Plimpton 322: Babylonian Ratio-Based Triples, Not Modern Trigonometry — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian table of reciprocal pairs generating Pythagorean triples, not a trigonometric table in the modern sense; it uses base-60 ratio-based methods. | MATH: For a normalized rectangle with short side 1, long side \( b = \frac{1}{2}(x - 1/x) \) and diagonal \( d = \frac{1}{2}(x + 1/x) \), where \( x \) is a regular sexagesimal number. Triples satisfy \( d^2 - b^2 = 1 \). Pell-type recurrence: \( x_{n+1} = 2x_n + x_{n-1} \) (or similar) generates successive regular numbers. | CONNECTION: The ratio \( b/d \) approximates slopes; key ratios include 0.618 (inverse of golden ratio) and 0.786 (√(φ-1)?). Base-60 regular numbers link to 5-fold and 6-fold symmetries. | DEPTH: 8 FINDING: Old Babylonian trigonometry uses exact ratios (e.g., 3:4:5 triangle) and reciprocal pairs, avoiding irrationals; it is more accurate for practical computation than modern sine/cosine. | MATH: For a right triangle with sides \( a, b, c \) (c diagonal), the ratio \( a/b \) defin Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com