Geodesics in the context of Distance (graph theory)

Geodesics in the context of Distance (graph theory)

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⭐ Core Definition: Geodesics

In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line".

The noun geodesic and the adjective geodetic come from geodesy, the science of measuring the size and shape of Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between two points on the Earth's surface. For a spherical Earth, it is a segment of a great circle (see also great-circle distance). The term has since been generalized to more abstract mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph.

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Geodesics in the context of Spherical triangle

Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation.

The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam. The subject came to fruition in Early Modern times with important developments by John Napier, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Isaac Todhunter's textbook Spherical trigonometry for the use of colleges and Schools.Since then, significant developments have been the application of vector methods, quaternion methods, and the use of numerical methods.

View the full Wikipedia page for Spherical triangle
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LINKED FROM (PARENTS)
← Spherical triangle ← Spherical trigonometry
LINKS TO (CHILDREN)
Klein quartic → Geometry → Curve → Arc (geometry) → Differential geometry of surfaces → Riemannian manifold → Differentiable manifold → Connection (mathematics) → Line (geometry) → Geodesy → Earth → Ellipsoidal geodesic → Planetary surface → Spherical Earth → Line segment → Great circle → Great-circle distance → Graph theory → Distance (graph theory) → Vertex (graph theory) → Graph (discrete mathematics) →