Fixing a Fixed Point

A simple example of a fixed point theorem.
A rectangle on a brown background is repeatedly transformed by a composition of shrinking, rotating, and translating; the successive images of the rectangle are colored alternately black and white. There can be a point on all the smaller images that is directly above the same point on the largest image: the limiting point of the transformation. Drag the locators to control the three parameters of the transformation: the first locator controls translating and the polar coordinates of the second locator control rotating and scaling.



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Source: D. Wells, The Penguin Dictionary of Curious and Interesting Geometry, London: Penguin, 1991 p. 80.


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