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A Pisot number is a positive algebraic integer greater than 1 all of whose conjugate elements have absolute value less than 1. A real quadratic algebraic integer greater than ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...

A quadrilateral, sometimes also known as a tetragon or quadrangle (Johnson 1929, p. 61) is a four-sided polygon. If not explicitly stated, all four polygon vertices are ...

The resistance distance between vertices i and j of a graph G is defined as the effective resistance between the two vertices (as when a battery is attached across them) when ...

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

The m×n knight graph is a graph on mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a knight (which may ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

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 ...