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Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...

The toroidal crossing number cr_(1)(G) of a graph G is the minimum number of crossings with which G can be drawn on a torus. A planar graph has toroidal crossing number 0, ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

Gaussian primes are Gaussian integers z=a+bi satisfying one of the following properties. 1. If both a and b are nonzero then, a+bi is a Gaussian prime iff a^2+b^2 is an ...

The Golomb graph is a unit-distance graph discovered around 1960-1965 by Golomb (Soifer 2008, p. 19). It is implemented in the Wolfram Language as GraphData["GolombGraph"]. A ...

Let omega_1 and omega_2 be periods of a doubly periodic function, with tau=omega_2/omega_1 the half-period ratio a number with I[tau]!=0. Then Klein's absolute invariant ...

In the fields of functional and harmonic analysis, the Littlewood-Paley decomposition is a particular way of decomposing the phase plane which takes a single function and ...

A random walk is a sequence of discrete steps in which each step is randomly taken subject to some set of restrictions in allowed directions and step lengths. Random walks ...

A real polynomial P is said to be stable if all its roots lie in the left half-plane. The term "stable" is used to describe such a polynomial because, in the theory of linear ...