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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 arithmetic-geometric mean agm(a,b) of two numbers a and b (often also written AGM(a,b) or M(a,b)) is defined by starting with a_0=a and b_0=b, then iterating a_(n+1) = ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...

The sum-of-factorial powers function is defined by sf^p(n)=sum_(k=1)^nk!^p. (1) For p=1, sf^1(n) = sum_(k=1)^(n)k! (2) = (-e+Ei(1)+pii+E_(n+2)(-1)Gamma(n+2))/e (3) = ...

There are a number of algebraic equations known as the icosahedral equation, all of which derive from the projective geometry of the icosahedron. Consider an icosahedron ...

The Pochhammer symbol (x)_n = (Gamma(x+n))/(Gamma(x)) (1) = x(x+1)...(x+n-1) (2) (Abramowitz and Stegun 1972, p. 256; Spanier 1987; Koepf 1998, p. 5) for n>=0 is an ...

Square triangle picking is the selection of triples of points (corresponding to endpoints of a triangle) randomly placed inside a square. n random triangles can be picked in ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...

Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects ...