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Consider the average volume of a tetrahedron picked at random inside an octahedron of unit volume. The answer is difficult to compute analytically (Zinani 2003), but the mean ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

A polygonal diagonal is a line segment connecting two nonadjacent polygon vertices of a polygon. The number of ways a fixed convex n-gon can be divided into triangles by ...

A set S and a binary operator * are said to exhibit closure if applying the binary operator to two elements S returns a value which is itself a member of S. The closure of a ...

A number of attractive 12-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

There are no fewer than three distinct notions of curve throughout mathematics. In topology, a curve is a one-dimensional continuum (Charatonik and Prajs 2001). In algebraic ...

A cylindrical wedge, also called a cylindrical hoof or cylindrical ungula, is a wedge cut from a cylinder by slicing with a plane that intersects the base of the cylinder. ...

Approximants derived by expanding a function as a ratio of two power series and determining both the numerator and denominator coefficients. Padé approximations are usually ...

The Pell graph Pi_n is the graph defined as follows. Consider n-tuples of (0,1,2) such that maximal blocks of an odd number of 2's are forbidden. Take these as the vertices ...

The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity of a ...