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One name for the figure used by Euclid to prove the Pythagorean theorem.

First stated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of ...

A metric space X is boundedly compact if all closed bounded subsets of X are compact. Every boundedly compact metric space is complete. (This is a generalization of the ...

A doubly stochastic matrix is a matrix A=(a_(ij)) such that a_(ij)>=0 and sum_(i)a_(ij)=sum_(j)a_(ij)=1 is some field for all i and j. In other words, both the matrix itself ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

A short theorem used in proving a larger theorem. Related concepts are the axiom, porism, postulate, principle, and theorem. The late mathematician P. Erdős has often been ...

Ergodic theory can be described as the statistical and qualitative behavior of measurable group and semigroup actions on measure spaces. The group is most commonly N, R, R-+, ...

A version of set theory which is a formal system expressed in first-order predicate logic. Zermelo-Fraenkel set theory is based on the Zermelo-Fraenkel axioms. ...

The Mertens constant B_1, also known as the Hadamard-de la Vallee-Poussin constant, prime reciprocal constant (Bach and Shallit 1996, p. 234), or Kronecker's constant ...

Every odd integer n is a prime or the sum of three primes. This problem is closely related to Vinogradov's theorem.