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The Sierpiński sieve is a fractal described by Sierpiński in 1915 and appearing in Italian art from the 13th century (Wolfram 2002, p. 43). It is also called the Sierpiński ...

A simple graph, also called a strict graph (Tutte 1998, p. 2), is an unweighted, undirected graph containing no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, ...

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 ...

The Weierstrass elliptic functions (or Weierstrass P-functions, voiced "p-functions") are elliptic functions which, unlike the Jacobi elliptic functions, have a second-order ...

The xi-function is the function xi(z) = 1/2z(z-1)(Gamma(1/2z))/(pi^(z/2))zeta(z) (1) = ((z-1)Gamma(1/2z+1)zeta(z))/(sqrt(pi^z)), (2) where zeta(z) is the Riemann zeta ...

Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is ...

A square number, also called a perfect square, is a figurate number of the form S_n=n^2, where n is an integer. The square numbers for n=0, 1, ... are 0, 1, 4, 9, 16, 25, 36, ...

The Bernoulli numbers B_n are a sequence of signed rational numbers that can be defined by the exponential generating function x/(e^x-1)=sum_(n=0)^infty(B_nx^n)/(n!). (1) ...

An amicable pair (m,n) consists of two integers m,n for which the sum of proper divisors (the divisors excluding the number itself) of one number equals the other. Amicable ...

In August 2002, M. Agrawal and colleagues announced a deterministic algorithm for determining if a number is prime that runs in polynomial time (Agrawal et al. 2004). While ...