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A figurate number which is given by Ptop_n=1/4Te_n(n+3)=1/(24)n(n+1)(n+2)(n+3), where Te_n is the nth tetrahedral number. The first few pentatope numbers are 1, 5, 15, 35, ...

If f is a continuous function that satisfies the Lipschitz condition |f(x,t)-f(y,t)|<=L|x-y| (1) in a surrounding of (x_0,t_0) in Omega subset ...

Plancherel's theorem states that the integral of the squared modulus of a function is equal to the integral of the squared modulus of its spectrum. It corresponds to ...

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 ...

The maximum distance between n points in three dimensions can occur no more than 2n-2 times. Also, there exists a fixed number c such that no distance determined by a set of ...

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 ...

A very general theorem that allows the number of discrete combinatorial objects of a given type to be enumerated (counted) as a function of their "order." The most common ...

A Pólya plot is a plot of the vector field of (R[f(z)],-I[f(z)]) of a complex function f(z). Several examples are shown above. Pólya plots can be created in the Wolfram ...

Let DeltaA^'B^'C^' be the reflection of the orthic triangle of the reference triangle DeltaABC in the nine-point center. Then DeltaA^'B^'C^' and DeltaABC are in perspective, ...

Consider a bivariate normal distribution in variables x and y with covariance rho=rho_(11)=<xy>-<x><y> (1) and an arbitrary function g(x,y). Then the expected value of the ...