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Surface area is the area of a given surface. Roughly speaking, it is the "amount" of a surface (i.e., it is proportional to the amount of paint needed to cover it), and has ...

666 is the occult "number of the beast," also called the "sign of the devil" (Wang 1994), associated in the Bible with the Antichrist. It has figured in many numerological ...

A number which is simultaneously square and triangular. Let T_n denote the nth triangular number and S_m the mth square number, then a number which is both triangular and ...

A complete set of mutually conjugate group elements. Each element in a group belongs to exactly one class, and the identity element (I=1) is always in its own class. The ...

A double-toroidal graph is a graph with graph genus 2 (West 2000, p. 266). Planar and toroidal graphs are therefore not double-toroidal. Some known double-toroidal graphs on ...

In 1638, Fermat proposed that every positive integer is a sum of at most three triangular numbers, four square numbers, five pentagonal numbers, and n n-polygonal numbers. ...

A polygonal number and 6-polygonal number of the form n(2n-1). The first few are 1, 6, 15, 28, 45, ... (OEIS A000384). The generating function for the hexagonal numbers is ...

The inverse tangent integral Ti_2(x) is defined in terms of the dilogarithm Li_2(x) by Li_2(ix)=1/4Li_2(-x^2)+iTi_2(x) (1) (Lewin 1958, p. 33). It has the series ...

Odd values of Q(n) are 1, 1, 3, 5, 27, 89, 165, 585, ... (OEIS A051044), and occur with ever decreasing frequency as n becomes large (unlike P(n), for which the fraction of ...

A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...