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For any Abelian group G and any natural number n, there is a unique space (up to homotopy type) such that all homotopy groups except for the nth are trivial (including the ...

The center of an inner Soddy circle. It has equivalent triangle center functions alpha = 1+(2Delta)/(a(b+c-a)) (1) alpha = sec(1/2A)cos(1/2B)cos(1/2C)+1, (2) where Delta is ...

An equalizer of a pair of maps f,g:X->Y in a category is a map e:E->X such that 1. f degreese=g degreese, where degrees denotes composition. 2. For any other map e^':E^'->X ...

There exists a triangulation point Y for which the triangles BYC, CYA, and AYB have equal Brocard angles. This point is a triangle center known as the equi-Brocard center and ...

The equilateral cevian triangle point of a triangle is the unique point P such that the Cevian triangle of P is equilateral. This point is Kimberling center X_(370).

The unique even prime number 2. All other primes are odd primes. Humorously, that means 2 is the "oddest" prime of all. The sequence 2, 4, 6, 10, 14, 22, 26, 34, 38, ... ...

Given a field F and an extension field K superset= F, if alpha in K is an algebraic element over F, the minimal polynomial of alpha over F is the unique monic irreducible ...

For any nonzero lambda in C, either 1. The equation Tv-lambdav=0 has a nonzero solution v, or 2. The equation Tv-lambdav=f has a unique solution v for any function f. In the ...

When referring to a planar object, "free" means that the object is regarded as capable of being picked up out of the plane and flipped over. As a result, mirror images are ...

The game of life is the best-known two-dimensional cellular automaton, invented by John H. Conway and popularized in Martin Gardner's Scientific American column starting in ...