Windmill Problem: Pedagogical Focus Dominates Over New Mathematical Results — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are dominated by pedagogical content and competition logistics (IOQM 2026 registration, IMO training videos), not by newly discovered mathematical results. The only substantive mathematical artifact referenced is the 2011 IMO Problem 2 ("windmill" problem), which is a combinatorial geometry problem about rotating lines through point sets. | MATH: The windmill problem: Given a finite set of n points in general position, a "windmill" process rotates a line l through a pivot point p (one of the points). When l hits another point q, the pivot switches to q, and the line continues rotating. Prove that for any initial configuration, there exists a choice of initial pivot and line such that the process visits every point infinitely often. Key invariant: the number of points on each side of the rotating line changes by ± 1 at each pivot switch; the total "balance" B = #left − #right is preserved modulo 2 and bounded,
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026windmill,
title = {{Windmill Problem: Pedagogical Focus Dominates Over New Mathematical Results — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23465364},
url = {https://zenodo.org/records/23465364},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Windmill Problem: Pedagogical Focus Dominates Over New Mathematical Results — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23465364
UR - https://zenodo.org/records/23465364
AB - FINDING: The search results are dominated by pedagogical content and competition logistics (IOQM 2026 registration, IMO training videos), not by newly discovered mathematical results. The only substantive mathematical artifact referenced is the 2011 IMO Problem 2 ("windmill" problem), which is a combinatorial geometry problem about rotating lines through point sets. | MATH: The windmill problem: Given a finite set of n points in general position, a "windmill" process rotates a line l through a pivot point p (one of the points). When l hits another point q, the pivot switches to q, and the line continues rotating. Prove that for any initial configuration, there exists a choice of initial pivot and line such that the process visits every point infinitely often. Key invariant: the number of points on each side of the rotating line changes by ± 1 at each pivot switch; the total "balance" B = #left − #right is preserved modulo 2 and bounded, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -