Windmill Problem Explained: 2011 IMO P2 and Garment Folding Robotics — E8 Intelligence Research

Abstract

FINDING: The search results are mostly video titles and abstracts, not actual solutions. The only concrete mathematical content is the 2011 IMO windmill problem (P2) and a robotics paper on garment folding. No IMO 2025/2026 solutions are present. | MATH: Windmill problem (2011 IMO P2): Given a set of \(n\) points in general position, a "windmill" process rotates a line through a pivot point, switching pivot to the next point hit. The key result: for any initial line, the process eventually cycles, and the pivot visits every point infinitely often. The proof uses a potential function: the number of points on each side of the line changes by ±1 per step, and the sum of squared distances from pivot to points is invariant modulo a constant. No explicit constants or ratios appear. The robotics paper (arXiv:2606.27163v2) involves reinforcement learning for bimanual folding — no pure math. | CONNECTION: The windmill problem's cyclic structure and pivot-switching rule relate to **root systems Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com