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Given an arithmetic progression of terms an+b, for n=1, 2, ..., the series contains an infinite number of primes if a and b are relatively prime, i.e., (a,b)=1. This result ...

The toroidal crossing number cr_(1)(G) of a graph G is the minimum number of crossings with which G can be drawn on a torus. A planar graph has toroidal crossing number 0, ...

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...

A pentomino is a 5-polyomino. There are 12 free pentominoes, 18 one-sided pentominoes, and 63 fixed pentominoes. The twelve free pentominoes are known by the letters of the ...

A solution to a problem that can be written in "closed form" in terms of known functions, constants, etc., is often called an analytic solution. Note that this use of the ...

A problem asking for the shortest tour of a graph which visits each edge at least once (Kwan 1962; Skiena 1990, p. 194). For an Eulerian graph, an Eulerian cycle is the ...

A number h which satisfies the conditions of the congruum problem: x^2+h=a^2 and x^2-h=b^2, where x,h,a,b are integers. The list of congrua is given by 24, 96, 120, 240, 336, ...

As used in physics, the term "exact" generally refers to a solution that captures the entire physics and mathematics of a problem as opposed to one that is approximate, ...

In a given acute triangle DeltaABC, find the inscribed triangle whose perimeter is as small as possible. The answer is the orthic triangle of DeltaABC. The problem was ...

The discontinuous solution of the surface of revolution area minimization problem for surfaces connecting two circles. When the circles are sufficiently far apart, the usual ...