geodesic curve
Sign in to savethumb|Klein quartic with 28 geodesics (marked by 7 colors and 4 patterns) In geometry, a geodesic () 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".
Article
25 sectionsContents
- Introduction
- Examples
- Triangles{{anchor|Triangle}}
- Metric geometry
- Riemannian geometry
- Calculus of variations
- Affine geodesics
- Existence and uniqueness
- Geodesic flow{{anchor|Flow}}
- Geodesic spray
- Affine and projective geodesics
- Computational methods
- Ribbon test
- Examples of applications
- Topology and geometric group theory
- Probability, statistics and machine learning
- Physics
- Chemistry
- Biology
- Engineering
- See also
- Notes
- References
- Further reading
- External links
thumb|Klein quartic with 28 geodesics (marked by 7 colors and 4 patterns) In geometry, a geodesic () 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.