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A board is a subset of the polygons determined by a number of (usually regularly spaced and oriented) lines. These polygons form the spaces on which "pieces" can be placed ...

A class formed by sets in R^n which have essentially the same structure, regardless of size, shape and dimension. The "essential structure" is what a set keeps when it is ...

A number of the form 2^n that contains the digits 666 (i.e., the beast number) is called an apocalyptic number. 2^(157) is an apocalyptic number. The first few such powers ...

A Brier number is a number that is both a Riesel number and a Sierpiński number of the second kind, i.e., a number n such that for all k>=1, the numbers n·2^k+1 and n·2^k-1 ...

Find consecutive powers, i.e., solutions to x^p-y^q=+/-1, excluding 0 and 1. Catalan's conjecture states that the only solution is 3^2-2^3=1, so 8 and 9 (2^3 and 3^2) are the ...

A circle bundle pi:E->M is a fiber bundle whose fibers pi^(-1)(x) are circles. It may also have the structure of a principal bundle if there is an action of SO(2) that ...

A sequence {a_j} of positive integers is called an iteration sequence if there exists a strictly increasing sequence {s_k} of positive integers such that a_1=s_1>=2 and ...

As Gauss showed in 1812, the hyperbolic tangent can be written using a continued fraction as tanhx=x/(1+(x^2)/(3+(x^2)/(5+...))) (Wall 1948, p. 349; Olds 1963, p. 138).

Let f and g be nonnegative and continuous functions on the closed interval [a,b], then the solid of revolution obtained by rotating the curves f(x) and g(x) about the x-axis ...

A patch (also called a local surface) is a differentiable mapping x:U->R^n, where U is an open subset of R^2. More generally, if A is any subset of R^2, then a map x:A->R^n ...