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The regular tetrahedron, often simply called "the" tetrahedron, is the Platonic solid with four polyhedron vertices, six polyhedron edges, and four equivalent equilateral ...

A tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes (n dimensions) is called a tessellation. Tessellations can be specified using a ...

In antiquity, geometric constructions of figures and lengths were restricted to the use of only a straightedge and compass (or in Plato's case, a compass only; a technique ...

The uniform polyhedra are polyhedra consisting of regular (possibly polygrammic) faces of equal edge length whose polyhedron vertices are all symmetrically equivalent. The ...

Complex Analysis

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

A space D is connected if any two points in D can be connected by a curve lying wholly within D. A space is 0-connected (a.k.a. pathwise-connected) if every map from a ...

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

Let P(z) and Q(z) be univariate polynomials in a complex variable z, and let the polynomial degrees of P and Q satisfy deg(Q)>=deg(P+2). Then int_gamma(P(z))/(Q(z))dz = ...

The regular hexagon is the regular polygon with six sides, as illustrated above. The inradius r, circumradius R, sagitta s, and area A of a regular hexagon can be computed ...