On rosettes and antipodal rosettes (Q917039)

Rosettes are smooth closed curves in the plane with nonvanishing curvature. The authors introduce the notion of an n-antipodal set for such a curve, generalizing the notion of an antipodal pair. Using the Fourier expansion of the curvature radius they derive a criterion for the existence of n-antipodal sets for a given rosette. Furthermore the existence of so-called n-antipodal rosettes is established which are defined by the property that every point of this curve belongs to an n- antipodal set.