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A requirement necessary for a given statement or theorem to hold. Also called a condition.

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

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...

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 group acts freely if there are no group fixed points. A point which is fixed by every group element would not be free to move.

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 Schur number S(k) is the largest integer n for which the interval [1,n] can be partitioned into k sum-free sets (Fredricksen and Sweet 2000). S(k) is guaranteed to exist ...

Seeks to obtain the best numerical estimate of an integral by picking optimal abscissas x_i at which to evaluate the function f(x). The fundamental theorem of Gaussian ...

The free part of the homology group with a domain of coefficients in the group of integers (if this homology group is finitely generated).

A hexomino is a 6-polyomino. There are 35 free hexominoes (illustrated above), 60 one-sided hexominoes, and 216 fixed hexominoes.