## MatheMUSEments

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

## May 30, 2007

### Dog Does Calculus

Some dogs live to play fetch. Others do it only when bribed. At least one really gonzo dog, however, takes the game seriously enough to do a bit of math to figure out the best way to catch the ball.

Or so it seems.

The dog is a Welsh corgi named Elvis, who belongs to mathematician (no surprise there) Tim Pennings of Hope College in Holland, Michigan. When Elvis and Pennings go to the beach, they always play fetch. Standing at the water's edge, Pennings throws a tennis ball out into the waves, and Elvis eagerly retrieves it.

Elvis may do calculus, but does he speak Elvish?

When Pennings throws the ball at an angle to the shoreline, Elvis has several options. He can run along the beach until he is directly opposite the ball, then swim out to get it. Or he can plunge into the water right away and swim all the way to the ball. What happens most the time, however, is that Elvis runs part of the way along the beach, then swims out to the ball.

That happens to be a good strategy. Swimming is slow compared to running, so swimming to the ball takes longer even if the route is more direct. On the other hand, the longer Elvis runs along the beach, the farther he must go to get to the ball. The best bet is a compromise between the two—running a certain distance along the beach before plunging into the water.

Figuring out the best plunge point is a problem that belongs to a branch of mathematics called calculus. Pennings found that Elvis usually picked a path that was very close to the one a mathematician would say was the fastest possible one.

Of course, Elvis doesn't actually know calculus. He just has a sixth sense for efficient fetching that was bred in the bone and honed by lots of practice.

Does your friend behave the same way? You could try throwing a ball into deep snow to see where he or she plunges off the sidewalk. Maybe, like Elvis, your friend does calculus without knowing it.

Muse, January 2004, p. 27.

Photo courtesy of Tim Pennings.