## JSTOR All-Stars: "Can One Hear the Shape of a Drum?"

**August 28, 2007**

The JSTOR database is an archive of important scholarly journals, offering researchers high-resolution, scanned images of journal issues and pages. It now includes 37,094 articles from *The American Mathematical Monthly*, from 1894 to 2003. The 1966 article "Can One Hear the Shape of a Drum?" by Mark Kac ranks as the sixth most frequently accessed *Monthly* article in the database.

"Can One Hear the Shape of a Drum?"

Mark Kac

*The American Mathematical Monthly*, Vol. 73, No. 4 (April 1966), pp. 1-23

When a membrane, held fixed along its boundary, is set in motion, its displacement obeys the wave equation. Certain solutions represent the pure tones the membrane is capable of producing. These special solutions are also known as normal modes (or, in mathematical terms, eigenvalues). Suppose that two plane regions, each bounded by a certain curve, have identical eigenvalues. Does this mean that the regions are congruent in the sense of Euclidean geometry? In effect, if you had perfect pitch, could you find the shape of a drum?

The top five *Monthly* articles are:

- "College Admissions and the Stability of Marriage" by David Gale and Lloyd Shapley, Vol. 69, No. 1 (January, 1962), pp. 9-15.
- "Introduction to Fermat's Last Theorem" by David A. Cox, Vol. 101, No. 1 (January, 1994), pp. 3-14.
- "Period Three Implies Chaos" by Tien-Yien Li and James A Yorke, Vol. 82, No. 10 (December, 1975), pp. 985-992.
- "History of Mathematics Before the Seventeenth Century" by Raymond Clare Archibald, Vol. 56, No. 1 (January, 1949), pp. 7-34.
- "Galois Theory for Beginners" by
John Stillwell, Vol. 101, No. 1 (January, 1994), pp. 22-27.

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