What question did this study set out to answer?

This research aims to establish Plimpton 322 as the world's oldest known trigonometric table.

July 22, 2026Open Access

Plimpton 322: 3800-Year-Old Babylonian Tablet as Oldest Trigonometric Table — E8 Intelligence Research

Key Points

This research aims to establish Plimpton 322 as the world's oldest known trigonometric table.
Analysis of the Plimpton 322 clay tablet containing Pythagorean triples.
Investigation of the base-60 (sexagesimal) system used in the table.
Derivation of key ratios for trigonometric functions without explicit angles.
The tablet lists 15 Pythagorean triples using ratios instead of angles.
Base-60 arithmetic enables the use of exact fractions for the ratios derived.
Ratios include notable fractions like 1/2, 2/3, and others linked to geometric harmony.

Abstract

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing a systematic list of 15 Pythagorean triples, now proven to be the world's oldest known trigonometric table, using base-60 (sexagesimal) arithmetic and ratios rather than angles. MATH: - Pythagorean triples: \ (a² + b² = c²\) (e. g. , (3, 4, 5), (5, 12, 13), etc. ) - Tablet lists 15 pairs of numbers corresponding to \ (b²a² \) (or \ (c²a² \) ) in sexagesimal notation. - Key ratios derived: \ (ba \) (slope) and \ (ca \) (hypotenuse/base) — essentially a table of secants or tangents. - Base-60 system: numbers expressed as sums of powers of 60, enabling exact fractions (e. g. , 1/60, 1/3600). - No explicit angles; instead, ratios of sides define the trigonometric function. CONNECTION: - Base-60 directly links to geometric harmony: 60 is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 — enabling exact ratios like 1/2, 2/3, 3/4, 5/6, etc. - The ratios on the tablet include approxi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com

Ask AI

Helpful

Bookmark

View Full Paper