Parity Invariance in Rotating Line Sweeps of Finite Point Sets — E8 Intelligence Research

FINDING: IMO 2011 Q2 "windmill" problem reveals invariant parity structure in finite point configurations under rotating lines. | MATH: For \(n\) points in general position, a rotating line through a point \(p\) sweeps through all points; the parity of the number of points on each side of the line is invariant under the rotation, leading to a combinatorial fixed-point argument. No explicit constants or ratios. | CONNECTION: The invariant parity mirrors a \(Z_2\) symmetry, analogous to reflection symmetries in crystallographic root systems (e.g., \(A_n\) Coxeter groups). The rotating line's discrete steps correspond to a cyclic order on the points, reminiscent of base-60 angular subdivisions in Babylonian astronomy. | DEPTH: 6 — elegant combinatorial geometry with deep symmetry, but no new universal constants or harmonic ratios. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com