Plimpton 322: Babylonian Secant-Squared Table Predates Greek Trigonometry by 1000 Years — E8 Intelligence Research

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 \(d^2 = a^2 + b^2\)), the tablet lists pairs \((a/d)^2\) and \((b/d)^2\) in sexagesimal. The key ratio is \(\sec^2 \theta = (d/b)^2\). 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 \(a = p^2 - q^2\), \(b = 2pq\), \(d = p^2 + q^2\). 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 \(b/a = 2pq/(p^2 - q^2)\) relates to the golden ratio \(\phi\) for certain \(p/q\) near \(\sqrt{\phi}\) (e.g., row 1: angle ~44.76°, \(b/a \approx 1.02\), c Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com