X-Nico

unusual facts about curvature



Abdalajís Tunnel

Although the AVE Class 102 is not speed-restricted in tunnels, but trains covering the Madrid-Málaga high-speed route slow down from 300 km/h to 160 km/h before entering the Abdalajís and Gobantes Tunnels, even though the Abdalajís Tunnel's curvature radius of 6900 m can theoretically support trains without tilting technology travelling at speeds of up to 392 km.

Acetylcarnitine

ALCAR has been shown to be more effective than tamoxifen in improving the curvature and reducing the pain and plaque sizes for men who sought treatment for their Peyronie's disease early and having low curvature deformities.

Billhook

Newtown/Montgomeryshire:
Has slightly more curvature than the Knighton.

Knighton/Radnorshire:
With similar measurements to the Pontypool/Monmouthshire style, this style has the least curvature of any hook and is almost a straight blade.

Brancacci Chapel

Roberto Longhi first identified an image of this lost fresco in a later drawing, which does not conform to the lunette's upper curvature, but appears today as a very probable hypothesis.

Carteret Islands

From the JASON satellite in orbit around the Earth, however, the real effects of even this small change, such as a change in the oblateness of the ocean surface across the curvature of the Earth, can still be clearly sorted out since that is exactly what the JASON satellite is doing when it maps variations in sea-level caused by gravitational field variations.

Cowan rail accident

Mr Hand also considered it likely that a passenger on 3801 had applied a handbrake on the third carriage, and that this, combined with the heavy load, the steep grade and the curvature of the line, had prevented the steam train from restarting.

Curvature of Riemannian manifolds

The curvature of n-dimensional Riemannian manifold is given by an antisymmetric n×n matrix \Omega^{} {}=\Omega^i {\ j} of 2-forms (or equivalently a 2-form with values in so(n), the Lie algebra of the orthogonal group O(n), which is the structure group of the tangent bundle of a Riemannian manifold).

For a more elementary discussion see the article on curvature which discusses the curvature of curves and surfaces in 2 and 3 dimensions, as well as Differential geometry of surfaces.

Davidon–Fletcher–Powell formula

The Davidon–Fletcher–Powell formula (or DFP; named after William C. Davidon, Roger Fletcher, and Michael J. D. Powell) finds the solution to the secant equation that is closest to the current estimate and satisfies the curvature condition (see below).

Ehrenfest paradox

1937: Jan Weyssenhoff (now perhaps best known for his work on Cartan connections with zero curvature and nonzero torsion) notices that the Langevin observers are not hypersurface orthogonal.

Eladio Dieste

A particular innovation was his Gaussian vault, a thin-shell structure for roofs in single-thickness brick, that derives its stiffness and strength from a double curvature catenary arch form that resists buckling failure.

Field artillery team

Corrections can be added for conditions such as a difference between target and howitzer altitudes, propellant temperature, atmospheric conditions, and even the curvature and rotation of the Earth.

Guofang Wei

Starting in 2000 Wei began working with Christina Sormani on limits of manifolds with lower Ricci curvature bounds using techniques of Jeff Cheeger and Tobias Colding, particularly Kenji Fukaya's metric measure convergence.

Hadamard's dynamical system

The system considers the motion of a free (frictionless) particle on a surface of constant negative curvature, the simplest compact Riemann surface, which is the surface of genus two: a donut with two holes.

History of manifolds and varieties

In the mid nineteenth century, the Gauss–Bonnet theorem linked the Euler characteristic to the Gaussian curvature.

Kaurna language

These include Ngangkiparringga (Onkaparinga) 'women's river place', Nurlongga (Noarlunga) 'corner/curvature place', Ngaltingga (Aldinga), Willangga (Willunga), Maitpangga (Myponga), Kanggarilla (Kangarilla) 'shepherding place', Yernkalyilla (Yankalilla) 'place of the fallen bits', Waitpingga (Waitpinga) 'wind place', Kauwandilla (Cowandilla) 'in the north', Yurridla (Uraidla) 'two ears' etc.

Lester Dubins

Besides probability, some of these were on curves of minimal length under constraints on curvature and initial and final tangents (see Dubins path), Tarski's circle squaring problem, convex analysis, and geometry.

Mathematics of general relativity

The connection and curvature of any Riemannian manifold are closely related, the theory of holonomy groups, which are formed by taking linear maps defined by parallel transport around curves on the manifold, providing a description of this relationship.

Poortjieskloof Dam

Poortjieskloof Dam is a double curvature arch type dam located in the Groot River in Western Cape, South Africa.

Principal direction

Principal directions - In differential geometry, one of the directions of principal curvature.

Ricci-flat manifold

Since Ricci curvature measures the amount by which the volume of a small geodesic ball deviates from the volume of a ball in Euclidean space, small geodesic balls will have no volume deviation, but their "shape" may vary from the shape of the standard ball in Euclidean space.

Spacetime algebra

Lasenby, Doran, and Gull of Cambridge University have proposed a new formulation of gravity, termed gauge theory gravity (GTG), wherein spacetime algebra is used to induce curvature on Minkowski space while admitting a gauge symmetry under "arbitrary smooth remapping of events onto spacetime" (Lasenby, et al.); a nontrivial proof then leads to the geodesic equation,

Thomas Maclear

In 1750 Abbe Nicolas Louis de Lacaille had measured a triangulation arc northwards from Cape Town, to determine the shape of the earth and found that the curvature of the earth was less in southern latitudes than at corresponding northern ones.


see also