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An orbifold is the object obtained by identifying any two points of a map which are equivalent under some symmetry of the map's group.

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...

If there is an integer 0<x<p such that x^2=q (mod p), (1) i.e., the congruence (1) has a solution, then q is said to be a quadratic residue (mod p). Note that the trivial ...

The spherical harmonics Y_l^m(theta,phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. Some ...

A plane tiling is said to be isohedral if the symmetry group of the tiling acts transitively on the tiles, and n-isohedral if the tiles fall into n orbits under the action of ...

The atom-spiral, also known as the atomic spiral, is the curve with polar equation r=theta/(theta-a) for a real parameter a (van Maldeghem 2002). When theta is allows to vary ...

A number of attractive 2-compounds of the regular dodecahedron can be constructed. The first (left figures) has the symmetry of the cube and arises by combining two regular ...

The Lorenz asymmetry coefficient is a summary statistic of the Lorenz curve that measures the degree of asymmetry of a Lorenz curve. The Lorenz asymmetry coefficient is ...

Symbols used to identify irreducible representations of groups: A= singly degenerate state which is symmetric with respect to rotation about the principal C_n axis, B= singly ...

There are a number of attractive polyhedron compounds consisting of two octahedra. The first (left figure) consists of two octahedra rotated above a common C_3 symmetry axes. ...