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An equilateral zonohedron is a zonohedron in which the line segments of the star on which it is based are of equal length (Coxeter 1973, p. 29). Plate II (following p. 32 of ...

The Gaussian integral, also called the probability integral and closely related to the erf function, is the integral of the one-dimensional Gaussian function over ...

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 ...

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

Green's theorem is a vector identity which is equivalent to the curl theorem in the plane. Over a region D in the plane with boundary partialD, Green's theorem states ...

A measure lambda is absolutely continuous with respect to another measure mu if lambda(E)=0 for every set with mu(E)=0. This makes sense as long as mu is a positive measure, ...

Given a regular surface M, an asymptotic curve is formally defined as a curve x(t) on M such that the normal curvature is 0 in the direction x^'(t) for all t in the domain of ...

The differential equation obtained by applying the biharmonic operator and setting to zero: del ^4phi=0. (1) In Cartesian coordinates, the biharmonic equation is del ^4phi = ...

A set of curvilinear coordinates defined by x = (asinhv)/(coshv-cosu) (1) y = (asinu)/(coshv-cosu) (2) z = z, (3) where u in [0,2pi), v in (-infty,infty), and z in ...

Two geometric figures are said to be concentric if their centers coincide. The region between two concentric circles is called an annulus. The following table summarizes some ...