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An Analogue of Napoleon’s Theorem in the Hyperbolic Plane

Published online by Cambridge University Press:  20 November 2018

Angela McKay
Angela McKay*
Affiliation:
University of Maryland Department of Mathematics College Park, MD USA
*
Current Address: University of Notre Dame Department of Philosophy Notre Dame, IN USA, e-mail: amckay@homer.helios.nd.edu
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Abstract

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There is a theorem, usually attributed to Napoleon, which states that if one takes any triangle in the Euclidean Plane, constructs equilateral triangles on each of its sides, and connects the midpoints of the three equilateral triangles, one will obtain an equilateral triangle. We consider an analogue of this problem in the hyperbolic plane.

Keywords

37D40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 3 , 01 September 2001 , pp. 292 - 297
Copyright
Copyright © Canadian Mathematical Society 2001

References

[1] Katok, Svetlanna, Fuchsian Groups. University of Chicago Press, Chicago, 1992 Google Scholar
[2] Meschkowski, Herbert, Noneuclidean Geometry. Academic Press, New York, 1964.Google Scholar