The geometry of the secant caustic of a planar curve |
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Affiliation: | 1. Warsaw University of Technology, Faculty of Mathematics and Information Science, ul. Koszykowa 75, 00-662 Warszawa, Poland;2. University of Valencia, Faculty of Mathematics, 46100 Burjassot, Valencia, Spain |
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Abstract: | The secant caustic of a planar curve M is the image of the singular set of the secant map of M. We analyze the geometrical properties of the secant caustic of a planar curve, i.e. the number of branches of the secant caustic, the parity of the number of cusps and the number of inflexion points in each branch of this set. In particular, we investigate in detail some of the geometrical properties of the secant caustic of a rosette, i.e. a smooth regular oriented closed curve with non-vanishing curvature. |
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Keywords: | Convex curve Rosette Secant caustic Secant map Singularity Wigner caustic |
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