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Most of us don’t associate solving a calculus problem with a day at the beach, but for Tim Pennings, a math professor at Hope College, this is exactly what comes to mind.

Pennings and his dog, a Welsh Corgi named Elvis, came to campus Monday to share their unique take on calculus with students and faculty members.

One day when Pennings was playing with Elvis at a Michigan beach, he noticed that their game of fetch imitated a familiar calculus problem of finding the optimal path from point A to point B. Usually the best route between two points is a straight line; optimal problems, however, incorporate different factors that influence that route.

As Pennings threw the ball into Lake Michigan he noticed that Elvis would run along the beach and then launch himself into the water and swim to the ball. Pennings also noticed that Elvis ran faster than he swam.

Since the different mediums of land and water affected Elvis’s speed it also affected his optimal route to the ball. Pennings set out to find if Elvis was indeed finding the optimal route and if so, could Elvis in fact do calculus?

Math professor Tim Pennings of Hope College and his dog Elvis demonstrate a calculus problem in 209 McGregory Hall. (Photo by Luke Connolly ’09)

Pennings first decided that Elvis’ objective was to get to the ball as fast as possible. This became obvious to the gathered students when Pennings and Elvis played fetch to start the lecture. It was clear that retrieving the ball as quickly as possible was Elvis’s main goal.

Back on the beach, once Pennings threw the ball into the water Elvis had a couple of choices. He could jump right into the water and swim in a direct line to the ball or he could try to cut down on his swimming time and run along the beach until the ball was the shortest swimming distance away and then jump in.

Elvis’ final choice was to try and take the optimal route, which would entail running down the beach and, at the optimal point, jumping into the water to swim to the ball.

Pennings took Elvis to the beach and timed his swimming and running rates. By plugging his measurements into a calculus equation, Pennings found the optimal point for Elvis to jump into the water. Then Pennings returned to the beach and measured the point where Elvis jumped into the water to see if he jumped in at the optimal point.

The results of these trials revealed, statistically, that Elvis consistently was jumping in near the optimal point.

So does Elvis do calculus? Pennings performed one more demonstration to try and resolve this question for the students.

As the students leaned forward, Pennings asked Elvis repeatedly to find the derivative of x3.

“Look at his eyes carefully.” Pennings suggested. “Look at his eyes and his mouth. See, he does that every time. Nothing. What were you expecting, something else?”

Pennings does not think Elvis can do calculus, though he thinks his pooch is an example of the optimizing ability of nature. Don’t feel too bad for Elvis though, he may not be able to do calculus but he still received an honorary doctorate from Hope College.