Magdalena Skrzypiec
Maria Curie-Sklodowska University, Lublin
Abstract: For a given plane convex curve, we investigate both its isoptics ([1]) and its inner isoptics ([2]). We describe the construction of the dual curves associated with isoptics ([4]) and inner isoptics. We then focus on the case of an ellipse, comparing its inner isoptics with the dual curves of its isoptics. Finally, we compare our findings with those of [3], where the projective duality between the isoptics and inner isoptics of an ellipse is established.
References:
[1] W. Cieślak, A. Miernowski, W. Mozgawa; Isoptics of a closed strictly convex curve, Global differential geometry and global analysis (Berlin, 1990), Lecture Notes in Math., pp. 28–35, (1991).
[2] W. Mozgawa; On billiards and Poncelet’s porism, Rend. Semin. Mat. Univ. Padowa, vol. 120, pp. 157–166, (2008).
[3] A. Naiman, M. Skrzypiec, W. Mozgawa; Implicit forms of inner isoptics of ellipses, Beitr Algebra Geom, vol. 63, pp. 561–-571, (2022). https://doi.org/10.1007/s13366-021-00615-x
[4] M. Skrzypiec; Dual curves to isoptics of ovals, Bulletin de la Société des sciences et des lettres de Łódź, Série: Recherches sur les déformations, vol. 68, nr 1, pp.85–95, (2018). https://doi.org/10.26485/0459-6854/2018/68.1/6