geodesics
Curves minimizing distance
Geodesics are the shortest paths between two points on a curved surface—the equivalent of straight lines in curved space.
On a sphere, geodesics are arcs of great circles; airplane routes follow geodesics across Earth's surface.
In general relativity, objects in free fall follow geodesics through curved spacetime.
The singular geodesic also functions as an adjective: geodesic dome, geodesic path.
Many and various
- curvatureDeviation from flatness
- parallel transportVector movement preserving covariant derivative
- covariant derivativeGeneralized derivative on manifolds
- Gaussian curvatureIntrinsic surface bending measure
Christoffel symbols · hyperbolic · spherical · elliptic · great circle · surface · intrinsic · extrinsic
Space between two points
- arc lengthCurved segment's measure
- straight lineUndeviated continuous path
- great circleMaximum spherical circumference
- direct routeStraightest path available
minimum · curve · trajectory · connecting · convexity
Merged dimensional framework
- EinsteinByword for genius
- general relativityGravity as curved spacetime
- gravityMutual mass attraction
- black holesRegions of inescapable gravity
event horizon · gravitational waves · time dilation · cosmology · wormholes · free fall · singularity
Determining position and course
- surveyingMeasuring and charting terrain
- flight pathsPredetermined aerial travel corridors
- satellite orbitsPaths spacecraft follow around bodies
- seismic wavesEnergy from earth movements
Able to operate correctly
- actionProcess of doing
- stationaryNot in motion
- minimizationMaking as small as possible
- variationalRelating to functional extremization
catenary · critical point · parametrization · boundary conditions
manifold
Many and various
- curvatureDeviation from flatness
- parallel transportVector movement preserving covariant derivative
- covariant derivativeGeneralized derivative on manifolds
Christoffel symbols · Gaussian curvature · hyperbolic · spherical · elliptic · great circle · surface · intrinsic · extrinsic · torsion
distance
Space between two points
- arc lengthCurved segment's measure
- straight lineUndeviated continuous path
- great circleMaximum spherical circumference
direct route · minimum · curve · trajectory · connecting · convexity
spacetime
Merged dimensional framework
- EinsteinByword for genius
- general relativityGravity as curved spacetime
- gravityMutual mass attraction
black holes · event horizon · gravitational waves · time dilation · cosmology · wormholes · free fall · singularity
navigation
Determining position and course
- surveyingMeasuring and charting terrain
- flight pathsPredetermined aerial travel corridors
- satellite orbitsPaths spacecraft follow around bodies
seismic waves · ray tracing · computer graphics · fiber optics
functional
Able to operate correctly
- actionProcess of doing
- stationaryNot in motion
- minimizationMaking as small as possible
variational · catenary · critical point · parametrization · boundary conditions
- gravitygravity, graviton, gravity well, gravitational pull, gravity wave
- group theorygroup, generators, relations, symmetric, dihedral
- Riemannian geometryparallel transport, Christoffel symbols
- Curved Geometrycurvature, Gaussian curvature, great circle, great circles
- Spacetime Geometryspacetime, curvature, general relativity, manifolds, spacetime curvature
- spherical geometrygreat circle, great circles, lune, lunes, central angle