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In 1638, Fermat proposed that every positive integer is a sum of at most three triangular numbers, four square numbers, five pentagonal numbers, and n n-polygonal numbers. ...

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

Minkowski space is a four-dimensional space possessing a Minkowski metric, i.e., a metric tensor having the form dtau^2=-(dx^0)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2. Alternatively ...

Cribbage is a game in which each of two players is dealt a hand of six cards. Each player then discards two of his six cards to a four-card "crib" which alternates between ...

There are many unsolved problems in mathematics. Several famous problems which have recently been solved include: 1. The Pólya conjecture (disproven by Haselgrove 1958, ...

In Note M, Burnside (1955) states, "The contrast that these results shew between groups of odd and of even order suggests inevitably that simple groups of odd order do not ...

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 distance-heredity graph, also known as a completely separable graph, is a graph G such that the distance matrix of every connected vertex-induced subgraph G_V of G is the ...

The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. The idea for quaternions occurred to him while he was walking along ...

The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the ...