Plimpton 322: Babylonian Pythagorean Triples and Number-Theoretic Generation, 1800 BCE — E8 Intelligence Research

FINDING: Plimpton 322 (Old Babylonian, ~1800 BCE) is a table of 15 rows encoding Pythagorean triples via reciprocal pairs in base-60, predating Pythagoras by ~1200 years and revealing systematic number-theoretic generation, not mere measurement. MATH: - Core relation: a² + b² = c², with the tablet listing the short side b and hypotenuse c (columns), and the square of the ratio (c/b)² or (b/c)² depending on interpretation. - Generation algorithm (standard reconstruction): pick a regular sexagesimal number x (i.e., x = 2^a·3^b·5^c, so 1/x terminates in base-60). Form the reciprocal pair (x, 1/x). Then: - b = (x − 1/x)/2, c = (x + 1/x)/2, a = 1 (normalized), giving a² + b² = c². - Equivalently, from parameters p, q: a = p² − q², b = 2pq, c = p² + q². - Base-60 (sexagesimal) arithmetic: regular numbers are those whose prime factors divide 60 (2, 3, 5). This is the *selection criterion* for the generating parameters. - Row 1 (largest): ratio (c/b)² ≈ 1.9834... corresponding to the t Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com