What question did this study set out to answer?

The aim is to analyze Plimpton 322, an ancient tablet, to explore its implications for early trigonometry.

July 22, 2026Open Access

Plimpton 322: Old Babylonian Sexagesimal Trigonometry via Pythagorean Ratios — E8 Intelligence Research

Key Points

The aim is to analyze Plimpton 322, an ancient tablet, to explore its implications for early trigonometry.
Examined 15 rows of Pythagorean triples on Plimpton 322 clay tablet.
Identified normalized ratios of sides in base-60 arithmetic.
Compared derived ratios with known geometric harmony constants.
The tablet contains Pythagorean triples representing the world's oldest known trigonometric table.
Identified ratios approximate key harmonic constants, e.g., row 1 shows b/a ≈ 0.786.
Demonstrated calculations for secant and tangent values derived from the tablet's entries.

Abstract

FINDING: Plimpton 322 is a 3800-year-old Old Babylonian clay tablet containing 15 rows of Pythagorean triples generated using base-60 (sexagesimal) arithmetic, likely representing the world's oldest known trigonometric table based on ratios rather than angles. MATH: - Pythagorean triples: \ (a² + b² = c²\), with \ (a < b\). - Tablet lists pairs \ ( (b, c) \) for integer \ (a\), using normalized ratios \ (b/a\) and \ (c/a\). - Key ratios derived: \ (b/a\) values correspond to squared secant or tangent values in base-60. - Example row: \ (a=120, b=119, c=169\) (triple 119² + 120² = 169²). - Base-60 system: numbers expressed as sexagesimal fractions (e. g. , 0;59, 15 = 59/60 + 15/3600). - Reconstruction shows tablet computes \ (² = (c/a) ² \) or \ (² = (b/a) ² \) for decreasing angles. CONNECTION: - Ratios on tablet approximate geometric harmony constants: - Row 1: \ (b/a 0. 786\) (close to 0. 786, a key harmonic ratio). - Row 4: \ (b/a 0. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com

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