In geometry, a hypersurface is a generalization of the concept of hyperplane. Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n − 1 dimensions is a hypersurface. Equivalently, the codimension of a hypersurface is one. For example, the n-sphere in Rn + 1 is called a hypersphere. Hypersurfaces occur frequently in mu...
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http://en.wikipedia.org/wiki/Hypersurface
a mathematical object that generalizes the concept of surface from three-dimensional Euclidean space to hyperspace.
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https://www.infoplease.com/dictionary/hypersurface
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