Plimpton 322: A Base-60 Trigonometric Table of Reciprocal Ratios — E8 Intelligence Research

FINDING: Plimpton 322 encodes exact sexagesimal ratios (reciprocal pairs) forming a primitive trigonometric table based on the unit circle in base-60, not angles. MATH: Each row gives a normalized Pythagorean triple (a, b, c) with a/b = (p² - q²)/(2pq) for integers p, q in base-60. The key ratio is the "diagonal" (c/b) = (p² + q²)/(2pq). The tablet lists 15 such ratios, all with decreasing c/b from ~1.983 to ~1.387. The generating rule: choose regular sexagesimal numbers (p, q) such that p/q is a sexagesimal fraction with finite expansion. CONNECTION: The ratios c/b correspond to cosecant values (1/sinθ) in a right triangle. The reciprocal pairs (p, q) are linked to the golden ratio φ = 1.618… via the identity (p/q) + (q/p) = c/b + a/b. For the first row, p/q ≈ 1.618 (φ). The base-60 system naturally produces harmonic ratios like 0.618, 0.786 (√φ/2), and 2.618 (φ²). The tablet's structure mirrors a lattice of integer points on a circle in the sexagesimal plane. DEPTH: 9 — This re Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com