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An O(nlgn) sorting algorithm which is not quite as fast as quicksort. It is a "sort-in-place" algorithm and requires no auxiliary storage, which makes it particularly concise ...

The 21 assumptions which underlie the geometry published in Hilbert's classic text Grundlagen der Geometrie. The eight incidence axioms concern collinearity and intersection ...

The illustrations above show a number of hyperbolic tilings, including the heptagonal once related to the Klein quartic. Escher was fond of depicting hyperbolic tilings, ...

The expected value B_n(s) of r^s from a fixed vertex of a unit n-cube to a point picked at random in the interior of the hypercube is given by B_n(s) = ...

A set of elements S is said to be infinite if the elements of a proper subset S^' can be put into one-to-one correspondence with the elements of S. An infinite set whose ...

The branch of mathematics dealing with the efficient and accurate storage, transmission, and representation of information.

Let (A,<=) be a well ordered set. Then the set {a in A:a<k} for some k in A is called an initial segment of A (Rubin 1967, p. 161; Dauben 1990, pp. 196-197; Moore 1982, pp. ...

In univariate interpolation, an interpolant is a function L=L(x) which agrees with a particular function f at a set of known points x_0,x_1,x_2,...,x_n and which is used to ...

Jung's theorem states that the generalized diameter D of a compact set X in R^n satisfies D>=Rsqrt((2(n+1))/n), where R is the circumradius of X (Danzer et al. 1963). This ...

An algorithm in control theory introduced by Kalman (1960) and refined by Kalman and Bucy (1961). It is an algorithm which makes optimal use of imprecise data on a linear (or ...