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A number of attractive 6-compounds of the regular dodecahedron can be constructed. The first (left figures) can be obtained by combining six dodecahedra, each rotated by 1/10 ...

Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no ...

Two quantities are said to be equal if they are, in some well-defined sense, equivalent. Equality of quantities a and b is written a=b. Equal is implemented in the Wolfram ...

Given a subset K of a vector space X, a nonempty subset S subset K is called an extreme set of K if no point of S is an internal point of any line interval whose endpoints ...

The far-out point F of a triangle DeltaABC is the inverse point of the triangle centroid with respect to the circumcircle of DeltaABC. For a triangle with side lengths a, b, ...

The harmonic conjugate to a given function u(x,y) is a function v(x,y) such that f(x,y)=u(x,y)+iv(x,y) is complex differentiable (i.e., satisfies the Cauchy-Riemann ...

A hyperfunction, discovered by Mikio Sato in 1958, is defined as a pair of holomorphic functions (f,g) which are separated by a boundary gamma. If gamma is taken to be a ...

Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with ...

Let P=p:q:r and U=u:v:w be points in trilinear coordinates, neither of which is on a side line of a reference triangle DeltaABC. Them the P-isoconjugate of U is the point ...

A lion and a man in a closed arena have equal maximum speeds. What tactics should the lion employ to be sure of his meal? This problem was stated by Rado in 1925 (Littlewood ...