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...

theory Noether's theorem Path integral formulation Plateau's problem Prime geodesic Principle of least action Soap bubble Soap film Tautochrone curve...

geometry, a geodesic bicombing distinguishes a class of geodesics of a metric space. The study of metric spaces with distinguished geodesics traces back...

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...

Perimeter Pi Plane curve Pochhammer contour Polar coordinate system Prime geodesic Projective line Ray Regular parametric representation Reuleaux triangle...

parallelism Prime geodesic Geodesic flow Exponential map (Lie theory) Exponential map (Riemannian geometry) Injectivity radius Geodesic deviation equation...

University Princeton University Institute for Advanced Study Thesis Prime geodesic theorems (1980) Doctoral advisor Paul Cohen Doctoral students Andrew...

group Kleinian model Poincaré disk model Poincaré half-plane model Prime geodesic Hershel M. Farkas and Irwin Kra, Riemann Surfaces (1980), Springer-Verlag...

\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...

solution of the Einstein field equations. Gödel's original chart is geodesically complete and free of singularities. Therefore, it is a global chart,...

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...

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...

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...

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...

believe Earth was prolate (wider at the poles). The subsequent French geodesic missions (1735-1739) to Lapland and Peru corroborated Newton, but also...

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...

flows between coordinates in computational anatomy are constrained to be geodesic flows satisfying the principle of least action for the Kinetic energy of...

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...

and technology. The building resembles a truncated cone capped with a geodesic dome. Among the themes featured in the exhibition galleries are an environmental...

measured along that circle of latitude, is slightly more than the shortest (geodesic) distance between those points (unless on the equator, where these are...

over closed geodesics rather than primes. The Selberg trace formula is the analogue for these functions of the explicit formulas in prime number theory...

surface's unit normal vector, including the: normal curvature geodesic curvature geodesic torsion Any non-singular curve on a smooth surface has its tangent...

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...

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...

Bessel who solved problems for geodesics on the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude...

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...

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...

mathematically plotted world map using coordinates measured east from a prime meridian at the westernmost known land, designated the Fortunate Isles,...

inverse stereographic projection from the plane to the sphere defines a geodesic distance between points in the plane equal to the spherical distance between...

single isoclinic geodesic, reaching its destination directly, instead of the bent line of two successive simple geodesics. A geodesic is the shortest path...