Yarn, spandex, and dogs teach new tricks

"Maybe there's something psychological about using the yarns and the handicraft.... It just takes out the anxiety. It's not the same as looking at some abstract formula," Dr. Taimina says. "People say, 'It's very important that we can touch it - we can learn through feeling.' "

Taimina's models are on display at the Smithsonian in Washington, and a virtual exhibit with mathematical explanations is available at the Institute For Figuring, a Web-based educational organization directed by Margaret Wertheim in Los Angeles (www.theiff.org). "We tend to think of math as masculine, but this feminine activity has had a powerful role in illuminating it," says Ms. Wertheim, who has helped organized workshops for artists and other nonmathematicians.

Who would have thought that spandex would come in handy to help people grasp Einstein's theory of relativity?

Jim Borgardt, an associate professor of physics at Juniata College in Huntingdon, Pa., brings out a stretchy membrane to represent space and time, and places a marble or heavy ball on it to show how it's affected by various objects. Dr. Borgardt explains that the moon orbits the earth not because the two masses are attracted to each other, as Newton theorized, but because the earth forms a dimple in the space/time membrane, and the moon is trapped in that dimple. A heavier ball gets the class talking about black holes, because the ball sinks so deeply that it's surrounded by the membrane. "If you sit there and try to explain that just with words, some people's heads are spinning, whereas if you get something they can see - even though it's not a perfect metaphor - at least it gives them a road map," Borgardt says.

Elvis has left the building. Actually he's jumped into a lake to fetch a ball. Elvis is the Welsh Corgi that tours with math professor Tim Pennings to illustrate a calculus problem at schools and colleges.

When Dr. Pennings noticed Elvis running along the beach part of the way before jumping in to swim to a ball, he checked a hunch with some calculations. Based on Elvis's running and swimming paces, Pennings discovered his dog was instinctively choosing just about the quickest route to the ball, known in calculus as the "optimal solution." In the real world, factories calculate the optimal number of a product to put out each day to maximize profits, and NASA finds the optimal time to send out a spacecraft, says Pennings, who teaches at Hope College in Holland, Mich.

After talking about Elvis's approach, Pennings puts younger kids to the test by tossing a candy bar onto the lawn and telling them to walk on the sidewalk and crawl once they hit the grass.

Turns out the children's instincts for finding the optimal path aren't quite as good as Elvis's, but surely they have fun trying.

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