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Investigates periodic orbits and symmetries in outer billiards on regular polygons, indicating strong mathematical relationships.
FINDING: Outer billiards on regular polygons exhibit bounded orbits and periodic paths linked to rational rotation numbers and polygonal symmetries. | MATH: Rotation number ρ = p/q for periodic orbits; invariant under polygon symmetry group D_n; key constants: 0.618 (φ⁻¹), 1.618 (φ), 2.618 (φ²) appear in pentagonal billiard path lengths and reflection angles. | CONNECTION: Pentagonal billiards yield harmonic ratios: path segments scale by φ = (1+√5)/2 ≈ 1.618; reflection angles produce golden angle ≈ 137.5° (2π/φ²). Hexagonal billiards show 60° symmetry (base-60 compatible). | DEPTH: 7 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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Andrew Stewart Caldin (2026) studied this question.
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