Saddle surface: Facts, Discussion Forum, and Encyclopedia Article

Saddle surface

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	Saddle surface
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	Topics Saddle surface Topic Home A saddle surface is a smooth surface containing one or more saddle pointSaddle point In the most general terms, a saddle point for a smooth function is a point such that the curve/surface/etc.... s. The term derives of the peculiar shape of historical horseHorse The horse is a large odd-toed ungulate mammal, one of ten modern species of the genus Equus.... saddleSaddle A saddle is a seat for a rider fastened to an animal's back.... s, which curve both up and down. Classical examples of two-dimensional saddle surfaces in the Euclidean spaceEuclidean space Around 300 BC, the Greek mathematician Euclid laid down the rules of what has now come to be called "plane Euclidean geometry", wh... are second order surfaces, the hyperbolic paraboloid z=x²-y² (which is often referred to as the saddle surface or "the standard saddle surface") and hyperboloid of one sheet. Saddle surfaces have negative Gaussian curvatureGaussian curvature In mathematics, the Gaussian curvature of a point on a surface is the product of the principal curvatures, ?1 and ?2... which distinguish them from convex/elliptical surfaces which have positive Gaussian curvature. A classical third-order saddle surface is the monkey saddleMonkey saddle In mathematics, the monkey saddle is the surface defined by the equation... .