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A quantity which takes on the value zero is said to vanish identically, or sometimes simply to vanish. The term "vanish identically" is preferred when emphasis is needed that ...

A method for constructing magic squares of odd order, also called the Siamese method.

Given a number field K, a Galois extension field L, and prime ideals p of K and P of L unramified over p, there exists a unique element sigma=((L/K),P) of the Galois group ...

Let C=C^+ union C^- (where C^+ intersection C^-=emptyset) be the disjoint union of two finite components C^+ and C^-. Let alpha and beta be two involutions on C, each of ...

The limaçon trisectrix is a trisectrix that is a special case of the rose curve with n=1/3 (possibly with translation, rotation, and scaling). It was studied by Archimedes, ...

If a group of men and women may date only if they have previously been introduced, then a complete set of dates is possible iff every subset of men has collectively been ...

The Napoleon-Feuerbach cubic is the pivotal isogonal cubic with nine-point center N as the pivot point. It therefore has trilinear equation ...

A set A of integers is productive if there exists a partial recursive function f such that, for any x, the following holds: If the domain of phi_x is a subset of A, then f(x) ...

A row-convex polyomino is a self-avoiding convex polyomino such that the intersection of any horizontal line with the polyomino has at most two connected components. A ...

Let X be a set. Then a sigma-algebra F is a nonempty collection of subsets of X such that the following hold: 1. X is in F. 2. If A is in F, then so is the complement of A. ...