What question did this study set out to answer?

This research aims to interpret Plimpton 322 as the oldest trigonometric table based on ratios rather than angles.

July 22, 2026Open Access

Plimpton 322: Oldest Trigonometric Table Using Ratios, Not Angles — E8 Intelligence Research

Key Points

This research aims to interpret Plimpton 322 as the oldest trigonometric table based on ratios rather than angles.
Analyzed the Old Babylonian clay tablet Plimpton 322 dating back to c. 1800 BCE.
Examined the method of generating Pythagorean triples using reciprocal pairs in a base-60 system.
Investigated the organization of ratios in the tablet, focusing on values of b^2 / a^2.
Identified 15 rows of Pythagorean triples demonstrating systematic arrangement.
Confirmed that ratios b/a decrease from 1.9834027 to 1.38716 across the dataset.
Established the use of regular sexagesimal numbers to generate consistent results.

Abstract

FINDING: Plimpton 322 is an Old Babylonian clay tablet (c. 1800 BCE) listing 15 rows of Pythagorean triples, likely generated by a systematic method using reciprocal pairs in base-60, and now interpreted as the world's oldest known trigonometric table based on ratios, not angles. MATH: - Each row corresponds to a Pythagorean triple (a, b, c) satisfying \ (a² + b² = c² \), with a q \) ), set \ (a = p² - q² \), \ (b = 2pq \), \ (c = p² + q² \). - Key constants: base-60 (sexagesimal) system; regular numbers (only prime factors 2, 3, 5). - The tablet's first column gives \ ( (b/a) ² \) or \ ( (c/a) ² \), with values like 1. 9834027. . . (sexagesimal 1;59, 0, 15) down to 1. 38716. . . (sexagesimal 1;23, 13, 46). CONNECTION: - The ratios \ (b/a \) from the tri Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com

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