Ancient Babylonian Tablet Reveals World's Oldest Trigonometry Table — E8 Intelligence Research

FINDING: Plimpton 322 is a 3800-year-old Babylonian table of 15 Pythagorean triples, now shown to encode exact sexagesimal trigonometry via ratios of squares, predating Greek trigonometry by over a millennium. MATH: - The tablet lists 15 rows of (a, c) pairs with b² = c² − a², all in base-60. - Key ratios: For row 1, a = 119, c = 169, b = 120 → ratio a/b = 119/120 ≈ 0.991667; c/b = 169/120 ≈ 1.40833. - The generating formula (standard OB): a = 2pq, b = p² − q², c = p² + q², with p, q regular sexagesimal numbers (e.g., p = 2, q = 1 gives 3-4-5; p = 12, q = 5 gives 119-120-169). - The tablet's column 1 (now known) lists (c/b)² = 1 + (a/b)², i.e., sec²θ in base-60. - Exact values: Row 1: (169/120)² = 28561/14400 = 1.983402777…; in base-60: 1;59,0,15. - The ratio 0.786 appears implicitly: for row 15, a = 56, b = 90, c = 106 → a/c = 56/106 = 28/53 ≈ 0.5283; but the *complementary* ratio (b−a)/c = 34/106 ≈ 0.3207, not 0.382. However, the *diagonal* ratio (c−b)/a = 16/56 = 2/7 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com