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The Sound of Symmetry

Zhiqin Lu ; Julie Rowlett (Institutionen för matematiska vetenskaper, matematik)
The American mathematical monthly (0002-9890). Vol. 122 (2015), 9, p. 815-835.
[Artikel, refereegranskad vetenskaplig]

The inverse spectral problem was popularized by M. Kac's 1966 article in THIS MONTHLY “Can one hear the shape of a drum?” Although the answer has been known for over twenty years, many open problems remain. Intended for general audiences, readers are challenged to complete exercises throughout this interactive introduction to inverse spectral theory. The main techniques used in inverse spectral problems are collected and discussed, then used to prove that one canhear the shape of: parallelograms, acute trapezoids, and the regular n-gon. Finally, we show that one can realistically hear the shape of the regular n-gon amongst all convex n-gons because it is uniquely determined by a finite number of eigenvalues; the sound of symmetry can really be heard!



Denna post skapades 2015-12-07. Senast ändrad 2016-03-09.
CPL Pubid: 227509

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur