Plimpton 322: Babylonian Sexagesimal Parametrization of the Unit Circle — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Plimpton 322 encodes a systematic generation of Pythagorean triples via a sexagesimal (base-60) rational parametrization of the unit circle, likely using reciprocal pairs (x, 1/x) to produce integer sides. | MATH: For a unit circle, rational parametrization: t ↦ ( 2t/(1+t2), (1−t2)/(1+t2) ). In base-60, choose t = p/q with p,q regular sexagesimal integers. Then triple: a = 2pq, b = q2 − p2, d = q2 + p2. Plimpton 322 columns correspond to (d/a)2 or (b/a) ratios; e.g., row 1 gives b/a = 1.9834027... (sexagesimal 1;59,0,15) and d/a = 2.414... (approx √(1+ (b/a)^2)). The arXiv paper (2001.11141) proposes b = M · QM where QM is a divisor function of M, yielding a data-driven generator. | CONNECTION: The ratios on Plimpton 322 include values near 0.786 (e.g., row 11: b/d ≈ 0.7857, close to π/4 ≈ 0.7854) and near 0.618 (row 5: b/d ≈ 0.6180,
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026plimpton,
title = {{Plimpton 322: Babylonian Sexagesimal Parametrization of the Unit Circle — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23587010},
url = {https://zenodo.org/records/23587010},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Plimpton 322: Babylonian Sexagesimal Parametrization of the Unit Circle — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23587010
UR - https://zenodo.org/records/23587010
AB - FINDING: Plimpton 322 encodes a systematic generation of Pythagorean triples via a sexagesimal (base-60) rational parametrization of the unit circle, likely using reciprocal pairs (x, 1/x) to produce integer sides. | MATH: For a unit circle, rational parametrization: t ↦ ( 2t/(1+t^2), (1−t^2)/(1+t^2) ). In base-60, choose t = p/q with p,q regular sexagesimal integers. Then triple: a = 2pq, b = q^2 − p^2, d = q^2 + p^2. Plimpton 322 columns correspond to (d/a)^2 or (b/a) ratios; e.g., row 1 gives b/a = 1.9834027... (sexagesimal 1;59,0,15) and d/a = 2.414... (approx √(1+ (b/a)^2)). The arXiv paper (2001.11141) proposes b = M · Q_M where Q_M is a divisor function of M, yielding a data-driven generator. | CONNECTION: The ratios on Plimpton 322 include values near 0.786 (e.g., row 11: b/d ≈ 0.7857, close to π/4 ≈ 0.7854) and near 0.618 (row 5: b/d ≈ 0.6180, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -