Plimpton 322 Decoded: A Sexagesimal Table of Regular Reciprocal Pairs Generating Pythagorean Triples — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Plimpton 322 is a sexagesimal table of regular reciprocal pairs (p, q) generating Pythagorean triples, with a reconstruction algorithm that predicts missing rows and reveals a systematic sequence of ratios. | MATH: Pythagorean triples (a, b, d) with a² + b² = d²; sexagesimal (base-60) regular numbers p, q (i.e., p, q with prime factors only 2, 3, 5); generating formula: a = p² − q², b = 2pq, d = p² + q² (or variants with scaling); Bruins' scheme uses p/q from reciprocal pairs; the "factor 12" algorithm proposes b = M·Q_M, with M, Q_M integers, yielding a data-driven family of algorithms. The tablet lists 15 rows, with ratios like (d/a)² or (b/d)² forming a decreasing sequence of squared secants/tangents. | CONNECTION: The ratios in Plimpton 322 are not the golden ratio directly, but the underlying structure is base-60 — the same sexagesimal system that makes 0.618, 0.786, 1.618 expressible as exact finite sexagesimal fractions (e.g., 0.618 = 37;04,48 in base-60; 0.786 = 47;09, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223672212