Vol. 11, No. 5, 2018

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Different definitions of conic sections in hyperbolic geometry

Patrick Chao and Jonathan Rosenberg

Vol. 11 (2018), No. 5, 753–768

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.

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conic section, hyperbolic plane, hyperbolic geometry, focus, directrix
Mathematical Subject Classification 2010
Primary: 51M10
Secondary: 51N15, 53A35
Received: 30 March 2016
Revised: 30 October 2017
Accepted: 14 November 2017
Published: 2 April 2018

Communicated by Józef H. Przytycki
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