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A subset is a portion of a set. B is a subset of A (written B subset= A) iff every member of B is a member of A. If B is a proper subset of A (i.e., a subset other than the ...

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 famous perceptual illusion in which the brain switches between seeing a young girl and an old woman (or "wife" and "mother in law"). An anonymous German postcard from 1888 ...

An integer whose decimal digits contain no zeros is said to be zerofree. The first few positive zerofree integers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, ...

A Hadamard matrix is a type of square (-1,1)-matrix invented by Sylvester (1867) under the name of anallagmatic pavement, 26 years before Hadamard (1893) considered them. In ...

The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and Parker 1997, p. 125) that has no inside or outside, originally described by Felix ...

A polyomino is a generalization of the domino to a collection of n squares of equal size arranged with coincident sides. Polyominos were originally called "super-dominoes" by ...

A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...

Catalan's constant is a constant that commonly appears in estimates of combinatorial functions and in certain classes of sums and definite integrals. It is usually denoted K ...