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Dijkstra's algorithm is an algorithm for finding a graph geodesic, i.e., the shortest path between two graph vertices in a graph. It functions by constructing a shortest-path ...

Einstein summation is a notational convention for simplifying expressions including summations of vectors, matrices, and general tensors. There are essentially three rules of ...

An ellipsoid can be specified parametrically by x = acosusinv (1) y = bsinusinv (2) z = ccosv. (3) The geodesic parameters are then P = sin^2v(b^2cos^2u+a^2sin^2u) (4) Q = ...

The elongated square gyrobicupola nonuniform polyhedron obtained by rotating the bottom third of a small rhombicuboctahedron (Ball and Coxeter 1987, p. 137). It is also ...

Euler's series transformation is a transformation that sometimes accelerates the rate of convergence for an alternating series. Given a convergent alternating series with sum ...

A graph is a forbidden minor if its presence as a graph minor of a given graph means it is not a member of some family of graphs. More generally, there may be a family of ...

Pick any two relatively prime integers h and k, then the circle C(h,k) of radius 1/(2k^2) centered at (h/k,+/-1/(2k^2)) is known as a Ford circle. No matter what and how many ...

The following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...

Let L be an extension field of K, denoted L/K, and let G be the set of automorphisms of L/K, that is, the set of automorphisms sigma of L such that sigma(x)=x for every x in ...

A generalization of the Fibonacci numbers defined by 1=G_1=G_2=...=G_(c-1) and the recurrence relation G_n=G_(n-1)+G_(n-c). (1) These are the sums of elements on successive ...