FINDING: Plimpton 322 encodes a trigonometric table of secant-squared values (sexagesimal rational numbers) derived from Pythagorean triples, predating Greek trigonometry by over 1000 years. MATH: For a right triangle with short side \ (a\), long side \ (b\), diagonal \ (d\) (with \ (d² = a² + b²\) ), the tablet lists pairs \ ( (a/d) ²\) and \ ( (b/d) ²\) in sexagesimal. The key ratio is \ (² = (d/b) ²\). The 15 rows correspond to angles decreasing from ~45° to ~30° in steps of ~1°. The generating rule: for regular sexagesimal reciprocals \ (p, q\) with \ (p > q\), set \ (a = p² - q²\), \ (b = 2pq\), \ (d = p² + q²\). CONNECTION: Base-60 arithmetic naturally yields rational points on the unit circle: \ ( (a/d, b/d) \) are rational coordinates. The angles correspond to regular sexagesimal fractions (e. g. , 1/60, 1/30). The ratio \ (b/a = 2pq/ (p² - q²) \) relates to the golden ratio \ (\) for certain \ (p/q\) near \ (\) (e. g. , row 1: angle ~44. 76°, \ (b/a 1. 02\), c Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Tue,) studied this question.