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The Hanoi graph H_n corresponding to the allowed moves in the tower of Hanoi problem. The above figure shows the Hanoi graphs for small n. The Hanoi graph H_n can be ...

The happy end problem, also called the "happy ending problem," is the problem of determining for n>=3 the smallest number of points g(n) in general position in the plane ...

The series sum_(k=1)^infty1/k (1) is called the harmonic series. It can be shown to diverge using the integral test by comparison with the function 1/x. The divergence, ...

In a 1847 talk to the Académie des Sciences in Paris, Gabriel Lamé (1795-1870) claimed to have proven Fermat's last theorem. However, Joseph Liouville immediately pointed out ...

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 ...

Let S(x) denote the number of positive integers not exceeding x which can be expressed as a sum of two squares (i.e., those n<=x such that the sum of squares function ...

A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving ...

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) ...