What question did this study set out to answer?

The aim is to demonstrate how Plimpton 322 serves as an ancient trigonometric table using a base-60 system.

July 23, 2026Open Access

Plimpton 322: The World's Oldest Trigonometric Table in Base-60 — E8 Intelligence Research

Key Points

The aim is to demonstrate how Plimpton 322 serves as an ancient trigonometric table using a base-60 system.
Analysis of the Plimpton 322 tablet's systematic ratios and entries in sexagesimal notation.
Identification of Pythagorean triples and their geometrical relevance.
Exploration of connections to rational points on the unit circle and geometric harmony ratios.
Plimpton 322 contains a systematic list of 15 Pythagorean triples, representing ancient trigonometric knowledge.
The tablet's use of side ratios effectively provides values for sine squared and cosine squared without explicit angles.
Key constants derived from the tablet approximate significant values in trigonometric calculations.

Abstract

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing a systematic list of 15 Pythagorean triples, now proven to represent the world's oldest known trigonometric table, using base-60 sexagesimal arithmetic and ratios rather than angles. MATH: - Pythagorean triples: \ (a² + b² = c²\), with entries in sexagesimal (base-60) notation. - Tablet columns correspond to ratios: \ (b²c² \) and \ (a²c² \), effectively giving \ (²\) and \ (²\) for a right triangle. - Key constants: 1;59, 15, 0 (≈1. 9834) and 1;24, 30, 0 (≈1. 4083) appear as normalized ratios. - No explicit angles; instead, the table uses side ratios to solve for missing lengths, a proto-trigonometry. CONNECTION: - Base-60 system naturally generates fractions like 1/60, 1/30, etc. , which relate to geometric harmony ratios (e. g. , 0. 618 ≈ 37/60, 0. 382 ≈ 23/60). - The triples correspond to rational points on the unit circle, linking to crystallographic lattice po Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com

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