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The van Aubel line is the line in the plane of a reference triangle that connects the orthocenter H and symmedian point K, and symmedian point of the orthic triangle. The ...

Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

van der Waerden's theorem is a theorem about the existence of arithmetic progressions in sets. The theorem can be stated in four equivalent forms. 1. If N=C_1 union C_2 union ...

von Neumann-Bernays-Gödel set theory (abbreviated "NBG") is a version of set theory which was designed to give the same results as Zermelo-Fraenkel set theory, but in a more ...

Given a Hilbert space H, a *-subalgebra A of B(H) is said to be a von Neumann algebra in H provided that A is equal to its bicommutant A^('') (Dixmier 1981). Here, B(H) ...

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 ...

Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...

Pascal's triangle is a number triangle with numbers arranged in staggered rows such that a_(nr)=(n!)/(r!(n-r)!)=(n; r), (1) where (n; r) is a binomial coefficient. The ...

A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection (or a squared square). Square dissections in which ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...