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The n-hypersphere (often simply called the n-sphere) is a generalization of the circle (called by geometers the 2-sphere) and usual sphere (called by geometers the 3-sphere) ...

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 ...

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m<2. If n/m>2, the curve is a hyperellipse.

There are a number of algebraic equations known as the icosahedral equation, all of which derive from the projective geometry of the icosahedron. Consider an icosahedron ...

A three-dimensional shadow of a four-dimensional Klein bottle.

The map which assigns every member of a set A to the same element id_A. It is identical to the identity function.

The symmetry operation corresponding to a rotation followed by an inversion operation, also called a rotoinversion. This operation is denoted n^_ for an improper rotation by ...

The incenter I is the center of the incircle for a polygon or insphere for a polyhedron (when they exist). The corresponding radius of the incircle or insphere is known as ...

The eight of Hilbert's axioms which concern collinearity and intersection; they include the first four of Euclid's postulates.

The indices of a contravariant tensor A^j can be lowered, turning it into a covariant tensor A_i, by multiplication by a so-called metric tensor g_(ij), e.g., g_(ij)A^j=A_i.