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A generalization of the binomial coefficient whose notation was suggested by Knuth, |_n; k]=(|_n]!)/(|_k]!|_n-k]!), (1) where |_n] is a Roman factorial. The above expression ...

The Schröder-Bernstein theorem for numbers states that if n<=m<=n, then m=n. For sets, the theorem states that if there are injections of the set A into the set B and of B ...

Simple harmonic motion refers to the periodic sinusoidal oscillation of an object or quantity. Simple harmonic motion is executed by any quantity obeying the differential ...

The Zipf distribution, sometimes referred to as the zeta distribution, is a discrete distribution commonly used in linguistics, insurance, and the modelling of rare events. ...

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 ...

The beautiful arrangement of leaves in some plants, called phyllotaxis, obeys a number of subtle mathematical relationships. For instance, the florets in the head of a ...

The rhombic hexecontahedron is a 60-faced polyhedron that can be obtained by stellating the rhombic triacontahedron by placing a plane along each edge which is perpendicular ...

Clebsch-Gordan coefficients are mathematical symbol used to integrate products of three spherical harmonics. Clebsch-Gordan coefficients commonly arise in applications ...

The 57-cell, also called the pentacontaheptachoron, is a regular self-dual locally projective polytope with 57 hemidodecahedral facets described by Coxeter (1982) and also ...

An aperiodic tiling is a non-periodic tiling in which arbitrarily large periodic patches do not occur. A set of tiles is said to be aperiodic if they can form only ...