## MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

## April 9, 2007

### Morphing Art

When you're riding along on your bike or in a car, you sometimes see the word "ONLY" painted on the roadway just before an intersection. The white letters look normal from where you're sitting. But if you were standing beside the "ONLY" instead of riding toward it, the letters would look stretched out. It's only when you look at them at the proper angle that they don't look distorted.

Artists have long used the same idea to create visual puzzles. A viewer sees an object in a picture correctly only if he or she finds the right angle at which to look at it. Such distorted pictures are called anamorphic images.

One of the most famous examples is a painting called The Ambassadors by the German artist Hans Holbein the Younger. It shows two young men standing in front of tables overflowing with books, instruments, and globes. At their feet, the artist painted a weird shape that turns out to be a grinning skull when you hold the picture at a slant (see http://www.abcgallery.com/H/holbein/holbein16.html).

You can create your own slant picture. You start with a piece of paper ruled into square cells and another ruled with the same number of trapezoids—squares that are stretched out in a special way. Draw your picture on the square grid. Then carefully copy the contents of each square of the original grid to the corresponding trapezoid of the other grid. You'll find that you'll need to stretch the lines of your drawing to make sure everything fits together. You end up with a stretched-out version of your original picture, but if you look at it from the right angle, it'll look undistorted again.

Some artists have tried more elaborate schemes. It's possible, for example, to draw or paint a picture you can understand only if you look at its reflection in a mirror shaped like a cylinder or a cone. The mirror takes the distortion out of the image.

About 200 years ago, anamorphic paintings for cylindrical or conical mirrors were popular toys in both Europe and Asia. You can still find examples in some museums. Nowadays, you can buy anamorphic jigsaw puzzles, which you can assemble and view with a special mirror to reveal a hidden image. And artists have created amazing pictures that must be reflected by shiny spheres, mirrored pyramids, or other mirrored shapes to show their true identity.

It's a neat game of hide-and-seek for the eye.

Muse, November 2000, p. 26.