Spherical Conic and the Fourth Parameter

As the same as planner ellipse in Euclidean plane, spherical ellipse on the unit sphere is determined by two parameters: two foci and a string with certain length. Spherical ellipse is also the intersection of an elliptic cone centered at the origin and the unit sphere. Spherical ellipse has three parameters; focus, major axis, and minor axis. In this paper, we will introduce the fourth parameter, asymptotic angle. There are seven relations between these four parameters. Duality is a key word to understand these relations.

Keywords: spherical conic, asymptotic angle, duality

Corresponding author: E-mail: maeda@keyaki.cc.u-tokai.ac.jp