Examples of using Geodesics in English and their translations into French
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loxodromes and ellipsoidal geodesics, have been adopted in State practice United Nations, 1989.
development, geodesics, and associated differential operators.
he invented a system of clustering dome structures by using small circle Catenatic Geometry principles rather than great circles, or geodesics, as Fuller had designed into geodesic dome structures.
The geodesics defined here are sometimes called affinely parametrized, since a given straight line
Affine connections may also be used to define(affine) geodesics on a manifold, generalizing the straight lines of Euclidean space,
this is not so for geodesics on the surface of the Earth: for example, lines of longitude
the Commission will employ geodesics on the surface of the official geodetic reference ellipsoid used by a State in each submission to define the path
Gauss needed to make an in-depth investigation of the properties of geodesics on the surface, i.e. paths of shortest length between two fixed points on the surface see below.
the theory of geodesics has been used to show this is true in the important case when the components of the metric are analytic.
although Euler developed the one variable equations to understand geodesics, defined independently of an embedding, one of Lagrange's
corresponding geometrically to closed geodesics on M. Examples. the Bolza surface of genus 2;
Meyer's homological criterion for the existence of infinitely many closed geodesics(1969), or its reinterpretation by Sullivan-Vigué from the viewpoint of rational homotopy theory(1976), have shown deep connections between spaces of loops and analysis, Lie group theory.
We can also reparametrize geodesics to be unit speed, so equivalently we can define expp(v)
Geology, prospecting, geodesics, hydrology and meteorology.
The properties of geodesics differ from those of straight lines.
Unparametrized geodesics are often studied from the point of view of projective connections.
The geodesics between two points on the sphere are the great circle arcs with these given endpoints.
In differential geometry, conjugate points are, roughly, points that can almost be joined by a 1-parameter family of geodesics.
For example, group betweenness centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.
we specify a"triangle" on M formed by three geodesics.