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The 5.1.2 fifth-order Diophantine equation A^5=B^5+C^5 (1) is a special case of Fermat's last theorem with n=5, and so has no solution. improving on the results on Lander et ...

The Feigenbaum constant delta is a universal constant for functions approaching chaos via period doubling. It was discovered by Feigenbaum in 1975 (Feigenbaum 1979) while ...

The regular polygon of 17 sides is called the heptadecagon, or sometimes the heptakaidecagon. Gauss proved in 1796 (when he was 19 years old) that the heptadecagon is ...

Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

There are four varieties of Airy functions: Ai(z), Bi(z), Gi(z), and Hi(z). Of these, Ai(z) and Bi(z) are by far the most common, with Gi(z) and Hi(z) being encountered much ...

The Alexander polynomial is a knot invariant discovered in 1923 by J. W. Alexander (Alexander 1928). The Alexander polynomial remained the only known knot polynomial until ...

The number obtained by adding the reciprocals of the odd twin primes, B=(1/3+1/5)+(1/5+1/7)+(1/(11)+1/(13))+(1/(17)+1/(19))+.... (1) By Brun's theorem, the series converges ...