Sexagesimal Roots of the 360° Circle: Base-60 Arithmetic, Not Solar Year — E8 Intelligence Research

FINDING: The 360° circle division arises from base-60 arithmetic, not from solar-year approximation; 360 is the highly composite product of 6×60, maximizing divisibility for astronomical fractions. MATH: - Base-60 system: 60 = 2²×3×5; 360 = 6×60 = 2³×3²×5. - Divisor count: τ(360) = (3+1)(2+1)(1+1) = 24 divisors. - Key fractions in sexagesimal: 1/2=30′, 1/3=20′, 1/4=15′, 1/5=12′, 1/6=10′, 1/8=7.5′, 1/9=6.666…′, 1/10=6′, 1/12=5′ — all terminating in base-60. - The arXiv paper (0707.0676) shows a geometric construction where inscribing regular hexagons (6-fold symmetry) around a circle yields natural multiples of 6: 6, 12, 24, 60, 360 — via successive angle bisection (2^n × 6). CONNECTION: - 360 = 6 × 60 directly links hexagonal (6-fold) rotational symmetry to the sexagesimal system. - The golden ratio φ = 1.618 appears in pentagonal (5-fold) symmetry, but 360° is divisible by 5 (72°) — so both 5-fold and 6-fold symmetries coexist in the circle's degree division. - The r Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com