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The Pierce expansion, or alternated Egyptian product, of a real number 0<x<1 is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon with n vertices. If each point of intersection is associated with a node and diagonals are ...

A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a,b and hypotenuse c. By the Pythagorean theorem, this is ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...

The truncated dodecahedron is the 32-faced Archimedean solid with faces 20{3}+12{10}. It is also uniform polyhedron with Maeder index 26 (Maeder 1997), Wenninger index 10 ...

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 ...

Some interesting properties (as well as a few arcane ones not reiterated here) of the number 239 are discussed in Schroeppel (1972). 239 appears in Machin's formula ...

If A is a normed algebra, a net {e_i} in A is called an approximate identity for A if sup_(i)|e_i|<infty and if for each a in A, e_ia->a and ae_i->a. Though this definition ...

Successive application of Archimedes' recurrence formula gives the Archimedes algorithm, which can be used to provide successive approximations to pi (pi). The algorithm is ...

An interpolation formula, sometimes known as the Newton-Bessel formula, given by (1) for p in [0,1], where delta is the central difference and B_(2n) = 1/2G_(2n) (2) = ...