Wladimir Boskoff, Lucy, H. Odom, and Bogdan Suceava,
An elementary view of Gromov hyperbolic spaces,
Forum Geometricorum, 12 (2012) 283--286.
Abstract. In the most recent decades, metric spaces have been studied from a variety of viewpoints. One of the important characterizations developed in the study of distances is Gromov hyperbolicity. Our goal here is to provide two approachable, but also intuitive examples of Gromov hyperbolic metric spaces. The authors believe that such examples could be of interest to readers interested in advanced Euclidean geometry; such examples are in fact a familiar introduction into coarse geometries. They are both elementary and fundamental. A scholar familiar with concepts like Ptolemy's cyclicity theorem or various geometric loci in the Euclidean plane could find a familiar environment by working with the concepts presented here.
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