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Hypersurface


A generalization of an ordinary two-dimensional surface embedded in three-dimensional space to an (n-1)-dimensional surface embedded in n-dimensional space. A hypersurface is therefore the set of solutions to a single equation

 f(x_1,...,x_n)=0

and so it has codimension one. For instance, the n-dimension hypersphere S^n corresponds to the equation x_1^2+...+x_n^2=1.


See also

Hypersphere, Surface

Portions of this entry contributed by Todd Rowland

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Cite this as:

Rowland, Todd and Weisstein, Eric W. "Hypersurface." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Hypersurface.html

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