“You can’t hear the shape of a drum,” says Professor Carolyn Gordon

Editor’s note: This article was initially published in The Daily Gazette, Swarthmore’s online, daily newspaper founded in Fall 1996. As of Fall 2018, the DG has merged with The Phoenix. See the about page to read more about the DG.

Professor Carolyn Gordon, winner of the 1990 Centennial Research Scholarship, visited Swat this week from Dartmouth College to present the 2005 Arnold Dresden Lectures in mathematics. Professor Gordon, who specializes in Riemannian geometry, gave two talks exploring the question of whether two drums with the same overtone necessarily have the same shape.

The problem has its roots in 1882, when Sir H. Schuster offered the challenge of finding the shape of a bell from its sound. In the analogous situation of a vibrating string, the length can be determined by its sound as each tone has its own distinct wave shape. However, the wave patterns of the membrane of a drum, however, are much more complex, and increasingly so with higher pitches.

While the exact shape of the drum eludes mathematicians, it is possible to “hear” the area and perimeter of the membrane.

The lectures were given over the course of two days. On Monday Professor Gordon presented a more general overview of the topic while on Tuesday she went into greater detail with a higher level of mathematical rigor. Math major Arvind Nair ’06 enjoyed the Monday lecture, commenting “[the lecture] was very engaging. [Gordon] made an effort to not make it too technical, but I could tell we were just at the surface of the topic.”

Professor Maurer felt that the lecture “intrigued people” and that the speaker was both “accessible and friendly,” as seen by those students who took part in the dinner held after the lecture on Monday. Professor Maurer also pointed out there were available seats at the dinner, and those students who did not show “definitely missed out.”

Arnold Dresden, for whom this special lecture series is named, was chair of the math department at Swat from 1935 to 1950 and distinguished in academic circles in both Europe and America. In the annual lecture series, the math department brings in a speaker distinguished in his or her own right and asks for two lectures, one general and one specialized.

Students who were unable to attend can check out http://www.falstad.com/circosc to get a small sense of Professor Gordon’s lectures, with one caveat: the site allows for playing with a virtual drum and watching the resultant waves, which becomes insanely addictive, and is perhaps better left for after exams.

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