English

(Not) hearing where certain triangular drums are struck

Spectral Theory 2026-07-12 v1
Authors: Tyler Dixon , Alif Miah , Nikita Safronov , Sean Snyder , Anatolii Vakaryuk , Emmett Wyman
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Abstract

We investigate whether or not one can hear at what point (up to symmetry) a drum is struck for some special planar triangles. We prove that one can hear where the equilateral and isosceles right triangles are struck. We also prove that the 30-60-90 triangle, surprisingly, has two audibly indistinguishable points. This is the first known topologically connected such example.

Cite

@article{arxiv.2607.10556,
  title  = {(Not) hearing where certain triangular drums are struck},
  author = {Tyler Dixon and Alif Miah and Nikita Safronov and Sean Snyder and Anatolii Vakaryuk and Emmett Wyman},
  journal= {arXiv preprint arXiv:2607.10556},
  year   = {2026}
}

Comments

29 pages, 8 figures