Plimpton 322: A Hidden Sexagesimal Trigonometric Table — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Plimpton 322 is not merely a list of Pythagorean triples but encodes a systematic sexagesimal trigonometric table built from regular-number parameter pairs, with a missing-pair structure explained by a natural algorithmic constraint.
MATH: - Tablet rows correspond to right triangles with sides (a, b, d), a < b < d, satisfying a2 + b2 = d2. - Bruins' reconstruction: parameters p, q (sexagesimal regular numbers, i.e., integers whose only prime factors are 2, 3, 5) generate triples via a = p2 − q2, b = 2pq, d = p2 + q2 (or variants). - New insight (arXiv:1109.3814): missing pairs arise from requiring p/q to lie in a specific interval and p, q to be regular — the "gaps" are not errors but systematic exclusions. - Factor-12 algorithm (arXiv:2001.11141): proposes b = M · QM, with M, QM positive integers, yielding a data-driven generative rule that reproduces all 15 rows exactly. - Trigonometric interpretation (arX
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
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BibTeX
@misc{caldin2026plimpton,
title = {{Plimpton 322: A Hidden Sexagesimal Trigonometric Table — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23465066},
url = {https://zenodo.org/records/23465066},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Plimpton 322: A Hidden Sexagesimal Trigonometric Table — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23465066
UR - https://zenodo.org/records/23465066
AB - FINDING: Plimpton 322 is not merely a list of Pythagorean triples but encodes a systematic sexagesimal trigonometric table built from regular-number parameter pairs, with a missing-pair structure explained by a natural algorithmic constraint. MATH: - Tablet rows correspond to right triangles with sides (a, b, d), a < b < d, satisfying a^2 + b^2 = d^2. - Bruins' reconstruction: parameters p, q (sexagesimal regular numbers, i.e., integers whose only prime factors are 2, 3, 5) generate triples via a = p^2 − q^2, b = 2pq, d = p^2 + q^2 (or variants). - New insight (arXiv:1109.3814): missing pairs arise from requiring p/q to lie in a specific interval and p, q to be regular — the "gaps" are not errors but systematic exclusions. - Factor-12 algorithm (arXiv:2001.11141): proposes b = M · Q_M, with M, Q_M positive integers, yielding a data-driven generative rule that reproduces all 15 rows exactly. - Trigonometric interpretation (arX Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -