Inducing the Symmetries Out of the Complexity: The Kepler Triangle and Its Kin as a Model Problem

Abstract

This essay is intended to exemplify how to solve a complex problem with several symmetries. The sample problem is a generalisation of the Kepler triangle. In 1597 Kepler discussed the golden-ratio related right-triangle, which is embedded in the cross-section of the Pharaoh Khufu’s pyramid. Three hundred years have passed since the first report, there are only three ‘such’ specimens known to mankind in the 21 Century. But the author broke through the solution space to reveal the three aspects: the golden ratio, the Fibonacci sequence and the Pythagorean Theorem. The path to the solution is explained from the starting point of collecting the data, by way of finding the invariants and to the goal of deriving the laws governing the solution space.