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Finding the geodesic between two points on the Earth, the so-called inverse geodetic problem, was the focus of many mathematicians and geodesists over the course of the 18th and 19th centuries with major contributions by Clairaut, [5] Legendre, [6] Bessel, [7] and Helmert English translation of Astron. Nachr. 4, 241–254 (1825).
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such ...
Klein quartic with 28 geodesics (marked by 7 colors and 4 patterns). In geometry, a geodesic (/ ˌ dʒ iː. ə ˈ d ɛ s ɪ k,-oʊ-,-ˈ d iː s ɪ k,-z ɪ k /) [1] [2] is a curve representing in some sense the locally [a] shortest [b] path between two points in a surface, or more generally in a Riemannian manifold.
Solving the geodesic equations is a procedure used in mathematics, particularly Riemannian geometry, and in physics, particularly in general relativity, that results in obtaining geodesics. Physically, these represent the paths of (usually ideal) particles with no proper acceleration , their motion satisfying the geodesic equations.
Wasserstein metrics measure the distance between two measures on the same metric space. The Wasserstein distance between two measures is, roughly speaking, the cost of transporting one to the other. The set of all m by n matrices over some field is a metric space with respect to the rank distance (,) = ().
The shortest path between two points on a spheroid is known as a geodesic. Such paths are developed using differential geometry. The equator and meridians are great ellipses that are also geodesics [a]. The maximum difference in length between a great ellipse and the corresponding geodesic of length 5,000 nautical miles is about 10.5 meters.
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
A metric space defined over a set of points in terms of distances in a graph defined over the set is called a graph metric. The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is connected. The eccentricity ϵ(v) of a vertex v is the greatest distance between v and any other vertex; in ...