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The term "Cartan algebra" has two meanings in mathematics, so care is needed in determining from context which meaning is intended. One meaning is a "Cartan subalgebra," ...

The circumsphere of given set of points, commonly the vertices of a solid, is a sphere that passes through all the points. A circumsphere does not always exist, but when it ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

Given an affine variety V in the n-dimensional affine space K^n, where K is an algebraically closed field, the coordinate ring of V is the quotient ring ...

What is the area of the largest square that can be inscribed on a unit cube (Trott 2004, p. 104)? The answer is 9/8, given by a square with vertices (1/4, 0, 0), (0, 1, 1/4), ...

The disk model is the standard Boolean-Poisson model in two-dimensional continuum percolation theory. In particular, the disk model is characterized by the existence of a ...

An (m+1)-dimensional subspace W of an (n+1)-dimensional vector space V can be specified by an (m+1)×(n+1) matrix whose rows are the coordinates of a basis of W. The set of ...

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

A special nonsingular map from one manifold to another such that at every point in the domain of the map, the derivative is an injective linear transformation. This is ...

The insphere of a solid is a sphere that is tangent to all faces of the solid. An insphere does not always exist, but when it does, its radius r is called the inradius and ...