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Mathematics of classical mechanics, including Hamiltonian mechanics, Lagrangian mechanics, applications of symplectic geometry to mechanics, deterministic chaos, resonance etc.
16
votes
Why is the billiard problem for obtuse triangles so hard?
Start from the simplest path, a triangle with angles $\alpha, \beta, \gamma$, and build the unique triangle for which this path is a billiard path. It's easy to see that the latter triangle has angles …