FINDING: Old Babylonian tablet Plimpton 322 contains a systematic list of 15 Pythagorean triples generated using sexagesimal reciprocal pairs, effectively a trigonometric table based on ratios. MATH: - Pythagorean triple generation: For sexagesimal regular numbers \ (p > q \) (both with only 2, 3, 5 prime factors), triple \ ( (a, b, c) \) given by \ (a = p² - q² \), \ (b = 2pq \), \ (c = p² + q² \). - Tablet lists \ ( (b²/ (c²) ) \) values (i. e. , \ (²\) ) in descending order, with \ (b/c \) ratios from ~0. 8 to ~0. 038. - Key constants: sexagesimal base 60; regular numbers include 2, 3, 5 and their products. CONNECTION: - The ratios \ (b/c \) (sine-like) and \ (a/c \) (cosine-like) produce slopes approximating 0. 382, 0. 618, 0. 786, 1. 618 when inverted or complemented — e. g. , \ (b/a \) for triples near 45° yields ~1. 0, but extreme triples give ratios near golden ratio conjugates. - Base-60 arithmetic directly links to 12-fold and 60-fold rotational symmetries (crystallogra Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
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