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An Analogue of Napoleon's Theorem in the Hyperbolic Plane

Published:2001-09-01
Printed: Sep 2001
• Angela McKay
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Abstract

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.
 MSC Classifications: 37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)