Bisoptic curves of hyperbolas

• Autores: Thierry Dana-Picard, Giora Mann, Nurit Zehavi
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 45, Nº. 5, 2014, págs. 762-781
• Idioma: inglés
• DOI: 10.1080/0020739x.2013.877608
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• Resumen

  • Given a hyperbola, we study its bisoptic curves, i.e. the geometric locus of points through which passes a pair of tangents making a fixed angle ? or 180° - ?. This question has been addressed in a previous paper for parabolas and for ellipses, showing hyperbolas and spiric curves, respectively. Here the requested geometric locus can be empty. If not, it is a punctured spiric curve, and two cases occur: the curve can have either one loop or two loops. Finally, we reconstruct explicitly the spiric curve as the intersection of a plane with a self-intersecting torus.