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A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

A dissection fallacy is an apparent paradox arising when two plane figures with different areas seem to be composed by the same finite set of parts. In order to produce this ...

The dodecadodecahedron is the uniform polyhedron with Maeder index 36 (Maeder 1997), Wenninger index 73 (Wenninger 1989), Coxeter index 45 (Coxeter et al. 1954), and Har'El ...

A double-toroidal graph is a graph with graph genus 2 (West 2000, p. 266). Planar and toroidal graphs are therefore not double-toroidal. Some known double-toroidal graphs on ...

The generalized Gell-Mann matrices are the n^2-1 matrices generating the Lie algebra associated to the special unitary group SU(n), n>=2. As their name suggests, these ...

The polar sine is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the lengths of the n edges of the ...

Informally, an L^2-function is a function f:X->R that is square integrable, i.e., |f|^2=int_X|f|^2dmu with respect to the measure mu, exists (and is finite), in which case ...

The augmented sphenocorona is Johnson solid J_(87), which is formed from augmentation of one of the square faces of the sphenocorona by an equilateral square pyramid. The ...

The augmented truncated tetrahedron is Johnson solid J_(66) constructed by affixing a square cupola to one of the octagonal faces of a truncated cube such that the cupola's ...

A fake knot (i.e., a knot equivalent to the unknot) created by tying a square knot, then looping one end twice through the knot such that when both ends are pulled, the knot ...