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A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

A nonplanar graph is a graph that is not planar. The numbers of simple nonplanar graphs on n=1, 2, ... nodes are 0, 0, 0, 0, 1, 14, 222, 5380, 194815, ... (OEIS A145269), ...

The Fibonacci numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation F_n=F_(n-1)+F_(n-2) (1) with F_1=F_2=1. As a result of the ...

The Chebyshev polynomials of the first kind are a set of orthogonal polynomials defined as the solutions to the Chebyshev differential equation and denoted T_n(x). They are ...

Chess is a two-player board game believed to have been played in India as early as the sixth century AD. In different parts of this world, different chess games are played. ...

The Fourier transform is a generalization of the complex Fourier series in the limit as L->infty. Replace the discrete A_n with the continuous F(k)dk while letting n/L->k. ...

A Haar graph H(n) is a bipartite regular indexed by a positive integer and obtained by a simple binary encoding of cyclically adjacent vertices. Haar graphs may be connected ...

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

An integral of the form intf(z)dz, (1) i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite ...

Machin-like formulas have the form mcot^(-1)u+ncot^(-1)v=1/4kpi, (1) where u, v, and k are positive integers and m and n are nonnegative integers. Some such formulas can be ...