Plimpton 322: Old Babylonian Pythagorean Triples Without Golden Ratio — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Plimpton 322 lists 15 Pythagorean triples generated by a systematic Old Babylonian method, with no explicit golden ratio or phi constants in the surviving data. MATH: - Triples include (119, 120, 169) and (65, 72, 97). - Generating method: likely \( p, q \) parameters (sexagesimal reciprocals) producing \( a = p^2 - q^2 \), \( b = 2pq \), \( c = p^2 + q^2 \). - Ratios on tablet: column I contains \( (c/a)^2 \) values (or \( \cot^2 \theta \)), e.g., 1.9834…, 1.9490…, etc. - No constants 0.382, 0.618, 1.618, 2.618 appear in any known transcription. CONNECTION: - Base-60 (sexagesimal) arithmetic is used throughout. - Triples correspond to right triangles with rational sides; the angles involved are not golden-ratio-related (e.g., 119/120 ≈ 0.9917, not 0.618). - No crystallographic symmetry or root system link is evident from the tablet's content. DEPTH: 6 - Profound for history of number theory and trigonometry (pre-Greek). - No direct geometric harmony link 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: W7170050530
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