Babylonian Tablets Reveal Ancient Trigonometry and Proto-Proof of √2 Irrationality — E8 Intelligence Research

FINDING: Babylonian tablet Plimpton 322 is a 3700-year-old exact sexagesimal trigonometric table, not a school exercise; a separate Babylonian geometry tablet series encodes an implicit proto-proof of √2 irrationality via reciprocal-pair algorithms. | MATH: Sexagesimal (base-60) reciprocal pairs \(p, q\) with \(p/q\) generating Pythagorean triples \((a,b,c)\) where \(a = p^2 - q^2\), \(b = 2pq\), \(c = p^2 + q^2\); tablet columns list \(\frac{b^2}{a^2}\) (or \(\tan^2\theta\)) in exact sexagesimal fractions. For √2: geometry tablets use the standard approximation \(1;24,51,10 = 1 + 24/60 + 51/3600 + 10/216000 = 305470/216000 ≈ 1.41421296\) (error ~6×10⁻⁷), paired with its reciprocal \(0;42,25,35\). The arxiv paper (1603.06656) argues two tablets contain a *reductio* style argument: assuming √2 = \(p/q\) in lowest terms leads to an infinite descent in the reciprocal-pair algorithm — a proto-irrationality proof. | CONNECTION: The sexagesimal system is base-60, whose divisors include 2,3,5 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com