Rotational Symmetry Solves the 2011 IMO Windmill Problem — E8 Intelligence Research

FINDING: The 2011 IMO windmill problem (Q2) is a combinatorial geometry problem whose solution hinges on a rotational symmetry argument, not on any fixed ratio or constant. | MATH: The problem: Given \(n\) points in general position, find a line through one point that rotates continuously, switching pivot points, such that it visits each point as pivot exactly once per \(180^∘\) rotation. The key invariant is that the number of points on each side of the rotating line changes by \(± 1\) at each pivot switch; the solution uses a "windmill" process where the line rotates through \(180^∘\), and the pivot sequence is a permutation of the \(n\) points. No explicit equation or constant emerges — the depth is combinatorial. | CONNECTION: The rotational symmetry of the windmill process is a discrete analogue of continuous rotation groups (SO(2)), but there is no golden ratio, no 0.618/1.618, no base-60, and no crystallographic root system. The only geometric harmony is the cyclic per Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com