Ali lahko slišimo obliko bobna?

V prvem delu je predstavljena Helmholtzova enačba in preprost dokaz izospektralnosti dveh biljardov v obliki večkotnika. Naslednji del je posvečen geometrijskim lastnostim biljardov, ki so dobljene s pomočjo lastnih vrednosti, in raziskavi statističnega obnašanja spektra. V zadnjem delu sta predstavljeni dve eksperimentalni potrditvi izospektralnosti različnih biljardov.

Can one hear the shape of a drum?

In the first part, the Helmholtz equation is presented and a simple proof of isospectrality between two polygonal billiards is provided. Next, the geometric properties of billiards that can be deduced from the eigenvalue spectrum are examined and the statistical behavior of the spectrum is explored. In the last part, we two experimental realizations of isospectral billiards are provided which give experimental confirmation of isospectrality.