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Szemerédi's theorem states that every sequence of integers that has positive upper Banach density contains arbitrarily long arithmetic progressions. A corollary states that, ...

The nth taxicab number Ta(n) is the smallest number representable in n ways as a sum of positive cubes. The numbers derive their name from the Hardy-Ramanujan number Ta(2) = ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy ...

The nth k-statistic k_n is the unique symmetric unbiased estimator of the cumulant kappa_n of a given statistical distribution, i.e., k_n is defined so that <k_n>=kappa_n, ...

B-trees were introduced by Bayer (1972) and McCreight. They are a special m-ary balanced tree used in databases because their structure allows records to be inserted, ...

Intuitively, a model of d-dimensional percolation theory is said to be a Bernoulli model if the open/closed status of an area is completely random. In particular, it makes ...

The Cartesian product of two sets A and B (also called the product set, set direct product, or cross product) is defined to be the set of all points (a,b) where a in A and b ...

"Conext 21 polyhedron" is the name given here to the solid underlying the soccer ball of the 2020 Tokyo Olympic Games (held in 2021). It is implemented in the Wolfram ...

"Jabulani polyhedron" is a term introduced here to refer to the polyhedron illustrated above which underlies the shape of the soccer ball used in the 2010 World Cup in South ...