MERLIN SCIENCE — Plimpton 322 as a Sexagesimal Lattice of Rational Points on the Unit C — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
Plimpton 322 is not a random list of Pythagorean triples but a systematic enumeration of rational points on the unit circle, generated by reciprocal pairs of regular sexagesimal numbers.
For the working scientist, this touches a deeper question: did an ancient culture encode a group-theoretic structure, the arithmetic of Gaussian integers restricted to primes two, three, and five, without leaving us a proof? The tablet's fifteen rows, with diagonals that are all regular sexagesimal integers, suggest they were not merely computing but sampling a lattice.
Here is the mechanism. Every rational point on the unit circle can be written as x equals two p q over p squared plus q squared, and y equals p squared minus q squared over p squared plus q squared. For p and q regular in base sixty, meaning their prime factors are only two, three, and five, these coordinates are rational and the diagonal, p squared plus q squared, is itself regular. The tablet's entries correspond to specific p o
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Plimpton 322's Sexagesimal Algorithm as Rational Circle Parametrization — 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
- Plimpton 322 Decoded: A Sexagesimal-Optimized Table of Squared Secants — E8 Intelligence Research
- Babylonian Tablet Plimpton 322: Ancient Sexagesimal Trigonometry Predates Greeks — E8 Intelligence Research
BibTeX
@misc{caldin2026merlin,
title = {{MERLIN SCIENCE — Plimpton 322 as a Sexagesimal Lattice of Rational Points on the Unit C — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23447144},
url = {https://zenodo.org/records/23447144},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - MERLIN SCIENCE — Plimpton 322 as a Sexagesimal Lattice of Rational Points on the Unit C — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23447144
UR - https://zenodo.org/records/23447144
AB - Plimpton 322 is not a random list of Pythagorean triples but a systematic enumeration of rational points on the unit circle, generated by reciprocal pairs of regular sexagesimal numbers. For the working scientist, this touches a deeper question: did an ancient culture encode a group-theoretic structure, the arithmetic of Gaussian integers restricted to primes two, three, and five, without leaving us a proof? The tablet's fifteen rows, with diagonals that are all regular sexagesimal integers, suggest they were not merely computing but sampling a lattice. Here is the mechanism. Every rational point on the unit circle can be written as x equals two p q over p squared plus q squared, and y equals p squared minus q squared over p squared plus q squared. For p and q regular in base sixty, meaning their prime factors are only two, three, and five, these coordinates are rational and the diagonal, p squared plus q squared, is itself regular. The tablet's entries correspond to specific p o Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -