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The regular decagon is constructible 10-sided regular polygon with Schläfli symbol {10}. The inradius r, circumradius R, and area can be computed directly from the formulas ...

A shuffle-exchange graph is a nonsimple graph (due to the existence of graph loops) whose vertices are length n binary strings with an edge from w to w^' if 1. w^' differs ...

A 30-sided polygon. The regular triacontagon with side length 1 has inradius r, circumradius R, and area A given by r = 1/4(sqrt(15)+3sqrt(3)+sqrt(2)sqrt(25+11sqrt(5))) (1) R ...

Let F be the set of complex analytic functions f defined on an open region containing the set closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each ...

Borsuk conjectured that it is possible to cut an n-dimensional shape of generalized diameter 1 into n+1 pieces each with diameter smaller than the original. It is true for ...

A moment mu_n of a univariate probability density function P(x) taken about the mean mu=mu_1^', mu_n = <(x-<x>)^n> (1) = int(x-mu)^nP(x)dx, (2) where <X> denotes the ...

Chebyshev-Gauss quadrature, also called Chebyshev quadrature, is a Gaussian quadrature over the interval [-1,1] with weighting function W(x)=(1-x^2)^(-1/2) (Abramowitz and ...

The Coulomb wave function is a special case of the confluent hypergeometric function of the first kind. It gives the solution to the radial Schrödinger equation in the ...

Given a system of ordinary differential equations of the form d/(dt)[x; y; v_x; v_y]=-[0 0 -1 0; 0 0 0 -1; Phi_(xx)(t) Phi_(yx)(t) 0 0; Phi_(xy)(t) Phi_(yy)(t) 0 0][x; y; ...

The geometric mean of a sequence {a_i}_(i=1)^n is defined by G(a_1,...,a_n)=(product_(i=1)^na_i)^(1/n). (1) Thus, G(a_1,a_2) = sqrt(a_1a_2) (2) G(a_1,a_2,a_3) = ...