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Cribbage is a game in which each of two players is dealt a hand of six cards. Each player then discards two of his six cards to a four-card "crib" which alternates between ...

The quasiperiodic function defined by d/(dz)lnsigma(z;g_2,g_3)=zeta(z;g_2,g_3), (1) where zeta(z;g_2,g_3) is the Weierstrass zeta function and lim_(z->0)(sigma(z))/z=1. (2) ...

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...

Let kappa_1 and kappa_2 be the principal curvatures, then their mean H=1/2(kappa_1+kappa_2) (1) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to ...

Iff p is a prime, then (p-1)!+1 is a multiple of p, that is (p-1)!=-1 (mod p). (1) This theorem was proposed by John Wilson and published by Waring (1770), although it was ...

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

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 ...

The inverse tangent is the multivalued function tan^(-1)z (Zwillinger 1995, p. 465), also denoted arctanz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 311; ...

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...