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Simply stated, floating-point arithmetic is arithmetic performed on floating-point representations by any number of automated devices. Traditionally, this definition is ...

A set of real numbers x_1, ..., x_n is said to possess an integer relation if there exist integers a_i such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. For ...

Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...

Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...

A parabola (plural "parabolas"; Gray 1997, p. 45) is the set of all points in the plane equidistant from a given line L (the conic section directrix) and a given point F not ...

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 ...

A simple graph, also called a strict graph (Tutte 1998, p. 2), is an unweighted, undirected graph containing no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, ...

The spherical harmonics Y_l^m(theta,phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. Some ...

Vassiliev invariants, discovered around 1989, provided a radically new way of looking at knots. The notion of finite type (a.k.a. Vassiliev) knot invariants was independently ...

The associated Legendre polynomials P_l^m(x) and P_l^(-m)(x) generalize the Legendre polynomials P_l(x) and are solutions to the associated Legendre differential equation, ...