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The prime spiral, also known as Ulam's spiral, is a plot in which the positive integers are arranged in a spiral (left figure), with primes indicated in some way along the ...

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

The Fibonacci numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation F_n=F_(n-1)+F_(n-2) (1) with F_1=F_2=1. As a result of the ...

There are several statistical quantities called means, e.g., harmonic mean, geometric mean, arithmetic-geometric mean, and root-mean-square. When applied to two elements a ...

The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

A random matrix is a matrix of given type and size whose entries consist of random numbers from some specified distribution. Random matrix theory is cited as one of the ...

When the elliptic modulus k has a singular value, the complete elliptic integrals may be computed in analytic form in terms of gamma functions. Abel (quoted in Whittaker and ...

Clausen's _4F_3 identity _4F_3(a,b,c,d; e,f,g;1)=((2a)_(|d|)(a+b)_(|d|)(2b)_(|d|))/((2a+2b)_(|d|)a_(|d|)b_(|d|)), (1) holds for a+b+c-d=1/2, e=a+b+1/2, a+f=d+1=b+g, where d a ...

Pairs of partitions for a single number whose Ferrers diagrams transform into each other when reflected about the line y=-x, with the coordinates of the upper left dot taken ...

Let a Gram point g_n be called "good" if (-1)^nZ(g_n)>0, and "bad" otherwise (Rosser et al. 1969; Edwards 2001, p. 180). Then the interval between two consecutive good Gram ...