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Alhazen's
hyperbolic billiard problem
Nathan Poirier and Michael McDaniel
Vol. 5 (2012), No. 3, 273–282
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Abstract |
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Given two points inside a circle in the hyperbolic plane, we study the problem of finding an isosceles triangle inscribed in the circle so that the two points belong to distinct congruent sides. By means of a reduction to the corresponding result in Euclidean geometry, we prove that this problem cannot generally be solved with hyperbolic ruler and compass. |
Keywords
hyperbolic geometry, Alhazen
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Mathematical Subject Classification 2010
Primary: 51M04, 51M10, 51M15
Secondary: 51M09
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Milestones
Received: 18 January 2011
Revised: 24 June 2011
Accepted: 26 June 2011
Published: 14 April 2013
Communicated by Joseph Gallian
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Authors |
| Nathan Poirier | |
| Department of Mathematics Aquinas College 1607 Robinson Road SE Grand Rapids 49506 United States |
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| Michael McDaniel | |
| Department of Mathematics 1903 W. Michigan Ave. Western Michigan University Kalamazoo, MI 49008-5248 United States |
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