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REV: You can't hear the shape of a drum
Posted:
Sep 10, 1992 10:28 AM
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Cipra, Barry, You can't hear the shape of a drum, Science 255 (27 March
1992) 1642-1643.
In 1966, Mark Kac asked "Can you hear the shape of a drum?" (American
Mathematical Monthly 73 (4, Part II) 1-23). In one dimension, the answer
is yes (the length of a violin string is determined by the lowest
frequency produced by plucking it); in dimensions greater than two, the
answer is no (there are "hyperdrums" of different shapes that make the
same "hypersounds"). What about dimension 2? For a vibrating membrane,
are the size and shape of the bounding curve uniquely determined by the
eigenvalues of the wave motions of the membrane? Kac thought not, but "I
may well be wrong and I am not prepared to bet large sums either way."
Perhaps he should have trusted his intuition, because Carolyn Gordon and
David Webb (Washington University) and Scott Wolpert (University of
Maryland) have exhibited counterexamples at last.
This review was reprinted with permission from Mathematics Magazine, June
1992 issue.
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