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

• Non-Euclidean geometryRelated: Geodesics play the role of straight lines in curved geometries.

• Equivalence principleRelated: General relativity describes freely falling bodies as following paths through curved spacetime.

• SphereRelated: On a sphere, great-circle arcs are geodesics.

• Hyperbolic geometryRelated: Geodesics play the role of straight lines in hyperbolic geometry.

• Metric tensorRelated: The metric determines which curves are geodesics through its associated connection.

• Tangent spaceRelated: Its velocity lies in tangent spaces along the curve.

• Riemannian geometryRelated: Geodesics generalize straight lines and locally minimize distance.

• SpacetimeRelated: Freely falling bodies follow geodesics in curved spacetime.

• Arc lengthRelated: Geodesics minimize path length under a space's geometry, unlike arbitrary arcs.

• Covariant derivativeRelated: Its defining equation sets the covariant derivative of the tangent along the curve to zero.

• Free fallRelated: General relativity models freely falling bodies as following spacetime geodesics.

• Riemannian manifoldRelated: Geodesics generalize straight lines and locally extremize curve length.

• Proper timeRelated: In free fall, an ideal clock follows a timelike geodesic and locally maximizes elapsed proper time.

• Gravitational forceRelated: In general relativity, freely falling bodies follow spacetime geodesics rather than being pulled by a force.

• Smooth manifoldRelated: Geodesics generalize straight lines once a manifold has suitable geometric structure.

• Map scaleRelated: For long distances, the ground distance may follow a curved-surface path rather than a flat line.

• Cayley graphRelated: Geodesics encode shortest generator expressions for group elements.

• Line (geometry)Related: In curved spaces, geodesics generalize straight lines.

• Spherical trigonometryRelated: On a sphere, great-circle arcs are geodesics and supply spherical-triangle sides.

• CurvatureRelated: Surface curvature influences how geodesics behave and converge.

• Affine connectionRelated: The connection determines which curves have tangent vectors that transport themselves parallelly.

• Exponential mapRelated: The map’s output is the point reached along a geodesic launched with the input vector.

• Hamilton's principleRelated: Free-particle paths in suitable settings can be derived by extremizing an action.

• MeridianRelated: Meridians are geodesics on an ideal spherical Earth.

• Morse theoryRelated: Morse applied critical-point methods to the space of paths between points on a manifold.

• Nikolai LobachevskyRelated: Hyperbolic geometry treats geodesics as its straight lines.

• Oblate spheroidRelated: On an oblate spheroid, geodesics differ from great circles on a sphere.

• GravitationRelated: Freely falling bodies follow geodesics in general relativity.

• WorldlineRelated: Free-falling objects follow geodesic worldlines in general relativity.

• Great-circle distanceRelated: A great-circle arc is a geodesic on a sphere.

• Riemannian distanceRelated: Locally, geodesics realize the shortest lengths between sufficiently close points.

• Direct method in the calculus of variationsRelated: Energy minimization can establish the existence of geodesics under suitable geometric assumptions.

• PseudosphereRelated: Geodesics on the pseudosphere illustrate how straightest paths behave in negative curvature.

• Tullio Levi-CivitaRelated: The connection he defined determines geodesics in spaces equipped with a metric.

• Elliptic integralRelated: Geodesics on an ellipsoid lead to integrals reducible to elliptic forms.

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

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

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

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

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

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

• 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.