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What are geodesics?

What are geodesics? Here are some definitions.

Noun
  1. plural of geodesic
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Examples
The photons that reached its senses followed paths that varied slightly from the straight-line geodesics of flat spacetime.
Since no strong theoretical reason exists to confine the analysis to geodesics, Stephenson and Zelen's measure might be preferable.
Since geodesics aren't always straight, light doesn't always travel in straight lines.
Those distortions guide the moving masses along straight-line geodesics, which look like the curved trajectories that physicists call orbits.
Hence, we can produce poles, polars, points, geodesics, angles, and so forth readily by converting back to the Poincare model.
He then considered the problem of when the geodesics on a surface could be represented as straight lines on the plane.

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