Curves with constant geodesic curvature in the Bolyai-Lobachevskian plane
Keywords:
hyperbolic geometry, geodesics, orthogonal trajectory, polar coordinates.Abstract
The aim of this note is to present the curves with constant geodesic curvature of the Bolyai-Lobachevskian hyperbolic plane. By using the Lobachevskian metric the equations of the circle, paracycloid and hipercycloid are given. Furthermore, we determine a new family of curves with constant curvature which was not emphasized before. During the analysis we use Cartesian and polar coordinates.
Mathematics Subject Classification (2010): 53A35.
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