Plimpton 322: Oldest Trig Table Using Base-60 Ratios and Exact Fractions — E8 Intelligence Research

Abstract

FINDING: Babylonian tablet Plimpton 322 is the world's oldest trigonometric table, using base-60 ratios. | MATH: Pythagorean triples (a² + b² = c²) in sexagesimal; ratios b²/(b²+a²) and a²/(b²+a²) yield exact values. | CONNECTION: Base-60 system enables exact fractions (e.g., 1/2, 1/3, 1/4, 1/5, 1/6) without repeating decimals; ratios approximate 0.618 (golden ratio conjugate) in some triples. | DEPTH: 9 FINDING: Babylonian geometry tablets show implicit understanding of irrationality of √2 via geometric construction and approximation. | MATH: √2 ≈ 1;24,51,10 in sexagesimal = 1.41421296... (error < 0.000001). | CONNECTION: Diagonal of unit square yields √2; ratio 1:√2 appears in root-2 rectangle (1:1.414), related to silver ratio (1+√2 ≈ 2.414). | DEPTH: 8 FINDING: Cuneiform tablets contain systematic tables of reciprocals, squares, cubes, and compound interest. | MATH: Base-60 place-value system; reciprocal pairs (e.g., 2 and 30, 3 and 20, 4 and 15, 5 and 12, 6 and 10). | CONNECTION Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com