Plimpton 322's Genesis: A Modified Bruins Reconstruction for Missing Pairs — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are dominated by generic numerical-methods tutorials (spline, Newton forward, Vandermonde, IK solvers) — none of which address Plimpton 322 or ancient secant tables. The sole relevant item is an arXiv paper on Plimpton 322's genesis, which proposes a modified Bruins reconstruction to account for "missing pairs" and predicts subsequent entries.
MATH: The paper (arXiv:1109.3814v2) does not provide explicit equations in the snippet. However, the standard Plimpton 322 mathematical content is: 15 rows of Pythagorean triples (a, b, c) with b² = c² − a², expressed in sexagesimal. The ratios b/c and a/c correspond to secant and tangent values. Bruins' original method uses reciprocal pairs (x, 1/x) from regular sexagesimal numbers, generating triples via: a = (x − 1/x)/2, b = (x + 1/x)/2, c = 1 (or scaled). The "missing pairs" refer to regular numbers skipped between consecutive rows. The paper's modification likely uses a systematic angular spacing — but the sn
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's Genesis: A Modified Bruins Reconstruction for Missing Pairs — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658217},
url = {https://zenodo.org/records/23658217},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Plimpton 322's Genesis: A Modified Bruins Reconstruction for Missing Pairs — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658217
UR - https://zenodo.org/records/23658217
AB - FINDING: The search results are dominated by generic numerical-methods tutorials (spline, Newton forward, Vandermonde, IK solvers) — none of which address Plimpton 322 or ancient secant tables. The sole relevant item is an arXiv paper on Plimpton 322's genesis, which proposes a modified Bruins reconstruction to account for "missing pairs" and predicts subsequent entries. MATH: The paper (arXiv:1109.3814v2) does not provide explicit equations in the snippet. However, the standard Plimpton 322 mathematical content is: 15 rows of Pythagorean triples (a, b, c) with b² = c² − a², expressed in sexagesimal. The ratios b/c and a/c correspond to secant and tangent values. Bruins' original method uses reciprocal pairs (x, 1/x) from regular sexagesimal numbers, generating triples via: a = (x − 1/x)/2, b = (x + 1/x)/2, c = 1 (or scaled). The "missing pairs" refer to regular numbers skipped between consecutive rows. The paper's modification likely uses a systematic angular spacing — but the sn Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -