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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 ...

The product of primes p_n#=product_(k=1)^np_k, (1) with p_n the nth prime, is called the primorial function, by analogy with the factorial function. Its logarithm is closely ...

The abc conjecture is a conjecture due to Oesterlé and Masser in 1985. It states that, for any infinitesimal epsilon>0, there exists a constant C_epsilon such that for any ...

Gaussian primes are Gaussian integers z=a+bi satisfying one of the following properties. 1. If both a and b are nonzero then, a+bi is a Gaussian prime iff a^2+b^2 is an ...

The logarithm of the reciprocal of a number, equal to the negative of the logarithm of the number itself, cologx=log(1/x)=-logx.

A complex translation is a map of the form z|->z+a, where a is a fixed complex number, which corresponds to translation (shifting) of points the complex plane by the complex ...

A dual number is a number x+epsilony, where x,y in R and epsilon is a matrix with the property that epsilon^2=0 (such as epsilon=[0 1; 0 0]).

A number D that possesses no common divisor with a prime number p is either a quadratic residue or nonresidue of p, depending whether D^((p-1)/2) is congruent mod p to +/-1.

The rank of a graph G is defined as r(G)=n-c, where n is the number of vertices on G and c is the number of connected components (Biggs 1993, p. 25).

A flexagon made by folding a strip into adjacent equilateral triangles. The number of states possible in a hexaflexagon is the Catalan number C_5=42.