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A random polygon is a polygon generated in some random way. Kendall conjectured that the shape of a random polygon is close to a disk as the area of the polygon becomes large ...

A pair of zips, each zip being half a zipper, which can be zippered up to close a surface along a curve. The concept of a zip-pair can be extremely useful in topological ...

Given integers a and b with close to 2n bits each, the half-GCD of a and b is a 2×2 matrix [u v; u^' v^'] with determinant equal to -1 or 1 such that ua+vb=r and ...

In 1611, Kepler proposed that close packing (either cubic or hexagonal close packing, both of which have maximum densities of pi/(3sqrt(2)) approx 74.048%) is the densest ...

Let K be a class of topological spaces that is closed under homeomorphism, and let X be a topological space. If X in K and for every Y in K such that X subset= Y, X is a ...

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

Using a Chebyshev polynomial of the first kind T(x), define c_j = 2/Nsum_(k=1)^(N)f(x_k)T_j(x_k) (1) = 2/Nsum_(k=1)^(N)f[cos{(pi(k-1/2))/N}]cos{(pij(k-1/2))/N}. (2) Then f(x) ...

With a large enough sample, any outrageous thing is likely to happen (Diaconis and Mosteller 1989). Littlewood (1986) considered an event which occurs one in a million times ...

A Liouville number is a transcendental number which has very close rational number approximations. An irrational number beta is called a Liouville number if, for each n, ...

The function z=f(x)=ln(x/(1-x)). (1) This function has an inflection point at x=1/2, where f^('')(x)=(2x-1)/(x^2(x-1)^2)=0. (2) Applying the logit transformation to values ...