geodesic
Adjective:
- Relating to geodesy: Pertaining to the branch of mathematics dealing with the measurement and representation of the Earth's shape and gravitational field.
- Relating to a geodesic line: Of or determined by the shortest possible line between two points on a curved surface.
Noun:
- A geodesic (line): In mathematics, the shortest path between two points on a mathematically defined surface, such as a straight line on a plane or an arc of a great circle on a sphere.
Adjective:
- The surveyors used geodesic principles to map the region accurately.
- A geodesic dome is a structure based on a network of great circles.
Noun:
- On a sphere, the geodesic connecting two points is an arc of a great circle.
- In navigation, finding the geodesic is crucial for determining the shortest route.
"Geodesic distance": The length of the shortest path (the geodesic) between two points on a curved surface.
- The geodesic distance between two cities accounts for the Earth's curvature.
"Geodesic flow": In differential geometry and dynamical systems, a concept describing the motion along geodesics.
- The study of geodesic flow on a manifold reveals important geometric properties.
Geodesy (n): The science of measuring and understanding the Earth's geometric shape, orientation in space, and gravity field.
- Modern geodesy relies heavily on satellite data.
Geodetic (adj): Often used interchangeably with "geodesic," especially in contexts relating to Earth measurement.
- The geodetic survey provided precise coordinates.
- Adjective (relating to shortest path): Minimal-path, shortest-route.
- Noun (shortest line): Great-circle arc (on a sphere), minimal curve.
"Geodesic completeness": A property in mathematics where a manifold has no "edges" and geodesics can be extended indefinitely.
- A key question in cosmology is whether spacetime is geodesically complete.
"Geodesic deviation": The phenomenon where initially parallel geodesics may converge or diverge due to curvature, central to the theory of general relativity.
- Geodesic deviation explains how tidal forces are a manifestation of spacetime curvature.
(Note: "Geodesic" is a technical term, so common idioms are not typically associated with it. Its usage is primarily in scientific and mathematical contexts.)
- of or relating to or determined by geodesy
- (mathematics) the shortest line between two points on a mathematically defined surface (as a straight line on a plane or an arc of a great circle on a sphere)