Pedagogical Videos and an Arxiv Paper on Number Theory, Lacking Cuneiform Sources — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are largely pedagogical videos on Pythagorean triples and irrationality of √2, with one substantive arxiv paper on rational approximants to ζ(3). No direct cuneiform or sexagesimal primary-source material surfaced. | MATH: Pythagorean triple parametrization: a = m²−n², b = 2mn, c = m²+n² (m>n, coprime, opposite parity). Irrationality of √2 via infinite descent. Apéry-like recurrence for ζ(3) approximants (arxiv:1204.6712) — rational pₙ/qₙ with qₙ satisfying a three-term recurrence; continued fraction coefficients linked to integer sequences. | CONNECTION: Pythagorean triples (3,4,5) etc. are integer points on the unit circle — rational parametrization t ↦ ((1−t²)/(1+t²), 2t/(1+t²)). This is the same stereographic projection structure underlying root system A2 (hexagonal lattice) where the shortest roots have length √2 and the angle between simple roots is 120° (cos = −1/2). The triple (3,4,5) corresponds to a lattice vector (3,4) with norm 25 = 5² — in the G
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026pedagogical,
title = {{Pedagogical Videos and an Arxiv Paper on Number Theory, Lacking Cuneiform Sources — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23465483},
url = {https://zenodo.org/records/23465483},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pedagogical Videos and an Arxiv Paper on Number Theory, Lacking Cuneiform Sources — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23465483
UR - https://zenodo.org/records/23465483
AB - FINDING: The search results are largely pedagogical videos on Pythagorean triples and irrationality of √2, with one substantive arxiv paper on rational approximants to ζ(3). No direct cuneiform or sexagesimal primary-source material surfaced. | MATH: Pythagorean triple parametrization: a = m²−n², b = 2mn, c = m²+n² (m>n, coprime, opposite parity). Irrationality of √2 via infinite descent. Apéry-like recurrence for ζ(3) approximants (arxiv:1204.6712) — rational pₙ/qₙ with qₙ satisfying a three-term recurrence; continued fraction coefficients linked to integer sequences. | CONNECTION: Pythagorean triples (3,4,5) etc. are integer points on the unit circle — rational parametrization t ↦ ((1−t²)/(1+t²), 2t/(1+t²)). This is the same stereographic projection structure underlying root system A2 (hexagonal lattice) where the shortest roots have length √2 and the angle between simple roots is 120° (cos = −1/2). The triple (3,4,5) corresponds to a lattice vector (3,4) with norm 25 = 5² — in the G Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -