Linked from

The 68 pages that link to Geodesic, each with the reason it gives.

• Ray (geometry)Compared with: A geodesic generalizes straightness on curved spaces rather than extending along a Euclidean line.

• Flat torusRelated: Straight lines in the covering plane project to geodesics on the torus.

• Gravitational singularityBroader topic: Incomplete freely falling geodesics provide a principal way to identify singular spacetimes.

• Hopf–Rinow theoremNarrower topic: Geodesic completeness asks whether every such curve extends indefinitely.

• Hyperbolic triangleNarrower topic: Each side is a geodesic, rather than an arbitrary curve in the hyperbolic plane.

• Theory of relativityRelated: In general relativity, freely falling bodies follow spacetime geodesics.

• Brachistochrone curveCompared with: A geodesic optimizes geometric length, whereas the brachistochrone optimizes travel time with changing speed.

• Hilbert's theoremRelated: Geodesic behavior on a complete negatively curved surface underlies the global obstruction.

• Penrose–Hawking singularity theoremsNarrower topic: The theorems define incompleteness by showing that certain geodesics end after finite affine or proper time.

• Azimuthal equidistant projectionRelated: The radial distances represented by this projection follow spherical geodesics.

• Curved spacetimeRelated: Freely falling bodies follow spacetime geodesics in general relativity.

• Circle of latitudeCompared with: A latitude circle other than the equator is not a geodesic.

• Clairaut's relationNarrower topic: Clairaut's relation describes how a geodesic travels across a surface of revolution.

• Fundamental theorem of Riemannian geometryRelated: The Levi-Civita connection defines the geodesics used to study Riemannian distance.

• Gauss's lemma (differential geometry)Narrower topic: Radial curves under the exponential map are geodesics, and their constant speed drives the lemma.

• Hjelmslev's theoremRelated: Hyperbolic triangles are bounded by geodesics, whose lengths are the sides in the theorem.

• Mathematics of general relativityRelated: Freely falling bodies follow geodesics of the spacetime metric.

• Meusnier's theoremRelated: For a geodesic, the curve’s bending is entirely normal to the surface.