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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 ...

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 ...

The distance p (sometimes also denoted k) from the focus to the conic section directrix of a conic section. The following table gives the focal parameter for the different ...

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 Harborth graph is the smallest known 4-regular matchstick graph. It is therefore both planar and unit-distance. It has 104 edges and 52 vertices. This graph was named ...

A metric on a bunch of segments with a common endpoint O, which defines the distance between two points P_1 and P_2 as the length of the shortest path connecting them inside ...

A shell bounded by two similar ellipsoids having a constant ratio of axes. Given a chord passing through a homeoid, the distance between inner and outer intersections is ...

The circle with respect to which an inverse curve is computed or relative to which inverse points are computed. In three dimensions, inverse points can be computed relative ...