68.32.123.116: /* Construction */

2013-11-23T03:45:35Z

Construction

← Older revision		Revision as of 05:45, 23 November 2013
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	~~Office Manager Frankie Dorothy~~ from ~~Gold River~~, ~~spends time with hobbies~~ and ~~interests including hula hooping~~, ~~como~~ [~~http:~~//~~comoganhardinheiropelainternet~~.~~comoganhardinheiro101~~.~~com ganhar dinheiro~~] ~~na internet and rc model cars. Wants to travel and~~ was ~~enthused after paying a visit~~ to ~~Tipasa~~.		[[Image:HyperbolicParaboloid.png\|thumb\|right\|[[Hyperbolic paraboloid]]]]
			[[Image:Ruled hyperboloid.jpg\|thumb\|right\|A model of an [[elliptic hyperboloid]] of one sheet]]
			[[Image:Monkey Saddle Surface (Shaded).png\|thumb\|right\|A [[monkey saddle]]\|300px]]

			A '''saddle surface''' is a [[smooth surface]] containing one or more [[saddle point]]s. The term derives from the peculiar shape of historical<!--modern [[saddle]]s evolved away from clean-cut "saddle surface"--> [[horse]] [[saddle]]s, which curve both up and down.

			Classical examples of two-dimensional saddle surfaces in the [[Euclidean space]] are second order surfaces, the [[hyperbolic paraboloid]] <math>z=x^2-y^2</math> (which is often referred to as '''the''' saddle surface or "the standard saddle surface") and the [[hyperboloid of one sheet]]. The [[Pringles]] potato chip or crisp is an everyday example of a hyperbolic paraboloid shape.

			Saddle surfaces have negative [[Gaussian curvature]] which distinguish them from convex/elliptical surfaces which have positive Gaussian curvature. A classical third-order saddle surface is the [[monkey saddle]].

			The Ph.D. thesis of [[Grigori Perelman]], titled "Saddle surfaces in Euclidean spaces," was devoted to saddle surfaces.<ref>{{cite book\|author=Перельман, Григорий Яковлевич \|title=Седловые поверхности в евклидовых пространствах: Автореф. дис. на соиск. учен. степ. канд. физ.-мат. наук\|language=Russian\| publisher=Ленинградский Государственный Университет\| year=1990}}</ref>

			== References ==
			* {{cite book
			\| author = [[David Hilbert\|Hilbert, David]]; Cohn-Vossen, Stephan
			\| title = Geometry and the Imagination
			\| edition = 2nd
			\| year = 1952
			\| publisher = Chelsea
			\| isbn = 0-8284-1087-9}}
			{{reflist}}

			{{DEFAULTSORT:Saddle Surface}}
			[[Category:Multivariable calculus]]
			[[Category:Surfaces]]

74.101.230.37: /* Hilbert scheme of points on a manifold */

2012-08-31T15:08:08Z

Hilbert scheme of points on a manifold

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Office Manager Frankie Dorothy from Gold River, spends time with hobbies and interests including hula hooping, como [http://comoganhardinheiropelainternet.comoganhardinheiro101.com ganhar dinheiro] na internet and rc model cars. Wants to travel and was enthused after paying a visit to Tipasa.

Hilbert scheme - Revision history

68.32.123.116: /* Construction */

74.101.230.37: /* Hilbert scheme of points on a manifold */