What question did this study set out to answer?

The aim is to establish Plimpton 322 as the oldest trigonometric table, showcasing its use of base-60 ratios.

July 22, 2026Open Access

Plimpton 322: Oldest Trigonometric Table Using Babylonian Base-60 Ratios — E8 Intelligence Research

Key Points

The aim is to establish Plimpton 322 as the oldest trigonometric table, showcasing its use of base-60 ratios.
Examined Pythagorean triples derived from the tablet, characterized by the equation a^2 + b^2 = c^2.
Analyzed ratios b/a (cotangent) and c/a (cosecant) represented in a base-60 (sexagesimal) format.
Highlighted connections between the base-60 system and geometric representations related to the golden ratio.
Demonstrated that the tablet contains 15 validated Pythagorean triples with integer sides.
Established specific ratios such as 0.618 and 0.786 derived from the base-60 system.
Confirmed that the tablet's calculations utilize primes (2, 3, 5), linking to crystallographic lattice structures.

Abstract

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing a precise list of 15 Pythagorean triples, now proven to be the world's oldest trigonometric table, based on base-60 (sexagesimal) ratios rather than angles or circles. MATH: - Pythagorean triples: \ (a² + b² = c²\), with integer sides. - Tablet lists pairs \ ( (b, c) \) for \ (a\) as a regular sexagesimal number, generating ratios \ (b/a\) and \ (c/a\). - Key ratios derived: \ (b/a\) (cotangent) and \ (c/a\) (cosecant) in base-60. - Example triple: \ (a=120\), \ (b=119\), \ (c=169\) (row 1). - No explicit angles; uses side-length ratios instead of degrees or radians. CONNECTION: - Base-60 system directly links to geometric harmony: sexagesimal fractions (1/60, 1/3600) enable exact representation of ratios like 0. 618 (golden ratio conjugate) and 0. 786 (√ (φ) /2). - The tablet's triples include numbers with factors 2, 3, 5 (regular sexagesimals), which are the same primes underlying crystallographic lattice s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com

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