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The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

The Koch snowflake is a fractal curve, also known as the Koch island, which was first described by Helge von Koch in 1904. It is built by starting with an equilateral ...

The Kronecker symbol is an extension of the Jacobi symbol (n/m) to all integers. It is variously written as (n/m) or (n/m) (Cohn 1980; Weiss 1998, p. 236) or (n|m) (Dickson ...

The lemniscate, also called the lemniscate of Bernoulli, is a polar curve defined as the locus of points such that the the product of distances from two fixed points (-a,0) ...

A one-person game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling ...

The plots above show the values of the function obtained by taking the natural logarithm of the gamma function, lnGamma(z). Note that this introduces complicated branch cut ...

A magic cube is an n×n×n version of a magic square in which the n^2 rows, n^2 columns, n^2 pillars, and four space diagonals each sum to a single number M_3(n) known as the ...

A magic tesseract is a four-dimensional generalization of the two-dimensional magic square and the three-dimensional magic cube. A magic tesseract has magic constant ...

The Mangoldt function is the function defined by Lambda(n)={lnp if n=p^k for p a prime; 0 otherwise, (1) sometimes also called the lambda function. exp(Lambda(n)) has the ...

Also called the ménage problem. In how many ways can n married couples be seated around a circular table in such a manner than there is always one man between two women and ...