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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 ...

In algebraic topology, the Reidemeister torsion is a notion originally introduced as a topological invariant of 3-manifolds which has now been widely adapted to a variety of ...

An elliptic curve is the set of solutions to an equation of the form y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6. (1) By changing variables, y->2y+a_1x+a_3, assuming the field ...

The residue classes of a function f(x) mod n are all possible values of the residue f(x) (mod n). For example, the residue classes of x^2 (mod 6) are {0,1,3,4}, since 0^2=0 ...

There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio ...

The complex numbers are the field C of numbers of the form x+iy, where x and y are real numbers and i is the imaginary unit equal to the square root of -1, sqrt(-1). When a ...

The cube-connected cycle graph of order n is the graph obtained by replacing each vertex in a n-dimensional hypercube by a cycle of length n. They were introduced by ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

The function frac(x) giving the fractional (noninteger) part of a real number x. The symbol {x} is sometimes used instead of frac(x) (Graham et al. 1994, p. 70; Havil 2003, ...

The Cartesian graph product G=G_1 square G_2, also called the graph box product and sometimes simply known as "the" graph product (Beineke and Wilson 2004, p. 104) and ...