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Let A={A_1,A_2,...,A_n} be a union-closed set, then the union-closed set conjecture states that an element exists which belongs to at least n/2 of the sets in A. Sarvate and ...

The Dehn invariant is a constant defined using the angles and edge lengths of a three-dimensional polyhedron. It is significant because it remains constant under polyhedron ...

An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn't be a triangle.) A ...

The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric ...

There are several equivalent definitions of a closed set. Let S be a subset of a metric space. A set S is closed if 1. The complement of S is an open set, 2. S is its own set ...

An n-dimensional disk (sometimes spelled "disc") of radius r is the collection of points of distance <=r (closed disk) or <r (open disk) from a fixed point in Euclidean ...

There are two possible definitions: 1. Possessing similarity of form, 2. Continuous, one-to-one, in surjection, and having a continuous inverse. The most common meaning is ...

A four-vector a_mu is said to be timelike if its four-vector norm satisfies a_mua^mu<0. One should note that the four-vector norm is nothing more than a special case of the ...

Given an acute angle in a right triangle, the adjacent side is the leg of the triangle from which the angle to the hypotenuse is measured. Lengths of adjacent and opposite ...

Extend the symmedians of a triangle DeltaA_1A_2A_3 to meet the circumcircle at P_1, P_2, P_3. Then the symmedian point K of DeltaA_1A_2A_3 is also the symmedian point of ...