Friday, September 30, 2011

In the free box

My family and I recently moved.  We had a "free box" out in front of our house, where we would throw miscellaneous junk that we didn't want to try to sell.  Almost everything in the free box was eventually taken, but one straggler remained: a handmade screen print of one of Ramanujan's formulas for the value of pi.  What is the world coming to?

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...