Geometric Harmony Through Convex Hulls: Solving the Windmill Problem from 2011 IMO — E8 Intelligence Research
Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) · 2026
FINDING: The windmill problem from the 2011 IMO is a challenging yet insightful geometric puzzle that demonstrates complex combinatorial geometry. MATH: The windmill problem involves proving that, given any set of points in the plane, there exists a line (the "windmill") such that all other points lie on one side of this line. The key insight relies on properties of convex hulls and rotation arguments. CONNECTION: None explicitly highlighted as part of geometric harmony like the golden ratio or base-60 mathematics. DEPTH: 4 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com