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Does anyone know which paper to cite or who to credit for the classification of curves of constant geodesic curvature in the hyperbolic plane?

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    $\begingroup$ I would guess Gauss... $\endgroup$
    – Igor Rivin
    Commented Oct 18, 2012 at 20:59
  • $\begingroup$ Given your choice of language, perhaps the first paper by Beltrami on this. Stillwell would know. $\endgroup$
    – Will Jagy
    Commented Oct 19, 2012 at 5:27

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I would cite Coxeter, Non-euclidean geometry, Ch. XI, which is a secondary source. Images of these curves are intersections of rectilinear planes with one sheet of a two-sheeted real hyperboloid. Faithful images are intersections of rectilinear planes with one sheet of an imaginary sphere of radius 1, embedded in iR x iR x R. If Gauss or Beltrami considered these curves, their treatments would have been less straightforward. (Gauss did not publish his analyses of hyperbolic geometry.)

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