Spherical Conic and the Fourth Parameter

Main Article Content

Yoichi Maeda

Abstract

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

Article Details

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Original Research Articles

References

[1] Berger, M., Geometry II Springer-Verlag, Berlin Heidelberg. (1987)
[2] Jennings, G., Geometry with Applications, Springer-Verlag, New York. (1994)