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A theory is decidable iff there is an algorithm which can determine whether or not any sentence r is a member of the theory.

A complete oriented graph (Skiena 1990, p. 175), i.e., a graph in which every pair of nodes is connected by a single uniquely directed edge. The first and second 3-node ...

There are several attractive polyhedron compounds consisting of three cubes. The first (left figures) arises by joining three cubes such that each shares two C_2 axes (Holden ...

There are (at least) three types of Euler transforms (or transformations). The first is a set of transformations of hypergeometric functions, called Euler's hypergeometric ...

The (circular) helicoid is the minimal surface having a (circular) helix as its boundary. It is the only ruled minimal surface other than the plane (Catalan 1842, do Carmo ...

A Diophantine problem (i.e., one whose solution must be given in terms of integers) which seeks a solution to the following problem. Given n men and a pile of coconuts, each ...

A second-order algebraic surface given by the general equation (1) Quadratic surfaces are also called quadrics, and there are 17 standard-form types. A quadratic surface ...

There are a number of equations known as the Riccati differential equation. The most common is z^2w^('')+[z^2-n(n+1)]w=0 (1) (Abramowitz and Stegun 1972, p. 445; Zwillinger ...

"The" Smarandache constant is the smallest solution to the generalized Andrica's conjecture, x approx 0.567148 (OEIS A038458). The first Smarandache constant is defined as ...

The triangle line that passes through the inner and outer Soddy centers S and S^'. The Soddy line is central line L_(657) and has trilinear equation ...