Plimpton 322: Old Babylonian Trigonometry via Pythagorean Triples — E8 Intelligence Research

FINDING: Old Babylonian tablet Plimpton 322 contains a systematic list of 15 Pythagorean triples generated using sexagesimal reciprocal pairs, effectively a trigonometric table based on ratios. MATH: - Pythagorean triple generation: For sexagesimal regular numbers \( p > q \) (both with only 2,3,5 prime factors), triple \((a,b,c)\) given by \( a = p^2 - q^2 \), \( b = 2pq \), \( c = p^2 + q^2 \). - Tablet lists \( (b^2/(c^2)) \) values (i.e., \(tan^2θ\)) in descending order, with \( b/c \) ratios from ~0.8 to ~0.038. - Key constants: sexagesimal base 60; regular numbers include 2,3,5 and their products. CONNECTION: - The ratios \( b/c \) (sine-like) and \( a/c \) (cosine-like) produce slopes approximating 0.382, 0.618, 0.786, 1.618 when inverted or complemented — e.g., \( b/a \) for triples near 45° yields ~1.0, but extreme triples give ratios near golden ratio conjugates. - Base-60 arithmetic directly links to 12-fold and 60-fold rotational symmetries (crystallogra Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com