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Betti numbers are topological objects which were proved to be invariants by Poincaré, and used by him to extend the polyhedral formula to higher dimensional spaces. ...

A Liouville number is a transcendental number which has very close rational number approximations. An irrational number beta is called a Liouville number if, for each n, ...

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

A Münchhausen number (sometimes spelled Münchausen number, with a single 'h') is a number equal to the sum of its digits raised to each digit's power. Münchhausen numbers ...

An even perfect number is perfect number that is even, i.e., an even number n whose sum of divisors (including n itself) equals n. All known perfect numbers are even, and ...

A generalization of Poncelet's continuity principle made by H. Schubert in 1874-1879. The conservation of number principle asserts that the number of solutions of any ...

666 is the occult "number of the beast," also called the "sign of the devil" (Wang 1994), associated in the Bible with the Antichrist. It has figured in many numerological ...

The smallest number of times u(K) a knot K must be passed through itself to untie it. Lower bounds can be computed using relatively straightforward techniques, but it is in ...

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 ...

The values of -d for which imaginary quadratic fields Q(sqrt(-d)) are uniquely factorable into factors of the form a+bsqrt(-d). Here, a and b are half-integers, except for ...