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Degen's eight-square identity is the incredible polynomial identity (1) found around 1818 by the Danish mathematician Ferdinand Degen (1766-1825). It was subsequently ...

The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...

Given a set X, let F be a nonempty set of subsets of X. Then F is a ring if, for every pair of sets in F, the intersection, union, and set difference is also in F. F is ...

In continuum theory, a dendrite is a locally connected continuum that contains no simple closed curve. A semicircle is therefore a dendrite, while a triangle is not. The term ...

Let f be a finite real-valued function defined on an interval [a,b]. Then at every point in [a,b] except on a set of Lebesgue measure zero, either: 1. There is a finite ...

A dependent variable is a variable whose value depends on the values of one or more other independent variables. This notion comes up regularly in a variety of contexts. In ...

The descending chain condition, commonly abbreviated "D.C.C.," is the dual notion of the ascending chain condition. The descending chain condition for a partially ordered set ...

Let DeltaA^'B^'C^' be a triangle perspective to a reference triangle DeltaABC with perspector D^(''). Let A^('') be the intersection of lines BC^' and CB^', B^('') the ...

A developable surface, also called a flat surface (Gray et al. 2006, p. 437), is a ruled surface having Gaussian curvature K=0 everywhere. Developable surfaces therefore ...

If A=(a_(ij)) is a diagonal matrix, then Q(v)=v^(T)Av=suma_(ii)v_i^2 (1) is a diagonal quadratic form, and Q(v,w)=v^(T)Aw is its associated diagonal symmetric bilinear form. ...