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Consider the consecutive number sequences formed by the concatenation of the first n positive integers: 1, 12, 123, 1234, ... (OEIS A007908; Smarandache 1993, Dumitrescu and ...

There are many unsolved problems in mathematics. Several famous problems which have recently been solved include: 1. The Pólya conjecture (disproven by Haselgrove 1958, ...

Somos's quadratic recurrence constant is defined via the sequence g_n=ng_(n-1)^2 (1) with g_0=1. This has closed-form solution ...

Picking two independent sets of points x and y from a unit uniform distribution and placing them at coordinates (x,y) gives points uniformly distributed over the unit square. ...

The standard deviation sigma of a probability distribution is defined as the square root of the variance sigma^2, sigma = sqrt(<x^2>-<x>^2) (1) = sqrt(mu_2^'-mu^2), (2) where ...

The number of cells in a generalized Chinese checkers board (or "centered" hexagram). Unlike the polygonal numbers, there is ambiguity in the case of the star numbers as to ...

The tangent plane to a surface at a point p is the tangent space at p (after translating to the origin). The elements of the tangent space are called tangent vectors, and ...

A tag system is set of rules that specifies a fixed number of elements (commonly denoted nu or beta) be removed from the beginning of a sequence and a set of elements to be ...

The problem of finding the mean triangle area of a triangle with vertices picked inside a triangle with unit area was proposed by Watson (1865) and solved by Sylvester. It ...

The Watkins snark is the snark on 50 vertices ad 75 nodes illustrated above. It is implemented in the Wolfram Language as GraphData["WatkinsSnark"].