Windmill Problem: IMO 2011's Rotating Line Geometry — E8 Intelligence Research

FINDING: The search results are dominated by pedagogical videos and media coverage of IMO problems, not raw mathematical discoveries. The only substantive mathematical artifact referenced is the 2011 IMO Problem 2 ("windmill" problem), which is a combinatorial geometry problem about rotating lines through points. MATH: The windmill problem (2011 IMO P2): Given a finite set \(S\) of \(n \geq 3\) points in the plane, no three collinear, a "windmill" process rotates a line \(l\) through a point \(P \in S\) (pivot). When \(l\) hits another point \(Q \in S\), the pivot switches to \(Q\) and rotation continues. The theorem: there exists a choice of initial line and pivot such that the windmill visits every point of \(S\) infinitely often. The proof uses a parity/invariant argument: define \(f(l)\) = number of points on one side of \(l\). When pivot switches, \(f(l)\) changes by \(\pm 1\) or stays constant depending on whether the new pivot lies on the same side. The key invariant is that \(

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com