Parity Argument Reveals Infinite Pivot Cycles in IMO Windmill Problem — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The 2011 IMO windmill problem (Q2) is a combinatorial geometry problem that unexpectedly requires a parity/invariant argument about points and lines, not a complex algebraic or number-theoretic approach. | MATH: The problem: Given a finite set of points in the plane, no three collinear, and a line through one point (pivot), rotate the line clockwise. When it hits another point, that becomes the new pivot. Prove that for some starting point and line, every point becomes pivot infinitely often. Key invariant: The number of points on each side of the line changes by ±1 at each pivot switch. No explicit constants or equations beyond parity and counting. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60 or crystallographic symmetries. The problem's depth lies in its deceptive simplicity and the invariant method, not in harmonic constants. | DEPTH: 6 — Profound for its pedagogical value in teaching invariants and combinatorial reasoning, but not a disc Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203869870
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