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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 it is possible to transform a coordinate system to a form where the metric elements g_(munu) are constants independent of x^mu, then the space is flat.

The Gauss-Bonnet formula has several formulations. The simplest one expresses the total Gaussian curvature of an embedded triangle in terms of the total geodesic curvature of ...

The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

The inverse of the Laplace transform, given by F(t)=1/(2pii)int_(gamma-iinfty)^(gamma+iinfty)e^(st)f(s)ds, where gamma is a vertical contour in the complex plane chosen so ...

A Maclaurin series is a Taylor series expansion of a function about 0, (1) Maclaurin series are named after the Scottish mathematician Colin Maclaurin. The Maclaurin series ...

A function f in C^infty(R^n) is called a Schwartz function if it goes to zero as |x|->infty faster than any inverse power of x, as do all its derivatives. That is, a function ...

An adaptive Gaussian quadrature method for numerical integration in which error is estimation based on evaluation at special points known as "Kronrod points." By suitably ...

A region in a knot or link projection plane surrounded by a circle such that the knot or link crosses the circle exactly four times. Two tangles are equivalent if a sequence ...

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...