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

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:

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

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If your library is not on one of the above lists, look for a nearby library that does have JSTOR access and is open to the public. Members of the MAA have the option of purchasing an individual subscription to JSTOR that gives them access to the archives of The American Mathematical Monthly, Mathematics Magazine, and The College Mathematics Journal.

News Date: 
Tuesday, August 28, 2007