Plimpton 322: A Secant-Squared Table of Regular Reciprocal Pairs for Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 contains 15 pairs of regular sexagesimal numbers (reciprocal pairs) used to generate Pythagorean triples via the OB scribal algorithm: take \ (p, q \) regular (divisors of 60ᵏ), then triple = \ ( (p² - q², 2pq, p² + q²) \). The tablet lists \ ( (p/q) ² \) values in descending order, effectively a secant-squared table. MATH: - Regular numbers: \ (2ᵃ 3ᵇ 5ᶜ \) (divisors of 60ᵏ). - Reciprocal pair generation: \ (p, q \) such that \ (p q = 60ᵏ \) (or \ (p/q \) rational with terminating sexagesimal expansion). - Triple: \ (a = p² - q², \; b = 2pq, \; c = p² + q² \). - Column I gives \ ( (c/a) ² = (p/q + q/p) ² / 4 \), i. e. , \ (² \) for angle \ (\) opposite side \ (a \). - Ratios on tablet: e. g. , line 1: \ (p/q 1. 9834 \) → \ ( (p/q) ² 3. 934 \), corresponding to angle ~45°. CONNECTION: - **Golden ratio link**: The regular number pairs \ (p, q \) produce ratios \ (p/q \) that cluster near 1. 618 (golden ratio) f Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com