The non-Euclidean Euclidean algorithm
نویسنده
چکیده
In this paper we demonstrate how the geometrically motivated algorithm to determine whether a twogenerator real Möbius group acting on the Poincaré plane is or is not discrete can be interpreted as a non-Euclidean Euclidean algorithm. That is, the algorithm can be viewed as an application of the Euclidean division algorithm to real numbers that represent hyperbolic distances. In the case that the group is discrete and free, the algorithmic procedure also gives a non-Euclidean Euclidean algorithm to find the three shortest curves on the corresponding quotient surface. © 2013 Elsevier Inc. All rights reserved.
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