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A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

A stable isolated (i.e., solitary) traveling nonlinear wave solution to a set of equations that obeys a superposition-like principle (i.e., solitons passing through one ...

A unimodular matrix is a real square matrix A with determinant det(A)=+/-1 (Born and Wolf 1980, p. 55; Goldstein 1980, p. 149). More generally, a matrix A with elements in ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...

A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

The concept of a space is an extremely general and important mathematical construct. Members of the space obey certain addition properties. Spaces which have been ...