Hearing The Shape Of A Drum
To hear the shape of a drum is to infer information about the shape of the drumhead from the sound it makes, i.e., from the list of overtones, via the use of mathematical theory. "Can One Hear the Shape of a Drum?" was the witty title of an article by Mark Kac in the American Mathematical Monthly 1966 (see the references below), but these questions can be traced back all the way to Hermann Weyl.
The frequencies at which a drumhead can vibrate depend on its shape. The Helmholtz equation tells us the frequencies if we know the shape. These frequencies are the eigenvalues of the Laplacian in the region. A central question is: can they tell us the shape if we know the frequencies? No other shape than a square vibrates at the same frequencies as a square. Is it possible for two different shapes to yield the same set of frequencies? Kac did not know the answer to that question.
Famous quotes containing the words drum, hearing and/or shape:
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As his corse to the rampart we hurried;”
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“We can say that the sound is the primary object of the act of hearing, and that the act of hearing itself is the secondary object.”
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“Most revolutionaries are potential Tories, because they imagine that everything can be put right by altering the shape of society; once that change is effected, as it sometimes is, they see no need for any other.”
—George Orwell (19031950)