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The median of a statistical distribution with distribution function D(x) is the value x such D(x)=1/2. For a symmetric distribution, it is therefore equal to the mean. Given ...

Taylor's theorem states that any function satisfying certain conditions may be represented by a Taylor series, Taylor's theorem (without the remainder term) was devised by ...

The thin plate spline is the two-dimensional analog of the cubic spline in one dimension. It is the fundamental solution to the biharmonic equation, and has the form ...

The de Longchamps point L is the reflection of the orthocenter H about the circumcenter O of a triangle. It has triangle center function alpha=cosA-cosBcosC, (1) and is ...

Informally, an elliptic curve is a type of cubic curve whose solutions are confined to a region of space that is topologically equivalent to a torus. The Weierstrass elliptic ...

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...

The Brocard circle, also known as the seven-point circle, is the circle having the line segment connecting the circumcenter O and symmedian point K of a triangle DeltaABC as ...

There are no fewer than three distinct notions of curve throughout mathematics. In topology, a curve is a one-dimensional continuum (Charatonik and Prajs 2001). In algebraic ...

A formula for the Bell polynomial and Bell numbers. The general formula states that B_n(x)=e^(-x)sum_(k=0)^infty(k^n)/(k!)x^k, (1) where B_n(x) is a Bell polynomial (Roman ...

The set of terms of first-order logic (also known as first-order predicate calculus) is defined by the following rules: 1. A variable is a term. 2. If f is an n-place ...