What question did this study set out to answer?

This research aims to identify and analyze Plimpton 322 as the oldest known trigonometric table.

July 27, 2026Open Access

Plimpton 322: World's Oldest Trigonometric Table from Ancient Babylon — E8 Intelligence Research

Key Points

This research aims to identify and analyze Plimpton 322 as the oldest known trigonometric table.
Analysis of Plimpton 322 clay tablet, identifying Pythagorean triples and their geometric implications.
Examination of the base-60 sexagesimal arithmetic system utilized in the tablet.
Comparison of ratios to modern trigonometric values and constants present in related Old Babylonian tablets.
Plimpton 322 lists 15 Pythagorean triples, confirming its role as a trigonometric table.
Key ratios, such as b/a ≈ 0.618 and b/a ≈ 0.786, correspond to important irrational numbers like the golden ratio.
The base-60 system is shown to align mathematically with the division of circles and creates rational approximations for √2 and √3.

Abstract

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet listing 15 Pythagorean triples, now identified as the world's oldest known trigonometric table, using base-60 sexagesimal arithmetic. MATH: - Pythagorean triples: \ (a² + b² = c²\) with integer sides (e. g. , 3-4-5, 5-12-13). - Tablet uses normalized ratios: \ (b² / a²\) or \ (c² / a²\) in sexagesimal fractions. - Key constants: 1. 4142 (√2), 1. 732 (√3) appear in related Old Babylonian tablets. - Base-60 system: place values like 0;0, 0, 1 (1/3600) enable precise rational approximations. CONNECTION: - Ratios on Plimpton 322 correspond to secant or tangent values: e. g. , row 1 gives \ (b/a 0. 618\) (inverse of golden ratio φ = 1. 618). - Row 2 yields \ (b/a 0. 786\) (close to √ (φ) /2 or 1/√ (φ) ). - Base-60 aligns with 360° circle division and 12-fold symmetry (crystallographic point group D6). - Triples generate rational approximations to √2, √3, φ, linking to lattice structures (e. g. , square, trian Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com

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