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Let gamma(t) be a smooth curve in a manifold M from x to y with gamma(0)=x and gamma(1)=y. Then gamma^'(t) in T_(gamma(t)), where T_x is the tangent space of M at x. The ...

The direction from an object A to another object B can be specified as a vector v=AB^-> with tail at A and head at B. However, since this vector has length equal to the ...

Due to Euler's prolific output, there are a great number of theorems that are know by the name "Euler's theorem." A sampling of these are Euler's displacement theorem for ...

Let phi be a map. Then phi is expansive if the statement that the distance d(phi^nx,phi^ny)<delta for all n in Z implies that x=y. Equivalently, phi is expansive if the ...

A graph G is said to be flexible if the vertices of G can be moved continuously so that (1) the distances between adjacent vertices are unchanged, and (2) at least two ...

Consider a finite collection of points p=(p_1,...,p_n), p_i in R^d Euclidean space (known as a configuration) and a graph G whose graph vertices correspond to pairs of points ...

The zeros of the derivative P^'(z) of a polynomial P(z) that are not multiple zeros of P(z) are the positions of equilibrium in the field of force due to unit particles ...

The generalized Petersen graph GP(n,k), also denoted P(n,k) (Biggs 1993, p. 119; Pemmaraju and Skiena 2003, p. 215), for n>=3 and 1<=k<=|_(n-1)/2_| is a connected cubic graph ...

The geometric span is largest possible distance between two points drawn from a finite set of points. It is therefore closely related to the generalized diameter of a closed ...

Let Y_n denote the graph with vertex set V(X_n), where X_n is the n-hypercube and two vertices are adjacent in Y_n iff they are at distance 1<=d<=2 in X_n. Y_n is not ...