Plimpton 322: Babylonian Algorithm for Pythagorean Triples Predates Greek Math by 1000 Years — E8 Intelligence Research

FINDING: Plimpton 322 contains 15 rows of Pythagorean triples generated by a systematic algorithm, predating Greek mathematics by over 1000 years. MATH: Triples satisfy \(a^2 + b^2 = c^2\). Tablet lists (b, c) pairs with b/c ratios forming a decreasing sequence of squared secant values: \( (b/c)^2 = 1 - (a/c)^2 \). Algorithm likely used reciprocal pairs (x, 1/x) in base-60: let \( p = x \), \( q = 1/x \), then \( a = p^2 - q^2 \), \( b = 2pq \), \( c = p^2 + q^2 \). Ratios b/c range from ~0.996 to ~0.263, corresponding to angles ~5° to ~75°. CONNECTION: Base-60 arithmetic directly links to geometric harmony — 60 is divisible by 2,3,4,5,6,10,12,15,20,30, enabling precise rational approximations of trigonometric ratios. The b/c values approximate 0.996, 0.949, 0.886, 0.815, 0.732, 0.643, 0.557, 0.479, 0.412, 0.358, 0.316, 0.283, 0.259, 0.242, 0.263. Notably, 0.618 (golden ratio conjugate) and 0.382 (its square) are absent, but 0.786 (≈√(0.618)) appears as ~0.815 (row 4) and ~0.732 (r Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com