Isospectral Manifolds

Drums that sound the same, i.e., have the same eigenfrequency spectrum. Two drums with differing Area,Perimeter, or Genus can always be distinguished. However, Kac (1966) asked if it was possible to constructdifferently shaped drums which have the same eigenfrequency spectrum. This question was answered in the affirmative by Gordonet al. (1992). Two such isospectral manifolds are shown in the right figure above (Cipra 1992).

References

Chapman, S. J. ``Drums That Sound the Same.'' Amer. Math. Monthly 102, 124-138, 1995.

Cipra, B. ``You Can't Hear the Shape of a Drum.'' Science 255, 1642-1643, 1992.

Gordon, C.; Webb, D.; and Wolpert, S. ``Isospectral Plane Domains and Surfaces via Riemannian Orbifolds.'' Invent. Math. 110, 1-22, 1992.

Gordon, C.; Webb, D.; and Wolpert, S. ``You Cannot Hear the Shape of a Drum.'' Bull. Amer. Math. Soc. 27, 134-138, 1992.

Kac, M. ``Can One Hear the Shape of a Drum?'' Amer. Math. Monthly 73, 1-23, 1966.

• Dilogarithm
• Dilworth's Lemma
• Dilworth's Theorem
• Dimension
• Dimensionality Theorem
• Dimension Axiom
• Dimension Invariance Theorem
• Diminished Polyhedron
• Diminished Rhombicosidodecahedron
• Dini Expansion
• Dini's Surface
• Dini's Test
• Dinitz Problem
• Diocles's Cissoid
• Diophantine Equation
• Diophantine Equation--10th Powers
• Diophantine Equation--5th Powers
• Diophantine Equation--6th Powers
• Diophantine Equation--7th Powers
• Diophantine Equation--8th Powers
• Diophantine Equation--9th Powers
• Diophantine Equation--Cubic
• Diophantine Equation--Linear
• Diophantine Equation nth Powers
• Diophantine Equation--Quadratic