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Given a "good" graph G (i.e., one for which all intersecting graph edges intersect in a single point and arise from four distinct graph vertices), the crossing number is the ...

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 ...

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection (or a squared square). Square dissections in which ...

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 ...

RSA numbers are difficult to-factor composite numbers having exactly two prime factors (i.e., so-called semiprimes) that were listed in the Factoring Challenge of RSA ...

The Tutte 12-cage, also called the Benson graph (Exoo and Jajcay 2008), is the unique 12-cage graph, equivalent to the generalized hexagon GH(2,2) and alternately called the ...

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 xi-function is the function xi(z) = 1/2z(z-1)(Gamma(1/2z))/(pi^(z/2))zeta(z) (1) = ((z-1)Gamma(1/2z+1)zeta(z))/(sqrt(pi^z)), (2) where zeta(z) is the Riemann zeta ...