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The great icosahedron, not to be confused with the great icosidodecahedron orgreat icosicosidodecahedron, is the Kepler-Poinsot polyhedronhose dual is the great stellated ...

The inverse cotangent is the multivalued function cot^(-1)z (Zwillinger 1995, p. 465), also denoted arccotz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. ...

Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

The logarithmic spiral is a spiral whose polar equation is given by r=ae^(btheta), (1) where r is the distance from the origin, theta is the angle from the x-axis, and a and ...

Expressions of the form lim_(k->infty)x_0+sqrt(x_1+sqrt(x_2+sqrt(...+x_k))) (1) are called nested radicals. Herschfeld (1935) proved that a nested radical of real nonnegative ...

Let lambda_(m,n) be Chebyshev constants. Schönhage (1973) proved that lim_(n->infty)(lambda_(0,n))^(1/n)=1/3. (1) It was conjectured that the number ...

In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc. In formal set theory, an ordinal ...

Given a Poisson process, the probability of obtaining exactly n successes in N trials is given by the limit of a binomial distribution P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n). ...

There are two kinds of power sums commonly considered. The first is the sum of pth powers of a set of n variables x_k, S_p(x_1,...,x_n)=sum_(k=1)^nx_k^p, (1) and the second ...

The nth taxicab number Ta(n) is the smallest number representable in n ways as a sum of positive cubes. The numbers derive their name from the Hardy-Ramanujan number Ta(2) = ...