given two lines <math>m_1 \,</math> and <math>m_2 \,</math>, lines <math>l_1 \,</math> and <math>l_2 \,</math> are anti-parallel with respect to <math>m_1 \,</math> and <math>m_2 \,</math> if <math>\angle 1 = \angle 2 \,</math>. ]]
			Given two lines <math>m_1 \,</math> and <math>m_2 \,</math>, lines <math>l_1 \,</math> and <math>l_2 \,</math> are anti-parallel with respect to <math>m_1 \,</math> and <math>m_2 \,</math> if <math>\angle 1 = \angle 2 \,</math>. If <math>l_1 \,</math> and <math>l_2 \,</math> are anti-parallel with respect to <math>m_1 \,</math> and <math>m_2 \,</math>, then <math>m_1 \,</math> and <math>m_2 \,</math> are also anti-parallel with respect to <math>l_1 \,</math> and <math>l_2 \,</math>.

			In any [[quadrilateral]] inscribed in a circle, any two opposite sides are anti-parallel with respect to the other two sides.
			[[File:anti5.svg\|thumb\|right\|In any quadrilateral inscribed in a circle, any two opposite sides are anti-parallel with respect to the other two sides. ]]

			Two lines <math>l_1 \,</math> and <math>l_2 \, </math>are said to be antiparallel with respect to the sides of an angle if they make the same angle <math>\angle APC</math> in the opposite senses with the [[bisector]] of that angle.

			[[File:anti2.svg\|thumb\|right\|Two lines <math>l_1 \,</math> and <math>l_2 \, </math> are said to be antiparallel with respect to the sides of an angle if they make the same angle <math>\angle APC</math> in the opposite senses with the bisector of that angle. Notice that our previous angles 1 and 2 are still equivalent. ]]

			[[File:anti3.svg\|thumb\|right\|If the lines <math>m_1 \,</math> and <math>m_2 \,</math> coincide, <math>l_1 \,</math> and <math>l_2 \, </math> are said to be anti-parallel with respect to a straight line.]]

			===Antiparallel vectors===
			In a [[vector space]] over <math> \mathbb{R} </math> (or some other [[ordered field]]),
			two nonzero vectors are called antiparallel if they are parallel but have opposite directions.<ref>{{cite book
			\|title=Handbook of mathematics and computational science
			\|first1=John
			\|last1=Harris
			\|first2=John W.
			\|last2=Harris
			\|first3=Horst
			\|last3=Stöcker
			\|publisher=Birkhäuser
			\|year=1998
			\|isbn=0-387-94746-9
			\|page=332
			\|url=http://books.google.com/books?id=DnKLkOb_YfIC}}, [http://books.google.com/books?id=DnKLkOb_YfIC&pg=PA332 Chapter 6, p. 332]
			</ref>
			In that case, one is a [[negative number\|negative]] [[scalar (mathematics)\|scalar]] times the other.

			==Relations==
			# The line joining the feet to two altitudes of a triangle is antiparallel to the third side.(any cevians which 'see' the third side with the same angle create antiparallel lines)
			# The tangent to a triangle's [[circumcircle]] at a vertex is antiparallel to the opposite side.
			# The radius of the circumcircle at a vertex is perpendicular to all lines antiparallel to the opposite sides.

			==References==
			{{reflist}}
			*A.B. Ivanov, Encyclopaedia of Mathematics - ISBN 1-4020-0609-8
			*Weisstein, Eric W. "Antiparallel." From MathWorld--A Wolfram Web Resource. [http://mathworld.wolfram.com/Antiparallel.html]

			[[Category:Elementary geometry]]

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-08T05:42:13Z

ISBNs (Build KE)

New page

Hello buddy. Allow me introduce myself. I am Luther Aubrey. Kansas is our beginning location and my mothers and fathers reside close by. I am a cashier and I'll be promoted quickly. What she loves doing is to play croquet but she hasn't made a dime with it.<br><br>My blog post: car warranty ([http://Pcresourcesllc.com/UserProfile/tabid/61/userId/94025/Default.aspx just click the next article])