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666 is the occult "number of the beast," also called the "sign of the devil" (Wang 1994), associated in the Bible with the Antichrist. It has figured in many numerological ...

There are at least two results known as "the area principle." The geometric area principle states that (|A_1P|)/(|A_2P|)=(|A_1BC|)/(|A_2BC|). (1) This can also be written in ...

If a plane cuts the sides AB, BC, CD, and DA of a skew quadrilateral ABCD in points P, Q, R, and S, then (AP)/(PB)·(BQ)/(QC)·(CR)/(RD)·(DS)/(SA)=1 both in magnitude and sign ...

Given any triangle ABC, the signed sum of perpendicular distances from the circumcenter O to the sides (i.e., signed lengths of the pedal lines from O) is OO_A+OO_B+OO_C=R+r, ...

Suppose f(x) is continuous at a stationary point x_0. 1. If f^'(x)>0 on an open interval extending left from x_0 and f^'(x)<0 on an open interval extending right from x_0, ...

A folding function is a function that maps the integers Z={...,-3,-2,-1,0,1,2,3,...} onto the nonnegative integers Z^*={0,1,2,3,...}. This type of function arises naturally ...

A set of generators (g_1,...,g_n) is a set of group elements such that possibly repeated application of the generators on themselves and each other is capable of producing ...

When two cycles have a transversal intersection X_1 intersection X_2=Y on a smooth manifold M, then Y is a cycle. Moreover, the homology class that Y represents depends only ...

A link invariant defined for a two-component oriented link as the sum of +1 crossings and -1 crossing over all crossings between the two links divided by 2. For components ...

A Lucas polynomial sequence is a pair of generalized polynomials which generalize the Lucas sequence to polynomials is given by W_n^k(x) = ...