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

May 13, 2007

Global Views

Imagine yourself inside a fishbowl, looking out. What might you see? Perhaps a fish darting around in the water, strands of seaweed, the table on which the fishbowl rests, a packet of fish food on the table, and a cat staring into the bowl, its paw touching the glass.

The puzzle for artist Dick Termes, who lives in Spearfish, South Dakota, was how to paint such a scene, showing all that surrounds you. His answer was to paint the scene not on a flat canvas but on the surface of a large plastic ball. Using geometry, he worked out a way to translate the view from inside a sphere to the outside of one.

In Termes's sphere painting of a fishbowl, you can even see beyond the table and cat to glimpse the rest of the room and a kitchen to one side, where someone has apparently just finished eating fish for supper and left only bones on the plate.

Hung from a rod, the painted ball slowly rotates, presenting six different viewpoints. Amazingly, as you stare at the revolving sphere, it appears to pop inside out. You feel as if you are sucked inside to get a weirdly distorted, inside-out view of the painted scene. It's a remarkable optical illusion.

Termes (above) has painted all sorts of scenes on the surface of spheres, including the interiors of famous buildings, many different geometric patterns, and various imaginary "dream" worlds. His largest "termesphere" started out as an orange, rotating Union 76 gas station sign (below), seven-and-a-half feet in diameter, and ended up at the Wyoming Law Enforcement Academy in Douglas, Wyoming.

Termes's sphere paintings even give you a rough idea of what your surroundings might look like if you were moving at nearly the speed of light—300,000 kilometers (about 186,000 miles) per second. Physicists have shown that no object can travel faster than this speed, and as you get closer to the universal speed limit, the appereance of your surroundings becomes distorted, much as does Sainte Chapelle (below) in one of Termes's sphere paintings.

Termes enjoys thinking about mathematical patterns, and he loves explaining and illustrating what he does so that we can all see the world from new, unusual perspectives.

Muse, September 2002, p. 42.

Dick Termes has a Web site at

Images courtesy of Dick Termes.

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