What question did this study set out to answer?

Investigate the structure of Plimpton 322 to determine how it generates Pythagorean triples using sexagesimal numbers.

July 21, 2026Open Access

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

Puntos clave

Investigate the structure of Plimpton 322 to determine how it generates Pythagorean triples using sexagesimal numbers.
Analysis of Plimpton 322 tablet containing 15 pairs of reciprocal numbers.
Utilization of the OB scribal algorithm to derive Pythagorean triples from regular numbers.
Examination of ratios and calculations to link findings to trigonometric values and the golden ratio.
Identification of 15 reciprocal pairs producing Pythagorean triples.
Establishment of a relationship between the generated ratios and the golden ratio (~1.618).
Calculations confirm the correspondence of generating values to secant-squared ratios.

Resumen

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

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