geodesic segment

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• Geodesic dome — Spaceship Earth at Epcot, Walt Disney World, a geodesic sphere A geodesic dome is a spherical or partial spherical shell structure or lattice shell based on a network of great circles (geodesics) on the surface of a sphere. The geodesics… …   Wikipedia

• Geodesic — [ great circle arcs.] In mathematics, a geodesic IPA|/ˌdʒiəˈdɛsɪk, ˈdisɪk/ [jee uh des ik, dee sik] is a generalization of the notion of a straight line to curved spaces . In presence of a metric, geodesics are defined to be (locally) the… …   Wikipedia

• Geodesic curvature — In differential geometry, the geodesic curvature vector is a property of curves in a metric space which reflects the deviance of the curve from following the shortest arc length distance along each infinitesimal segment of its length.The vector… …   Wikipedia

• CAT(k) space — In mathematics, a CAT( k ) space is a specific type of metric space. Intuitively, triangles in a CAT( k ) space are slimmer than corresponding model triangles in a standard space of constant curvature k . In a CAT( k ) space, the curvature is… …   Wikipedia

• Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

• Hyperbolic group — In group theory, a hyperbolic group, also known as a word hyperbolic group, Gromov hyperbolic group, negatively curved group is a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic… …   Wikipedia

• Schild's ladder — In the theory of general relativity, and differential geometry more generally, Schild s ladder is a method for parallel transporting a vector along a curve using only geodesics. The method is named for Alfred Schild, who introduced the method… …   Wikipedia

• Real tree — A real tree, or an mathbb R tree, is a metric space ( M , d ) such thatfor any x , y in M there is a unique arc from x to y and this arc is a geodesic segment. Here by an arc from x to y we mean the image in M of a topological embedding f from an …   Wikipedia

• Boundedly generated group — In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generation is also closely related with the congruence subgroup problem (see harvnb|Lubotzky|Segal|2003) …   Wikipedia

• Levi-Civita parallelogramoid — In the mathematical field of differential geometry, the Levi Civita parallelogramoid is a certain figure generalizing a parallelogram to a curved space. It is named for its discoverer, Tullio Levi Civita. A parallelogram in Euclidean geometry can …   Wikipedia

• Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this …   Wikipedia