An analogue of Napoleon’s theorem in the hyperbolic plane. (English) Zbl 0991.37014
The author deals with a slight variation of Napoleon’s theorem. More precisely, she shows that, for a given \(d\), the spaces of triangles (modulo orientation preserving isometry) under this map has a fixed point (an equilateral triangle whose side length can be written down explicitly in terms of \(d\)), and furthermore, that this fixed point is attracting.
Reviewer: Messoud Efendiev (Berlin)
MSC:
37D40 | Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) |
51M09 | Elementary problems in hyperbolic and elliptic geometries |