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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 ...

Given a Poisson process, the probability of obtaining exactly n successes in N trials is given by the limit of a binomial distribution P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n). ...

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 ...

The primitive part of a polynomial P(x) is P(x)/k, where k is the content. For a general univariate polynomial P(x), the Wolfram Language function FactorTermsList[poly, x] ...

If there is no integer 0<x<p such that x^2=q (mod p), i.e., if the congruence (35) has no solution, then q is said to be a quadratic nonresidue (mod p). If the congruence ...