Ancient Babylonian Tablets Reveal World's First Trigonometry and Implicit Proofs of √2's Irrationality — E8 Intelligence Research

FINDING: The Yale Babylonian Collection contains YBC 7194 (a 4,200-year-old tablet) and a 3,700-year-old tablet identified as the world's first trigonometric table; a separate arXiv paper demonstrates Babylonian geometric tablets contain implicit proofs of the irrationality of √2. | MATH: The trig tablet (Plimpton 322) uses base-60 (sexagesimal) ratios of sides of right triangles — specifically, it lists 15 entries of (short side, diagonal) pairs with the squared ratio (diagonal/short side)² = 1 + (long side/short side)², equivalent to sec²θ = 1 + tan²θ. The irrationality proof tablet (YBC 7289, likely) shows a sexagesimal approximation of √2 = 1;24,51,10 (base-60) = 1.41421296…, accurate to 6 decimal places. The arXiv paper (1603.06656) argues that paired problem tablets (e.g., YBC 6967) contain a *geometric* proof of irrationality via the Euclidean algorithm applied to the diagonal/side ratio of a square — showing the algorithm never terminates, implying √2 ∉ ℚ. | CONNECTION: The sex Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com