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The Pell constant is the infinite product P = 1-product_(k=0)^(infty)(1-1/(2^(2k+1))) (1) = 1-(1/2;1/4)_infty (2) = 0.58057755820489... (3) (OEIS A141848), where (a,q)_infty ...

The pentagonal rotunda is a convex polyhedron consisting of half of an icosidodecahedron, with the base being filled in by a decagon. It has 10 triangular and five pentagonal ...

All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.

Consider n intersecting ellipses. The maximal number of regions into which these divide the plane are N(n)=2n^2-2n+2=2(n^2-n+1), giving values for n=1, 2, ... of 2, 6, 14, ...

The point group C_1 is a group on a single element that is isomorphic to the trivial group. Its character table is given below. C_1 1 1 1

The Pontryagin number is defined in terms of the Pontryagin class of a manifold as follows. For any collection of Pontryagin classes such that their cup product has the same ...

A positive measure is a measure which is a function from the measurable sets of a measure space to the nonnegative real numbers. Sometimes, this is what is meant by measure, ...

A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived. The whole of ...

A positive integer n is kth powerfree if there is no number d such that d^k|n (d^k divides n), i.e., there are no kth powers or higher in the prime factorization of n. A ...

The volume of a prismatoid is equal to the sum of the volumes of a pyramid, a wedge, and a parallelepiped.