Plimpton 322 Decoded: A Sexagesimal-Optimized Table of Squared Secants — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Plimpton 322 is not a random list of Pythagorean triples but a systematic, sexagesimal-optimized table of exact squared-secant (or cotangent) values generated by a regular-number algorithm, with Bruins' reconstruction corrected to reveal a natural "missing pairs" structure.
MATH: - Core generation: For regular numbers p, q (sexagesimal reciprocals), set b = p2 − q2, d = p2 + q2, a = 2pq (or variant with b = M QM). - Bruins' scheme: d2/b2 = 1 + (a/b)2 → table lists (d/b)2 values as sexagesimal reciprocals of regular numbers. - New correction (arXiv:1109.3814): Missing pairs correspond to p,q where p/q yields ratios outside the tablet's chosen interval 1 < d/b < 1.5 (or equivalent), giving a complete, gap-free sequence under a single rule. - Factor-12 algorithm (arXiv:2001.11141): b = M QM with QM derived from M's sexagesimal factorization; generates all 15 rows exactly. - Trigonometric function value
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Plimpton 322 Decoded: A Sexagesimal Table of Regular Reciprocal Pairs Generating Pythagorean Triples — E8 Intelligence Research
- Plimpton 322 Refined: Reconstructing Missing Pairs in Babylonian Sexagesimal Triples — E8 Intelligence Research
- Plimpton 322: A Hidden Sexagesimal Trigonometric Table — E8 Intelligence Research
- Babylonian Tablet Plimpton 322: Ancient Sexagesimal Trigonometry Predates Greeks — E8 Intelligence Research
- Plimpton 322's Sexagesimal Algorithm as Rational Circle Parametrization — E8 Intelligence Research
BibTeX
@misc{caldin2026plimpton,
title = {{Plimpton 322 Decoded: A Sexagesimal-Optimized Table of Squared Secants — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23447065},
url = {https://zenodo.org/records/23447065},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Plimpton 322 Decoded: A Sexagesimal-Optimized Table of Squared Secants — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23447065
UR - https://zenodo.org/records/23447065
AB - FINDING: Plimpton 322 is not a random list of Pythagorean triples but a systematic, sexagesimal-optimized table of exact squared-secant (or cotangent) values generated by a regular-number algorithm, with Bruins' reconstruction corrected to reveal a natural "missing pairs" structure. MATH: - Core generation: For regular numbers p, q (sexagesimal reciprocals), set b = p^2 − q^2, d = p^2 + q^2, a = 2pq (or variant with b = M Q_M). - Bruins' scheme: d^2/b^2 = 1 + (a/b)^2 → table lists (d/b)^2 values as sexagesimal reciprocals of regular numbers. - New correction (arXiv:1109.3814): Missing pairs correspond to p,q where p/q yields ratios outside the tablet's chosen interval 1 < d/b < 1.5 (or equivalent), giving a complete, gap-free sequence under a single rule. - Factor-12 algorithm (arXiv:2001.11141): b = M Q_M with Q_M derived from M's sexagesimal factorization; generates all 15 rows exactly. - Trigonometric function value Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -