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If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.

A pair of functions phi_i(x) and phi_j(x) are orthonormal if they are orthogonal and each normalized so that int_a^b[phi_i(x)]^2w(x)dx = 1 (1) int_a^b[phi_j(x)]^2w(x)dx = 1. ...

Given a source S and a curve gamma, pick a point on gamma and find its tangent T. Then the locus of reflections of S about tangents T is the orthotomic curve (also known as ...

The number of outward directed graph edges from a given graph vertex in a directed graph.

A singular point such that every neighborhood of the point intersects itself. Pinch points are also called Whitney singularities or branch points.

Every bounded operator T acting on a Hilbert space H has a decomposition T=U|T|, where |T|=(T^*T)^(1/2) and U is a partial isometry. This decomposition is called polar ...

A point at which three or more polyhedron edges of a polyhedron meet. The concept can also be generalized to a polytope.

The equivalence of manifolds under continuous deformation within the embedding space. Knots of opposite chirality have ambient isotopy, but not regular isotopy.

A set of integers that give the orders of the blocks in a Jordan canonical form, with those integers corresponding to submatrices containing the same latent root bracketed ...

The semiminor axis (also called the minor semi-axis, minor semiaxis, or minor radius) of an ellipse (or related figure) is half its extent along the shorter of the two ...