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Math Trek

Hyperbolic Five

11:46am, August 28, 2003

Dutch graphic artist M.C. Escher (1898–1972) devised many highly original schemes in his attempts to capture the concept of infinity visually. One strategy he often employed was to create repeating patterns of interlocking figures. However, although he could imagine how such arrays extended to infinity, the actual pattern he drew represented only a fragment of an infinite expanse.

Another approach Escher tried was to draw replicas of a figure, such as a fish, that diminish in size as they recede from a point in the middle of a circular frame. In this case, he took advantage of the peculiarities of hyperbolic geometry to

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