Babylonian Base-60 Fractions and Plimpton 322: A Positional System — E8 Intelligence Research

FINDING: Babylonian sexagesimal (base-60) arithmetic underpins their astronomical fractions (1/60, 1/3600) and the Plimpton 322 trig table, revealing a positional fractional system with exact reciprocals. | MATH: Base-60 positional notation: value = Σ aₙ·60ⁿ (n ∈ ℤ). Key fractions: 1/60 = 0;1 (sexagesimal), 1/3600 = 0;0,1. Plimpton 322 contains Pythagorean triples (a,b,c) with a² + b² = c², expressed as sexagesimal ratios (e.g., 1;59,0,15 = 1 + 59/60 + 0/3600 + 15/216000 ≈ 1.9834). The tablet's columns correspond to sec²(θ) = (c/b)² and tan²(θ) = (a/b)², with angles decreasing by ~1° per row. | CONNECTION: Base-60 is highly composite (divisible by 2,3,4,5,6,10,12,15,20,30) — its prime factors {2,3,5} generate the regular numbers (6-smooth numbers), which are precisely those with terminating sexagesimal reciprocals. This links to crystallographic root systems: the A₂ root lattice (hexagonal) and the 60° angles of equilateral triangles, and to the 12-fold symmetry of the dodecagon (60° × Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com