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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 ...

Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, ...

A random number is a number chosen as if by chance from some specified distribution such that selection of a large set of these numbers reproduces the underlying ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

In general, a tetrahedron is a polyhedron with four sides. If all faces are congruent, the tetrahedron is known as an isosceles tetrahedron. If all faces are congruent to an ...

The Weierstrass elliptic functions (or Weierstrass P-functions, voiced "p-functions") are elliptic functions which, unlike the Jacobi elliptic functions, have a second-order ...

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 ...

Geometry

Just as many interesting integer sequences can be defined and their properties studied, it is often of interest to additionally determine which of their elements are prime. ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...