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The subset C of the Euclidean plane formed by the union of the x-axis, the line segment with interval [0,1] of the y-axis, and the sequence of segments with endpoints (1/n,0) ...

The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

The number 2^(1/3)=RadicalBox[2, 3] (the cube root of 2) which is to be constructed in the cube duplication problem. This number is not a Euclidean number although it is an ...

The Frobenius norm, sometimes also called the Euclidean norm (a term unfortunately also used for the vector L^2-norm), is matrix norm of an m×n matrix A defined as the square ...

A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point. When dealing with topological spaces, a ...

A lattice graph, also known as a mesh graph or grid graph, is a graph possessing an embedding in a Euclidean space R^n that forms a regular tiling. Examples include grid ...

The roots of a semisimple Lie algebra g are the Lie algebra weights occurring in its adjoint representation. The set of roots form the root system, and are completely ...

In Euclidean space R^3, the curve that minimizes the distance between two points is clearly a straight line segment. This can be shown mathematically as follows using ...

A radial function is a function phi:R^+->R satisfying phi(x,c)=phi(|x-c|) for points c in some subset Xi subset R^n. Here, |·| denotes the standard Euclidean norm in R^n and ...

A regular skew polyhedron is a polyhedron whose faces and vertex figures are regular skew polygons. There are only three regular skew polyhedra in Euclidean three-space ...