Gauss map

In differential geometry, the Gauss map (named, like so many things, after Carl F. Gauss) maps a surface in Euclidean space R3 to the unit sphere S^2. Namely, given a surface S lying in R3, the Gauss map is a continuous map N:S o S^2 such that N(p) is orthogonal to S at p.

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The Gauss map can be defined (globally) if and only if the surface is orientable, but it is always defined locally (i.e. on a small piece of the surface). The Jacobian of the Gauss map is equal to Gauss curvature, and the differential of the Gauss map is called the shape operator.

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Differential geometry: Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus, as well as linear and multilinear algebra, to study problems in geometry. The theory of plane and space curves and of surfaces in the three-dimensional Euclidean space formed the basis for...

So many things: "So Many Things" is a single by Sarah Brightman from her Eden album, released in 1999 (See 1999 in music)....

Carl F. Gauss: REDIRECTCarl Friedrich Gauss...

Gauss map related Images and Photos (experimental)

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