Undergraduate Research

Can one hear where certain triangular drums are struck?

This question seeks to answer whether or not we can hear where certain nice triangular drumheads are struck, namely the isosceles right triangle, equilateral triangle, and the 30-60-90 triangle. These, along with squares and rectangles, are the only class of planar domains which tile the plane via reflections over their sides such that each vertex is incident to an even number of triangles in the tiling. 

This program produced a paper that shows one can hear where the isosceles right and equilateral triangles are struck and, surprisingly, there are two audibly indistinguishable points in the 30-60-90 triangle.

This program started fall 2024 and ran through spring 2026.

Participants:

• Tyler Dixon

• Alif Miah

• Nikita Safronov

• Sean Snyder

• Anatolii Vakaryuk