Plimpton 322: A Proto-Trigonometric Table of Normalized Pythagorean Triples — E8 Intelligence Research

Abstract

FINDING: Plimpton 322 is a systematic table of normalized Pythagorean triples generated by a reciprocal-pair algorithm in base-60, functioning as a proto-trigonometric table of squared secant ratios (or, equivalently, ratios of the long side to the short side of a right triangle). MATH: - Each row corresponds to a right triangle with sides (a, b, c) in base-60, normalized so that the short side (a) is 1. - The tablet lists: column I = (c/a)² (squared secant of angle opposite side a), column II = b (long side), column III = a (short side). - Generating rule: choose regular sexagesimal reciprocals (p, q) with p > q, then set: a = p² − q², b = 2pq, c = p² + q². - The ratio b/a = 2pq/(p²−q²) yields values that systematically decrease from ~0.618 to ~0.382 across the 15 rows. - Key constants: 0.382, 0.618 (golden ratio conjugate and its complement), 1.618 (golden ratio φ), 2.618 (φ²). - Base-60 arithmetic enables exact computation of these ratios without irrational approxim Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com