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R. Radius of metric space is the infimum of radii of metric balls which contain the space completely. Radius of convexity at a point p of a Riemannian manifold is the largest radius of a ball which is a convex subset. Ray is a one side infinite geodesic which is minimizing on each interval. Riemann curvature tensor.
Contraction mapping. In mathematics, a contraction mapping, or contraction or contractor, on a metric space ( M , d) is a function f from M to itself, with the property that there is some real number such that for all x and y in M , The smallest such value of k is called the Lipschitz constant of f. Contractive maps are sometimes called ...
Inversive geometry. In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied.
Meridian arc. In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length . The purpose of measuring meridian arcs is to determine a figure of the Earth . One or more measurements of meridian arcs can be used ...
The azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar ...
Orthographic projection in cartography has been used since antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or azimuthal) projection in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic projection is at infinite distance.
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