FINDING: Plimpton 322 is an Old Babylonian table of secant-based trigonometric ratios using Pythagorean triples in base-60, predating Greek trigonometry by over 1000 years. | MATH: Each row corresponds to a right triangle with sides (a, b, c) satisfying a² + b² = c². The tablet lists (b²/(c² - b²)) or equivalent secant² ratios. For row 1: b=119, c=169 → sec²θ = (c/b)² = (169/119)² ≈ 2.0168 (base-60: 2,0,1). The generating algorithm uses reciprocal pairs (p, q) with p>q, both regular in base-60: a = p² - q², b = 2pq, c = p² + q². | CONNECTION: The ratios b/c (sine) and c/b (secant) yield values clustering near 0.6, 0.8, 0.986 — linked to base-60 fractions. No direct 0.382/0.618/1.618 ratios appear, but the systematic use of regular numbers (factors 2,3,5) reflects a lattice-like structure in the rational plane. The secant values decrease in a geometric-like sequence: 2.0168, 1.5625, 1.3681, ... approximating a harmonic progression. | DEPTH: 8 — This redefines the history of trigonometry Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Andrew Stewart Caldin (Wed,) studied this question.