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The tetrahedral group T_d is the point group of symmetries of the tetrahedron including the inversion operation. It is one of the 12 non-Abelian groups of order 24. The ...

A golden rhombohedron is a trigonal trapezohedron (and therefore rhombohedron with congruent rhombic faces) whose faces consist of six equal golden rhombi. There are two ...

In the American system, one billion equals 10^9=1000000000. In the French and German systems, one billion equals 10^(12). In recent years, the "American" system has become ...

In Robert Louis Stevenson's "bottle imp paradox," you are offered the opportunity to buy, for whatever price you wish, a bottle containing a genie who will fulfill your every ...

Caesar's method is an encryption scheme involving shifting an alphabet (so a->c, b->d, c->e, d->f, etc., x->z,y->a,z->b). It is one of the most basic encryption methods, and ...

Let X and Y be CW-complexes, and let f:X->Y be a continuous map. Then the cellular approximation theorem states that any such f is homotopic to a cellular map. In fact, if ...

A compactification of a topological space X is a larger space Y containing X which is also compact. The smallest compactification is the one-point compactification. For ...

Let f:R×R->R be a one-parameter family of C^2 map satisfying f(0,0)=0 [(partialf)/(partialx)]_(mu=0,x=0)=0 [(partial^2f)/(partialx^2)]_(mu=0,x=0)>0 ...

Four line geometry is a finite geometry subject to the following three axioms: 1. there exist exactly four lines, 2. any two distinct lines have exactly one point of on both ...

A triple (a,b,c) of positive integers satisfying a<b<c is said to be geometric if ac=b^2. In particular, such a triple is geometric if its terms form a geometric sequence ...