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A rigorous mathematical argument which unequivocally demonstrates the truth of a given proposition. A mathematical statement that has been proven is called a theorem. ...

A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic ...

A Riemann surface is a surface-like configuration that covers the complex plane with several, and in general infinitely many, "sheets." These sheets can have very complicated ...

Roman numerals are a system of numerical notations used by the Romans. They are an additive (and subtractive) system in which letters are used to denote certain "base" ...

A rooted tree is a tree in which a special ("labeled") node is singled out. This node is called the "root" or (less commonly) "eve" of the tree. Rooted trees are equivalent ...

Rule 30 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

A regular graph that is edge-transitive but not vertex-transitive is called a semisymmetric graph (Marušič and Potočnik 2001). In contrast, any graph that is both ...

Stellation is the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect (Wenninger 1989). The ...

The nth subfactorial (also called the derangement number; Goulden and Jackson 1983, p. 48; Graham et al. 2003, p. 1050) is the number of permutations of n objects in which no ...

A sultan has granted a commoner a chance to marry one of his n daughters. The commoner will be presented with the daughters one at a time and, when each daughter is ...