Isoperimetric Quotients and Building Pig Pens? Math Faculty Member Matt Simonson Explains.
Matthew Simonson’s undergraduate mathematics thesis has taken on a life of its own. Not only is it a published article, it’s an experience Mr. Simonson recreates in his math classrooms at Milton. At Williams College, Mr. Simonson investigated the isoperimetric problem: how to enclose a certain amount of area with the least perimeter. Or, as Mr. Simonson puts it, “Suppose you’re building a pig pen. Your pigs need a certain amount of space to wallow, but you want to spend as little money as possible on fencing. What shape should your fence be?” Ordinarily, the most efficient shape would be a circle. “However, if you’re building the pig pen against the side of a barn, then you only need a semicircle. And if the wall of the barn is curved, or the surface isn’t flat, then the problem gets really interesting.”
The article Mr. Simonson wrote, based on his research of hyperbolic geometry, was published in the November 2011 issue of the Journal of the Korean Mathematical Society. He brings his research and discovery experience into his Honors Geometry classroom, where students are writing, peer reviewing and publishing their own math journal.
“This exploration affirmed for me how creative math can be,” says Mr. Simonson. “When you’re tackling a problem that’s never been solved, there’s no right way to go about proving it. Crafting a proof is more like architecture than puzzle solving. There are so many tools to choose from, and you have to figure out which will work best.”
In his geometry class, after students finished their unit on triangles, Mr. Simonson moved them on to quadrilaterals on their own—researching, making discoveries and proving them. They typed up their best proofs, submitted them to their classmates for peer review, and will soon publish the results in a journal they titled, “The Deliberations and Annals of the Academy.”
“Working in a department that values investigation and discovery so highly is a great experience. I want to teach my students that math is more than just solving problems in a textbook. It is about creativity and excitement. I also want to expose them to what the entire academic research process is like from start to finish.”