Is there anything new to be said about Euclidean triangles in the 21st century? Yes!

I will present three recent results: The first one could be formulated as a problem in high school, but its solution requires higher analysis. The second result uses the first one to answer the question ‚Can you hear the shape of a triangle?‘ — this is about the spectral theory of the Laplace operator. The third result concerns the asymptotics of solutions of PDEs on ‚thin‘ triangles. It gives a new perspective on the second result, and its proof uses modern geometric methods of singular analysis.