In mathematics, a prime geodesic on a hyperbolic surface is a primitive closed geodesic, i.e. a geodesic which is a closed curve that traces out its image...
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geometry, a geodesic bicombing distinguishes a class of geodesics of a metric space. The study of metric spaces with distinguished geodesics traces back...
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Perimeter Pi Plane curve Pochhammer contour Polar coordinate system Prime geodesic Projective line Ray Regular parametric representation Reuleaux triangle...
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theory Noether's theorem Path integral formulation Plateau's problem Prime geodesic Principle of least action Soap bubble Soap film Tautochrone curve...
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\mathbb {P} } is the set of prime numbers. The Selberg zeta-function uses the lengths of simple closed geodesics instead of the prime numbers. If Γ {\displaystyle...
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List of differential geometry topics (section Geodesic)
parallelism Prime geodesic Geodesic flow Exponential map (Lie theory) Exponential map (Riemannian geometry) Injectivity radius Geodesic deviation equation...
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Rome du 15 au 24 Octobre 1863 [Proceedings of the Seventh International Geodesic Conference for the measurement of degrees in Europe. Held in Rome from...
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University Princeton University Institute for Advanced Study Thesis Prime geodesic theorems (1980) Doctoral advisor Paul Cohen Doctoral students Andrew...
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group Kleinian model Poincaré disk model Poincaré half-plane model Prime geodesic Hershel M. Farkas and Irwin Kra, Riemann Surfaces (1980), Springer-Verlag...
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Differential geometry of surfaces (redirect from Geodesic polar coordinates)
called a geodesic. By the Cauchy–Schwarz inequality a path minimising energy is just a geodesic parametrised by arc length; and, for any geodesic, the parameter...
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loops. A closed geodesic is simple if it does not cross itself. A previous result, known as the "prime number theorem for geodesics", established that...
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Gödel metric (section Null geodesics)
solution of the Einstein field equations. Gödel's original chart is geodesically complete and free of singularities. Therefore, it is a global chart,...
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magnetic meridian, because of the longitude from east to west being complete geodesic. The angle between the magnetic and the true meridian is the magnetic declination...
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is taken over all prime closed geodesics p {\displaystyle p} of the graph G = ( V , E ) {\displaystyle G=(V,E)} , where geodesics which differ by a cyclic...
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Computational anatomy (section Riemannian exponential (geodesic positioning) and Riemannian logarithm (geodesic coordinates))
flows between coordinates in computational anatomy are constrained to be geodesic flows satisfying the principle of least action for the Kinetic energy of...
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Earth radius (redirect from Prime vertical radius of curvature)
and geodesics, can also be derived from Earth's equatorial and polar radii. Likewise for surface area, either based on a map projection or a geodesic polygon...
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Geodetic datum (redirect from Geodesic datum)
believe Earth was prolate (narrower at the equator). The subsequent French geodesic missions (1735-1739) to Lapland and Peru corroborated Newton, but also...
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fictitious force. The relative acceleration of one geodesic to another in curved spacetime is given by the geodesic deviation equation: D 2 ξ α d s 2 = − R α β...
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over closed geodesics rather than primes. The Selberg trace formula is the analogue for these functions of the explicit formulas in prime number theory...
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of this French Geodesic Mission to the Equator, made in what is now Ecuador, last until November 3. The same year the French Geodesic Mission to Lapland...
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Rindler coordinates (section Geodesics)
acceleration with gravitation. The geodesic equations in the Rindler chart are easily obtained from the geodesic Lagrangian; they are t ¨ + 2 x x ˙ t...
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Paris meridian (redirect from Paris prime)
equator, the other in a high latitude. Thus arose the celebrated French Geodesic Missions [fr], to the Equator and to Lapland, the latter directed by Pierre...
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Academy of Sciences to deliver his report of the data gathered in the French Geodesic Mission, including the first precise measurement of the Earth's circumference...
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like a black hole, to be a geodesic. Both physicists and philosophers have often repeated the assertion that the geodesic equation can be obtained from...
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Inertial frame of reference (section Primed frames)
relativity theory, the fictitious (i.e. inertial) forces are attributed to geodesic motion in spacetime. Due to Earth's rotation, its surface is not an inertial...
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Complex projective space (section Geodesics)
complex line that contains p and q is a geodesic for the Fubini–Study metric. In particular, all of the geodesics are closed (they are circles), and all...
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Wormholes in fiction (redirect from Geodesic fold)
In the episode "Inside Man" an artificially created wormhole was named geodesic fold. In the 2009 Star Trek film, red matter is used to create artificial...
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surface's unit normal vector, including the: normal curvature geodesic curvature geodesic torsion Any non-singular curve on a smooth surface has its tangent...
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since dust particles feel no forces, this will turn out to be a timelike geodesic congruence, but this needs not be assumed in advance.) A simple ansatz...
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