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Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

An alternating permutation is an arrangement of the elements c_1, ..., c_n such that no element c_i has a magnitude between c_(i-1) and c_(i+1) is called an alternating (or ...

The backward difference is a finite difference defined by del _p=del f_p=f_p-f_(p-1). (1) Higher order differences are obtained by repeated operations of the backward ...

A procedure for decomposing an N×N matrix A into a product of a lower triangular matrix L and an upper triangular matrix U, LU=A. (1) LU decomposition is implemented in the ...

The base-4 method of counting in which only the digits 0, 1, 2, and 3 are used. The illustration above shows the numbers 0 to 63 represented in quaternary, and the following ...

Zeno's paradoxes are a set of four paradoxes dealing with counterintuitive aspects of continuous space and time. 1. Dichotomy paradox: Before an object can travel a given ...

A usually simple algorithm or identity. The term is frequently applied to specific orders of Newton-Cotes formulas. The designation "rule n" is also given to the nth ...

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 ...

The improvement of the convergence properties of a series, also called convergence acceleration or accelerated convergence, such that a series reaches its limit to within ...

The difference of two numbers n_1 and n_2 is n_1-n_2, where the minus sign denotes subtraction.