Sunday, September 25, 2011

Cylindrical perspective

My favorite Escher print is called "House of Stairs," which shows a tiled room inhabited by silly creatures called wentelteefje.

The image makes us of cylindrical perspective, the effect you would get if you projected the world onto a cylinder with your eye in the middle. I noticed this in a panoramic picture of my son and me, taken by a friend.

(The Escher-inspired t-shirt is pure coincidence).

The book M.C. Escher: Visions of Symmetry gives nice explanation of the effect (among the many other mathematical aspects of the art). Upper-level students may be able to generate a "proof" that parallel lines appear as sinusoids, while other students might be able to use sinusoidal templates to draw images of their own. Here's a video of someone doing just that...

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