Lion's Eye Favorite: What's the Length of a Potato?
March 19, 2010
Seems like a simple question, but is it?
Math Club was crowded – and busy – on a recent Sunday afternoon as students attacked the potato measurement problem, with help from Jeff Ibbotson, PEA math instructor.
Math Club participants on to out-of-the-ordinary problem solving, "showed that generalized curvatures are at the heart of all geometry.""If we abstract the process of counting and measuring in simple ways, we discover that we can assign a variety of measures to convex objects," says Ibbotson of the potato challenge. His presentation, designed to spur
Spencer '12, whose favorite subjects include literature and economics, enjoys Math Club because it provides "good, hard problems." He found the potato session "quite interesting and accessible to the club members." Spencer adds, "The entire session was about counting, Eulerian characteristics, and using polynomials to represent the characteristics of an object." When asked how Exeter has influenced his interest in mathematics, Spencer replies: "Exeter gave birth to it."
In Young '11, who has been a member of Exeter's American Regions Mathematics League team since her prep year, says this about Math Club, which meets 2 to 3 times each week: "Since we meet so often, we really bond with each other and usually hang out outside of club meetings as well. I think Mr. Feng [Math Club adviser with longtime involvement in the USA International Mathematical Olympiad] was right in saying that PEA's Math Club is one of the most structured clubs in the country. I do think that students get much better at critical and logical thinking just by virtue of coming to the meetings and working hard."
"My work with the Math Club combined abstract counting with geometric features of objects (like cubes, triangles and donuts)," explains Ibbotson of the potato challenge. "I wanted to show the students how the usual measures (like length, area, volume) can be combined into a formal polynomial. These polynomials can then be multiplied to generate 'sizes' of more unusual objects. The really amazing thing is that the 'number of an object' turns out to be the Euler characteristic of that object. The ideas behind the discussion are classical ones but the idea that the Euler characteristic is the simplest measure of a set is due to a teacher of mine, Stephen Schanuel."
"Mr. Ibbotson has great chemistry with students," says In Young. "Overall, the experience was positive for everyone, and I know that some non-regular math club members showed up just to hear Mr. Ibbotson talk."
And to think – all this high-level math born of the simple potato. Julia Child would have been impressed...
Interested in learning more?
Read about Exeter's Math Department…
Learn more about Math Club, which meets two to three times per week…
Lion's note: this article first appeared on October 10, 2009.
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