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A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. For example, the point is a degenerate case of the circle as ...

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 ...

The Delaunay triangulation is a triangulation which is equivalent to the nerve of the cells in a Voronoi diagram, i.e., that triangulation of the convex hull of the points in ...

A delay differential equation (also called a differential delay equation or difference-differential equation, although the latter term has a different meaning in the modern ...

Amazingly, the catacaustic of the deltoid when the rays are parallel in any direction is an astroid. In particular, for a deltoid with parametric equations x = 2cost+cos(2t) ...

A Julia set with constant c chosen at the boundary of the Mandelbrot set (Branner 1989; Dufner et al. 1998, p. 225). The image above was computed using c=i.

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 ...

Given a polygon with an even number of sides, the derived polygon is obtained by joining the points which are a fractional distance r along each side. If r=1/2, then the ...

Togliatti surfaces are quintic surfaces having the maximum possible number of ordinary double points (31). A related surface sometimes known as the dervish can be defined by ...