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Exotica

We've talked about transformations that preserve the size and shape of a figure or pattern. Other transformations will preserve some, but not all, properties of a figure. For example, scaling preserves shape but not size, and inversion through a circle preserves angles and circles but distorts distance. Some even odder transformations are illustrated below.

Each of the images shown above is a distortion of the first. How do you think each was made from the original? What properties have been retained, and what given up? In particular, did any of these transformations preserve angles? Area? Distances?

Exotic transformations such as these can lead to some amazing symmetries-- some of which have barely been explored. But for now we focus on isometries, transformations of the plane that leave size and shape unchanged.

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Author: Chaim Goodman-Strauss, revised and edited by Heidi Burgiel
Comments to: webmaster@geom.umn.edu
Created: Dec 7 1995 --- Last modified: Jun 11 1996
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