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The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

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 stella octangula is a polyhedron compound composed of a tetrahedron and its dual (a second tetrahedron rotated 180 degrees with respect to the first). The stella ...

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular ...

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...

An atlas is a collection of consistent coordinate charts on a manifold, where "consistent" most commonly means that the transition functions of the charts are smooth. As the ...

A Banach space is a complete vector space B with a norm ||·||. Two norms ||·||_((1)) and ||·||_((2)) are called equivalent if they give the same topology, which is equivalent ...

Bayesian analysis is a statistical procedure which endeavors to estimate parameters of an underlying distribution based on the observed distribution. Begin with a "prior ...

Given a set of n+1 control points P_0, P_1, ..., P_n, the corresponding Bézier curve (or Bernstein-Bézier curve) is given by C(t)=sum_(i=0)^nP_iB_(i,n)(t), where B_(i,n)(t) ...

The sequence a(n) given by the exponents of the highest power of 2 dividing n, i.e., the number of trailing 0s in the binary representation of n. For n=1, 2, ..., the first ...