Plimpton 322 and Tangent-Secant: A Search Result Disconnect — E8 Intelligence Research
FINDING: The search results are a mixed bag — mostly pedagogical videos on the tangent-secant theorem and golden ratio, plus one genuine research paper on hexaquark decay. No direct link between Plimpton 322 and the tangent-secant theorem is established in these results. | MATH: Tangent-secant theorem: \(PT^2 = PA \cdot PB\) (where PT is tangent, PA/PB are secant segments). Golden ratio: \(\phi = (1+\sqrt{5})/2 \approx 1.618\), with reciprocal \(1/\phi = \phi-1 \approx 0.618\). Plimpton 322: 15 rows of Pythagorean triples, parameterized by \(a = 2uv\), \(b = u^2-v^2\), \(c = u^2+v^2\) (standard form), with ratios \(b/a\) or \(c/a\) in sexagesimal. Hexaquark paper: SU(3) antidecuplet, decay widths via effective field theory — no explicit constants given in the abstract. | CONNECTION: The tangent-secant theorem yields power of a point: \(PA \cdot PB = PT^2\). If \(PT = 1\) and \(PA = \phi\), then \(PB = 1/\phi = 0.618\) — a direct geometric construction of the golden ratio via circle geo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Authors
- Andrew Stewart Caldin
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-09-05
- DOI
- https://doi.org/10.5281/zenodo.22324540
- Primary Topic
- Mathematics and Applications
- Type
- preprint