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geodesic
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Figure 2: The world line of an accelerating body moving slower than the speed of light; the tangent vector corresponds to the body's 4-velocity and the curvature vector to its 4-acceleration. Figure 5: The world lines of an electron (moving forward in time) and a positron (moving backward in time) that annihilate into two photons (see text). models of hyperbolic geometry example of straight line not being shortest distance between two points Figure 3: The world line of a particle moving forward in time (see text). Figure 1: The world line of a particle traveling with speed less than that of light.
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geodesic

mathematics
Also known as: geodesic curve, world line
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Figure 2: The world line of an accelerating body moving slower than the speed of light; the tangent vector corresponds to the body's 4-velocity and the curvature vector to its 4-acceleration.
Figure 2: The world line of an accelerating body moving slower than the speed of light; the tangent vector corresponds to the body's 4-velocity and the curvature vector to its 4-acceleration.

In mathematics, a geodesic is the shortest line between two points that lies on a given surface. This concept originates from geodesy, the science of measuring the Earth's shape and dimensions.12

Geodesics are fundamental in understanding curved surfaces and are a key element in non-Euclidean geometries. For instance, on a sphere, the shortest path between two points is an arc of a great circle. This idea contrasts with Euclidean geometry, where the shortest distance between two points is a straight line.345

The study of geodesics has been crucial in developing advanced mathematical concepts, including differential geometry and Einstein's theory of general relativity, where they describe the paths of objects in curved spacetime.6

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7 Britannica Sources
  1. geodesic
  2. geometry - A grand synthesis
  3. non-Euclidean geometry
  4. geodesy
  5. geometry - The real world
  6. Euclidean space
  7. sphere

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