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).

Dec 3, 2025 · A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight lines. On the sphere, …

The geodesic equation may not look particularly appealing, but we’ll get used to it and its properties. It is an equality of vectors, which we can separate into components c(t) = (x(t), y(t)).

A geodesic is a generalization of the notion of a “straight line” from a plane to a surface, on which it represents in some sense the shortest path between two points.

A geodesic, the shortest distance between any two points on a sphere, is an arc of the great circle through the two points. The formula for determining a sphere’s surface area is 4π r2; its volume is …

Feb 9, 2018 · This example also points out to us that between any two points there may be more than one geodesic. In fact, between a point and its antipodal point on the sphere, there are an infinite …

Intuitively, a geodesic is the shortest arc between two points on a surface. If we stretch a rubber band between two points on a convex surface, the rubber band will take the path of the geodesic. See Fig. 1.

Joseph Howlett, Quanta Magazine, 3 Mar. 2025 In fact, for curved spaces, the shortest path is what’s known as a geodesic: the generalization of a straight, flat line to a curved space.

Given any two points in a graph or hypergraph one can find a (not necessarily unique) shortest path (or “ geodesic ”) between them, as measured by the number of edges or hyperedges traversed to go from …

Theorem 1.5. For any p 2 M and any Xp 2 TpM, there exists an " > 0 and a unique geodesic de ned for jtj < " such that (0) = p a.