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The Ricci flow equation is the evolution equation d/(dt)g_(ij)(t)=-2R_(ij) for a Riemannian metric g_(ij), where R_(ij) is the Ricci curvature tensor. Hamilton (1982) showed ...

The d-dimensional rigidity matrix M(G) of a graph G with vertex count n, edge count m in the variables v_i=(x_1,...,x_d) is the m×(dn) matrix with rows indexed by the edges ...

A number of areas of mathematics have the notion of a "dual" which can be applies to objects of that particular area. Whenever an object A has the property that it is equal ...

A smooth manifold M=(M,g) is said to be semi-Riemannian if the indexMetric Tensor Index of g is nonzero. Alternatively, a smooth manifold is semi-Riemannian provided that it ...

The metric tensor g on a smooth manifold M=(M,g) is said to be semi-Riemannian if the index of g is nonzero. In nearly all literature, the term semi-Riemannian is used ...

Measurements of a centered convex body in Euclidean n-space (for n>=3) show that its brightness function (the volume of each projection) is smaller than that of another such ...

The surface of revolution obtained by cutting a conical "wedge" with vertex at the center of a sphere out of the sphere. It is therefore a cone plus a spherical cap, and is a ...

The average number of regions N(n) into which n lines divide a square is N^_(n)=1/(16)n(n-1)pi+n+1 (Santaló 1976; Finch 2003, p. 481). The maximum number of sequences is ...

A stadium, also called a discorectangle, obround, or sausage body, is a geometric figure consisting of a rectangle with top and bottom lengths a whose ends are capped off ...

The geometric centroid of the system obtained by placing a mass equal to the magnitude of the exterior angle at each vertex (Honsberger 1995, p. 120) is called the Steiner ...