Eastern and Western Mentalities as Golden and Silver Stationary Points in Probe Particle Dynamics within a Modular Domain
Sergei Nechaev (LPTMS)
We analyze flows generated by iterative dynamics of reflections of triangles. We interpret these flows as the probe particle adiabatic dynamics in the fundamental domain of the modular group. We consider two specific cases of lattices: (a) generated by reflections of equilateral triangles, and (b) generated by reflections of rectangular isosceles triangles. We show that stationary points of the flows for equilateral and isosceles triangles are correspondingly the « Golden » and the « Silver » ratios. We speculate about the manifestation of the difference between the Golden and the Silver ratios in cultural traditions of the « Western » and the « Eastern » world.