99-205 Lewis Bowen
Circle Packing in the Hyperbolic Plane (356K, postscript) Jun 1, 99
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Abstract. We consider circle packings in the hyperbolic plane, by finitely many congruent circles, which maximize the number of touching pairs. We show that such a packing has all of its centers located on the vertices of a triangulation of the hyperbolic plane by congruent equilateral triangles, provided the diameter d of the circles is such that an equilateral triangle in the hyperbolic plane of side length d has each of its angles is equal to 2 pi/N for some N > 6.

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