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To predict the result of a measurement requires (1) a model of the system under investigation, and (2) a physical theory linking the parameters of the model to the parameters ...

A (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

Let a spherical triangle be drawn on the surface of a sphere of radius R, centered at a point O=(0,0,0), with vertices A, B, and C. The vectors from the center of the sphere ...

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 adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

An alternating group is a group of even permutations on a set of length n, denoted A_n or Alt(n) (Scott 1987, p. 267). Alternating groups are therefore permutation groups. ...

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...

A copositive matrix is a real n×n square matrix A=(a_(ij)) that makes the corresponding quadratic form f(x)=x^(T)Ax nonnegative for all nonnegative n-vectors x. Copositive ...