Parity Invariant Solves the 2011 IMO Windmill Problem — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The 2011 IMO windmill problem (Q2) is a deceptively simple combinatorial geometry problem whose solution hinges on a parity/invariant argument over point configurations, not on any classical metric ratio. | MATH: Given \(n\) points in general position, a "windmill" process rotates a line through a pivot point, switching pivot to the newly crossed point. Key invariant: the number of points on each side of the line changes by \(\pm 1\) at each switch; the process is periodic with period \(n\) (for odd \(n\)) or \(2n\) (for even \(n\)). No explicit constants; the proof uses a discrete parity invariant (mod 2) and the fact that the line's orientation sweeps \(2\pi\) over the full cycle. | CONNECTION: The windmill's rotational symmetry (periodic angular sweep) echoes cyclic group \(C_n\) and the dihedral symmetry of regular \(n\)-gons, but no golden ratio or base-60 appears. The invariant is topological (winding number), not metrical. | DEPTH: 6 — elegant, but it's a combinatorial/ 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: W7212187290
Cites:
Cited by:
Related to: