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An algorithm which can be used to find integer relations between real numbers x_1, ..., x_n such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. Although the algorithm ...

Inspired by computer simulations of fossilized worms trails published by Raup and Seilacher (1969), computer scientist Mike Paterson at the University of Warwick and ...

The Pell numbers are the numbers obtained by the U_ns in the Lucas sequence with P=2 and Q=-1. They correspond to the Pell polynomial P_n(x) and Fibonacci polynomial F_n(x) ...

The Penrose triangle, also called the tribar (Cerf), tri-bar (Ernst 1987), impossible tribar (Pappas 1989, p. 13), or impossible triangle, is an impossible figure published ...

The permanent is an analog of a determinant where all the signs in the expansion by minors are taken as positive. The permanent of a matrix A is the coefficient of x_1...x_n ...

Plouffe's constants are numbers arising in summations of series related to r_n=f(2^n) where f is a trigonometric function. Define the Iverson bracket function rho(x)={1 for ...

Let p(d) be the probability that a random walk on a d-D lattice returns to the origin. In 1921, Pólya proved that p(1)=p(2)=1, (1) but p(d)<1 (2) for d>2. Watson (1939), ...

Circumscribe a triangle about a circle, another circle around the triangle, a square outside the circle, another circle outside the square, and so on. The circumradius and ...

The Pratt certificate is a primality certificate based on Fermat's little theorem converse. Prior to the work of Pratt (1975), the Lucas-Lehmer test had been regarded purely ...

A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...