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Let a_n and b_n be the perimeters of the circumscribed and inscribed n-gon and a_(2n) and b_(2n) the perimeters of the circumscribed and inscribed 2n-gon. Then a_(2n) = ...

A limiting value of a holonomic function near a singular point. Holonomic constants include Apéry's constant, Catalan's constant, Pólya's random walk constants for d>2, and ...

Elliptic alpha functions relate the complete elliptic integrals of the first K(k_r) and second kinds E(k_r) at elliptic integral singular values k_r according to alpha(r) = ...

Jenny's constant is the name given (Munroe 2012) to the positive real constant defined by J = (7^(e-1/e)-9)pi^2 (1) = 867.53090198... (2) (OEIS A182369), the first few digits ...

A number is said to be pandigital if it contains each of the digits from 0 to 9 (and whose leading digit must be nonzero). However, "zeroless" pandigital quantities contain ...

Construct a square equal in area to a circle using only a straightedge and compass. This was one of the three geometric problems of antiquity, and was perhaps first attempted ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

A continuous vector bundle is a vector bundle pi:E->M with only the structure of a topological manifold. The map pi is continuous. It has no smooth structure or bundle metric.

The identity function id(x) is the function id(x)=x which assigns every real number x to the same real number x. It is identical to the identity map. The identity function is ...

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...