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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 ...

The distribution with probability density function and distribution function P(x) = (ab^a)/(x^(a+1)) (1) D(x) = 1-(b/x)^a (2) defined over the interval x>=b. It is ...

The Pell polynomials P(x) are the W-polynomials generated by the Lucas polynomial sequence using the generator p(x)=2x, q(x)=1. This gives recursive equations for P(x) from ...

The pentagonal orthocupolarotunda is a convex equilateral solid that is Johnson solid J_(32). The unit pentagonal orthocupolarotunda has volume V=1/3(5+4sqrt(5)) (1) and Dehn ...

The pentagonal prism is a prism having two pentagonal bases and five rectangular sides. It is a heptahedron. The regular right pentagonal prism is uniform polyhedron U_(76). ...

A permutation matrix is a matrix obtained by permuting the rows of an n×n identity matrix according to some permutation of the numbers 1 to n. Every row and column therefore ...

A vector perpendicular to a given vector a is a vector a^_|_ (voiced "a-perp") such that a and a^_|_ form a right angle. In the plane, there are two vectors perpendicular to ...

A plesiohedron is the Voronoi cell of a so-called symmetric Delone set. Plesiohedra are space-filling polyhedra which have special symmetries that take any copy of the ...

Given a set of ordered quantities, a list of the fractions of values at or below each quantity is know as a plotting position. A quantile-quantile plot compares observed ...

Let Omega be an open, bounded, and connected subset of R^d for some d and let dx denote d-dimensional Lebesgue measure on R^d. In functional analysis, the Poincaré inequality ...