From conic intersections to toric intersections: The case of the isoptic curves of an ellipse

Authors

Thierry Dana-Picard
Nurit Zehavi
Giora Mann

Volume

9

Issue

1-2

Abstract

Starting from the study of the orthoptic curves of parabolas and ellipses, we generalize to the case of isoptic curves for any angle, i.e. the geometric locus of points from which a parabola or an ellipse are viewed under a given angle. This leads to the investigation of spiric curves and to the construction of these curves as an actual intersection of a self-intersecting torus with a plane. The usage of a Computer Algebra System facilitated this investigation.

First Page

59

Last Page

76

Recommended Citation

Dana-Picard, Thierry; Zehavi, Nurit; and Mann, Giora (2012) "From conic intersections to toric intersections: The case of the isoptic curves of an ellipse," The Mathematics Enthusiast: Vol. 9 : No. 1 , Article 4.
DOI: https://doi.org/10.54870/1551-3440.1235
Available at: https://scholarworks.umt.edu/tme/vol9/iss1/4

Digital Object Identifier (DOI)

10.54870/1551-3440.1235