Plimpton 322: Reciprocal Pairs in Base-60, Not Trigonometry — E8 Intelligence Research

FINDING: Plimpton 322 encodes a systematic method for generating reciprocal pairs in base-60, producing Pythagorean triples via sexagesimal regular numbers, not trigonometry. MATH: - Reciprocal pair generation: For regular sexagesimal numbers \( x \) and \( 1/x \) (both terminating in base-60), set \( a = (x - 1/x)/2 \), \( b = 1 \), \( c = (x + 1/x)/2 \) → yields Pythagorean triple \( (a, b, c) \). - Example from tablet row: \( x = 2;24 \) (i.e., \( 2 + 24/60 = 2.4 \)), \( 1/x = 0;25 \) (i.e., \( 25/60 ≈ 0.4167 \)), then \( a = (2.4 - 0.4167)/2 = 0.99165 \), \( c = (2.4 + 0.4167)/2 = 1.40835 \), scaled to integers → triple (119, 120, 169). - All triples on Plimpton 322 correspond to \( x \) of form \( p/q \) where \( p, q \) are regular sexagesimal integers (factors only 2,3,5). CONNECTION: - No explicit golden ratio (φ) or its derived ratios (0.618, 1.618) appear in the tablet's numbers. - Base-60 regular numbers are intimately linked to the lattice of integers in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com