Can one hear the shape of a drum?
E92906
"Can one hear the shape of a drum?" is a famous 1966 paper by mathematician Mark Kac that explores whether the geometric shape of a domain can be uniquely determined from the spectrum of its Laplacian, encapsulated in the question of whether one can infer a drum’s shape from the sound it makes.
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical paper
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research article → |
| addresses |
relationship between physical sound and mathematical spectrum
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| asksWhether |
the spectrum of the Laplacian uniquely determines the shape of a domain
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| associatedWith |
Mark Kac's work in probability and analysis
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| author |
Mark Kac
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| context |
Dirichlet eigenvalues of the Laplacian
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Laplacian on bounded planar domains → |
| field |
mathematical physics
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mathematics → partial differential equations → spectral geometry → |
| historicalSignificance |
became a central question in spectral geometry
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stimulated the search for non-isometric isospectral domains → |
| influencedField |
Riemannian geometry
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mathematical analysis → quantum mechanics → spectral geometry → |
| inspired |
construction of planar isospectral domains by Gordon, Webb, and Wolpert
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| involves |
eigenvalue problem for the Laplace operator
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inverse spectral problem → relationship between geometry and spectrum → spectral invariants → |
| language |
English
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| mainConcept |
Dirichlet boundary conditions
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Laplacian spectrum → eigenvalues of the Laplacian → isospectral domains → vibrating membrane → |
| mainQuestion |
whether the geometric shape of a domain is determined by the spectrum of its Laplacian
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| medium |
journal article
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| notableFor |
connecting physical intuition about sound with abstract spectral theory
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formulating the phrase "Can one hear the shape of a drum?" → popularizing inverse spectral problems → |
| popularizedQuestion |
Can one determine the shape of a drum from the sound it makes?
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| publicationYear |
1966
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| questionType |
inverse spectral question
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| relatedTo |
eigenvalue spectra of differential operators
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hearing the shape of a Riemannian manifold → inverse problems in mathematical physics → |
| timePeriod |
20th century
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| titleQuestion |
Can one hear the shape of a drum?
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Referenced by (1)
| Subject (surface form when different) | Predicate |
|---|---|
|
Mark Kac
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notableWork |