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A New Kind of Science is a seminal work on simple programs by Stephen Wolfram. In 1980, Wolfram's studies found unexpected behavior in a collection of simple computer ...

Newton's forward difference formula is a finite difference identity giving an interpolated value between tabulated points {f_p} in terms of the first value f_0 and the powers ...

A surface such as the Möbius strip or Klein bottle (Gray 1997, pp. 322-323) on which there exists a closed path such that the directrix is reversed when moved around this ...

A word is said to be overlapfree if it has no subwords of the form xyxyx. A squarefree word is overlapfree, and an overlapfree word is cubefree. The numbers t(n) of binary ...

An impossible figure in which a stairway in the shape of a square appears to circulate indefinitely while still possessing normal steps (Penrose and Penrose 1958). The Dutch ...

There are at least 15 classes of convex pentagonal tilings, as illustrated above. The first five were discovered during investigations of German mathematician Karl Reinhardt ...

A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a ...

A permutation group is a finite group G whose elements are permutations of a given set and whose group operation is composition of permutations in G. Permutation groups have ...

A polyhedron compound is an arrangement of a number of interpenetrating polyhedra, either all the same or of several distinct types, usually having visually attractive ...

A polynomial discriminant is the product of the squares of the differences of the polynomial roots r_i. The discriminant of a polynomial is defined only up to constant ...