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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Can one hear the shape of a drum? canonical | 1 |
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical paper
ⓘ
research article ⓘ |
| addresses | relationship between physical sound and mathematical spectrum ⓘ |
| asksWhether | the spectrum of the Laplacian uniquely determines the shape of a domain ⓘ |
| associatedWith | Mark Kac's work in probability and analysis ⓘ |
| author | Mark Kac ⓘ |
| context |
Dirichlet eigenvalues of the Laplacian
ⓘ
Laplacian on bounded planar domains ⓘ |
| field |
mathematical physics
ⓘ
mathematics ⓘ partial differential equations ⓘ spectral geometry ⓘ |
| historicalSignificance |
became a central question in spectral geometry
ⓘ
stimulated the search for non-isometric isospectral domains ⓘ |
| influencedField |
Riemannian manifolds
ⓘ
surface form:
Riemannian geometry
mathematical analysis ⓘ quantum mechanics ⓘ spectral geometry ⓘ |
| inspired | construction of planar isospectral domains by Gordon, Webb, and Wolpert ⓘ |
| involves |
eigenvalue problem for the Laplace operator
ⓘ
inverse spectral problem ⓘ relationship between geometry and spectrum ⓘ spectral invariants ⓘ |
| language | English ⓘ |
| mainConcept |
Dirichlet conditions
ⓘ
surface form:
Dirichlet boundary conditions
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 ⓘ |
| medium | journal article ⓘ |
| notableFor |
connecting physical intuition about sound with abstract spectral theory
ⓘ
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? ⓘ |
| publicationYear | 1966 ⓘ |
| questionType | inverse spectral question ⓘ |
| relatedTo |
eigenvalue spectra of differential operators
ⓘ
hearing the shape of a Riemannian manifold ⓘ inverse problems in mathematical physics ⓘ |
| timePeriod | 20th century ⓘ |
| titleQuestion | Can one hear the shape of a drum? ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.