en>Charles Matthews: copy edit

2013-10-03T13:09:23Z

copy edit

← Older revision		Revision as of 15:09, 3 October 2013
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	~~Myrtle Benny~~ is ~~how I~~'~~m called~~ and ~~I feel comfy when people use~~ the ~~full name~~. ~~South Dakota is exactly where me~~ and ~~my spouse live~~ and ~~my family loves it. Body building is what my family members~~ and ~~I appreciate~~. ~~My day occupation is~~ a ~~librarian~~.<br><br>~~Feel free~~ to ~~visit my web site~~ :: ~~[http://carnavalsite~~.~~com~~/~~demo-page-~~1/~~solid~~-~~advice~~-~~in-relation-to-yeast-infection~~/ ~~carnavalsite.com~~]		[[Image:Viviani curve.png\|thumb\|right\|200px\|Viviani's curve as intersection of a sphere and a cylinder]]

			In [[mathematics]], particularly [[geometry]], '''Viviani's curve''', also known as '''Viviani's window''', is a [[Lemniscate\|figure eight shaped]] space [[curve]] named after the Italian mathematician [[Vincenzo Viviani]], the intersection of a [[sphere]] with a [[cylinder (geometry)\|cylinder]] that is [[tangent]] to the sphere and passes through the center of the sphere.

			The projection of Viviani's curve onto a plane perpendicular to the line through the crossing point and the sphere center is the [[lemniscate of Gerono]].<ref>{{citation\|first1=Luisa Rossi\|last1=Costa\|first2=Elena\|last2=Marchetti\|contribution=Mathematical and Historical Investigation on Domes and Vaults\|pages=73–80\|title=Aesthetics and architectural composition : proceedings of the Dresden International Symposium of Architecture 2004\|year=2005\|location=Mammendorf\|publisher=Pro Literatur\|editor1-last=Weber\|editor1-first=Ralf\|editor2-last=Amann\|editor2-first=Matthias Albrecht}}.</ref>

			== Formula ==
			The curve can be obtained by intersecting a sphere of radius <math>2a</math> centered at the origin,

			:<math>x^2+y^2+z^2=4a^2 \, </math>

			with the cylinder centered at <math>(a,0,0)</math> of radius <math>a</math> given by

			:<math>(x-a)^2+y^2=a^2. \, </math>

			The resulting curve of intersection, <math>V</math>, can be parameterized by <math>t</math> to give the parametric equation of Viviani's curve:

			:<math>V(t)= \left\langle a( 1+\cos(t) ), a\sin(t), 2a\sin\left(\frac{t}{2}\right) \right\rangle. </math>

			This is a [[clelies\|clelie]] with <math>m=1</math>, where <math>\theta=\frac{t-\pi}{2}</math>.

			==See also==
			*[[Sphere-cylinder intersection]]

			==References==
			{{reflist}}

			==External links==
			* {{springer\|title=Viviani curve\|id=p/v096800}}
			* {{mathworld\|urlname=VivianisCurve\|title=Viviani's Curve}}

			[[Category:Curves]]


			{{geometry-stub}}

en>ArthurBot: r2.6.3) (Robot: Adding sl:Sintraktrisa

2011-09-25T19:25:27Z

r2.6.3) (Robot: Adding sl:Sintraktrisa

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Myrtle Benny is how I'm called and I feel comfy when people use the full name. South Dakota is exactly where me and my spouse live and my family loves it. Body building is what my family members and I appreciate. My day occupation is a librarian.<br><br>Feel free to visit my web site :: [http://carnavalsite.com/demo-page-1/solid-advice-in-relation-to-yeast-infection/ carnavalsite.com]

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en>Charles Matthews: copy edit

en>ArthurBot: r2.6.3) (Robot: Adding sl:Sintraktrisa