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Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

Define the first Brocard point as the interior point Omega of a triangle for which the angles ∠OmegaAB, ∠OmegaBC, and ∠OmegaCA are equal to an angle omega. Similarly, define ...

A prime partition of a positive integer n>=2 is a set of primes p_i which sum to n. For example, there are three prime partitions of 7 since 7=7=2+5=2+2+3. The number of ...

The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the ...

A binary tree is a tree-like structure that is rooted and in which each vertex has at most two children and each child of a vertex is designated as its left or right child ...

The complete elliptic integral of the first kind K(k), illustrated above as a function of the elliptic modulus k, is defined by K(k) = F(1/2pi,k) (1) = ...

For a bivariate normal distribution, the distribution of correlation coefficients is given by P(r) = (1) = (2) = (3) where rho is the population correlation coefficient, ...

A double Mersenne number is a number of the form M_(M_n)=2^(2^n-1)-1, where M_n is a Mersenne number. The first few double Mersenne numbers are 1, 7, 127, 32767, 2147483647, ...

A Gaussian integer is a complex number a+bi where a and b are integers. The Gaussian integers are members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often ...

The inverse hyperbolic secant sech^(-1)z (Beyer 1987, p. 181; Zwillinger 1995, p. 481), sometimes called the area hyperbolic secant (Harris and Stocker 1998, p. 271) and ...