“You’re in a big room and there’s a spider on one wall and on the opposite wall is a fly,” said Keith Mellinger, associate professor and chair of mathematics. “The question is, if the spider wants to walk along the walls and get to the fly, what’s the shortest path?”
The answer, perhaps surprisingly, is a spiral.
Mellinger takes exception to that conventional solution. He recently discovered that the conventional answer doesn’t always hold true. His research appears in a recent issue of the College Mathematics Journal, a publication of the Mathematical Association of America.
“If we tweak the conditions of the problem, the problem has a different solution,” he said, explaining that the dimensions of the room can change whether a spiral pattern or a straight line is in fact the shortest path.
The complexities of the problem have served as an effective teaching tool for Mellinger.
“It shows how to think about mathematics in a different way,” he said. “[The puzzle] is an excellent example to use in my geometry course.”
Although Mellinger’s research traditionally focuses on discrete mathematics applied to information technology, he is interested in many mathematical problems including one that is connected to music theory and tries to explain why musical chords have certain moods.