Geometric Invariants Linking Putnam and IMO Windmill Problems — E8 Intelligence Research

Abstract

FINDING: The Putnam problem's elegant solution likely involves combinatorial geometry or invariant theory; the IMO windmill problem uses projective geometry and parity invariants. | MATH: No explicit equations or constants extracted from summaries; the windmill problem involves a point-line incidence structure with a rotating line (windmill) that must hit each point infinitely often; invariant is parity of points on each side of the line. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries, or root systems evident in these competition problems. | DEPTH: 3 — These are problem-solving techniques, not fundamental discoveries about the universe's mathematical structure. The elegance lies in combinatorial reasoning, not in revealing new constants or symmetries. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com