FINDING: Plimpton 322 encodes a secant-based trigonometric table with angles from 44.8° to 31.9° in a geometric progression, using base-60 sexagesimal ratios. MATH: The tablet lists 15 rows of Pythagorean triples (a, b, c) with b² = c² - a². The key ratio is (c/b) = sec(θ), where θ decreases from ~44.8° to ~31.9°. The secant values follow a geometric progression: each step multiplies by a constant factor ≈ 1.033 (sexagesimal: 1;02). The generating algorithm uses reciprocal pairs (p, q) in base-60: a = p² - q², b = 2pq, c = p² + q², with p/q ≈ √( (1+sinθ)/(1-sinθ) ). CONNECTION: The angle range (44.8° to 31.9°) corresponds to secant ratios 1.414 to 1.176, which are close to √2 and √(3/2). The geometric progression of secants mirrors the harmonic ratio 0.618 (golden ratio conjugate) when inverted: 1/1.618 ≈ 0.618. Base-60 fractions enable exact rational approximations of these irrationals. The 15-row structure may reflect a 15° lunar or zodiacal division (360°/24 = 15°), linking to c Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Andrew Stewart Caldin (Tue,) studied this question.