What question did this study set out to answer?

The aim is to analyze Plimpton 322's encoding of Pythagorean triples through sexagesimal ratios.

July 24, 2026Open Access

Plimpton 322: A Sexagesimal Table of Secant-Squared Ratios for Pythagorean Triples — E8 Intelligence Research

Key Points

The aim is to analyze Plimpton 322's encoding of Pythagorean triples through sexagesimal ratios.
Examined pairs of values related to secant-squared ratios for right triangles.
Identified relationships between sides a, b, c listed in a tabular format.
Generated triples using reciprocal pairs (p, q) in base-60, focusing on specific conditions.
The method produces valid Pythagorean triples with (c/b)² values clustering around 1.9834.
The angles corresponding to these ratios approach 45° and 30°.
The pairs (p, q) are strategically chosen to maintain the required relationships.

Abstract

FINDING: Plimpton 322 encodes a systematic method for generating Pythagorean triples using base-60 (sexagesimal) ratios, specifically secant-squared (sec²) values as regular numbers in a tabular form. | MATH: For a right triangle with sides a, b, c (a q, both regular in base-60, to produce triples: a = p² - q², b = 2pq, c = p² + q². The tablet selects only those where (c/b)² is a regular sexagesimal number (i.e., finite base-60 expansion). | CONNECTION: The ratios (c/b)² cluster near 1.9834, 1.9492, 1.9188, ... which correspond to angles θ ≈ 45° to 30°. The reciprocal pairs (p, q) are chosen such that p/q ≈ √ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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