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A number of attractive cube 10-compounds can be constructed. The first can be obtained by beginning with an initial cube and rotating it by an angle theta=sin^(-1)(sqrt(3/8)) ...

Given triangle DeltaA_1A_2A_3, let the point of intersection of A_2Omega and A_3Omega^' be B_1, where Omega and Omega^' are the Brocard points, and similarly define B_2 and ...

Let N samples be taken from a population with central moments mu_n. The sample variance m_2 is then given by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ is the sample mean. ...

A fundamental result of de Rham cohomology is that the kth de Rham cohomology vector space of a manifold M is canonically isomorphic to the Alexander-Spanier cohomology ...

An initial point that provides safe convergence of Newton's method (Smale 1981; Petković et al. 1997, p. 1).

The Chern number is defined in terms of the Chern class of a manifold as follows. For any collection Chern classes such that their cup product has the same dimension as the ...

A node which is one graph edge further away from a given node in a rooted tree.

A solitaire game played with cards. The chance of winning is 1/13, and the arithmetic mean of the number of cards turned up is 42.4.

The property of being continuous.

Suppose that X^~,X are arcwise-connected and locally arcwise-connected topological spaces. Then (X^~,p) is said to be a covering space of X if p:X^~->X is a surjective ...