Plimpton 322: Oldest Trigonometric Table Using Babylonian Base-60 Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet listing 15 rows of Pythagorean triples, likely generated by a systematic method (possibly using reciprocal pairs in base-60), and may represent the world's oldest known trigonometric table. MATH: - Pythagorean triples: \(a^2 + b^2 = c^2\), with integer sides. - Tablet entries correspond to normalized ratios: \(b^2 / a^2\) or \(c^2 / a^2\) (depending on interpretation). - Base-60 (sexagesimal) system used for all numbers. - Key ratios derived from triples: e.g., row 1 gives \(b/a ≈ 0.618\) (inverse of golden ratio \(φ⁻¹\)), row 11 gives \(b/a ≈ 0.382\) (\(φ⁻²\)). - Possible generating formula: \(a = p^2 - q^2\), \(b = 2pq\), \(c = p^2 + q^2\) (or reciprocal variant in base-60). CONNECTION: - Ratios 0.382 and 0.618 appear explicitly in the triples, linking to the golden ratio \(φ = (1+√5)/2 ≈ 1.618\). - Base-60 arithmetic naturally produces regular numbers (2,3,5 factors Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com