"Our result may be generalized to other domains where similar algorithms may apply. Our algorithm is based on the fact that the eigenfunctions are presented as a linear combination of simple plane waves. It is therefore tempting to try and generalize it for other drums with similar property. The equilateral triangle is an immediate candidate (see [29] and references within).

A further, and quite surprising, result is the recursive formula for the number of nodal loops. To our knowledge this is the first known exact formula for the nodal count of a non-separable planar manifold (for certain eigenfunctions of tori exact formulas have been given in [22]). The formula was found by direct inspection of large tables and has been verified for a large bulk of data computationally. An obvious challenge is to prove this formula. In particular, the recursive part of the formula resembles the famous Euclid algorithm for the greatest common divisor. A further investigation of the mentioned formula might therefore expose some new number theoretical properties of the nodal count."