In mathematics, a prime geodesic on a hyperbolic surface is a primitive closed geodesic: one whose parametrization is not obtained by going repeatedly around a shorter closed geodesic. Informally, one follows the geodesic until its motion begins to repeat; the geodesic is prime if this first full return already completes the entire cycle, rather than repeating a shorter cycle several times.
In mathematics, a prime geodesic on a hyperbolic surface is a primitive closed geodesic: one whose parametrization is not obtained by going repeatedly around a shorter closed geodesic. Informally, one follows the geodesic until its motion begins to repeat; the geodesic is prime if this first full return already completes the entire cycle, rather than repeating a shorter cycle several times.
Source: Wikipedia "Prime geodesic" · CC BY-SA 4.0
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