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Different
definitions of conic sections in hyperbolic geometry
Patrick Chao and Jonathan Rosenberg
Vol. 11 (2018), No. 5, 753–768
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Abstract |
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In classical Euclidean geometry, there are several equivalent definitions of conic sections. We show that in the hyperbolic plane, the analogues of these same definitions still make sense, but are no longer equivalent, and we discuss the relationships among them. |
Keywords
conic section, hyperbolic plane, hyperbolic geometry,
focus, directrix
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Mathematical Subject Classification 2010
Primary: 51M10
Secondary: 51N15, 53A35
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Milestones
Received: 30 March 2016
Revised: 30 October 2017
Accepted: 14 November 2017
Published: 2 April 2018
Communicated by Józef H. Przytycki
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Authors |
| Patrick Chao | |
| Montgomery Blair High School Silver Spring, MD United States |
University of California Berkeley, CA |
| Jonathan Rosenberg | |
| Department of Mathematics University of Maryland College Park, MD United States |
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