Plimpton 322: Oldest Trigonometric Table Using Sexagesimal Ratios — E8 Intelligence Research

FINDING: Babylonian tablet Plimpton 322 is the world's first trigonometric table, using base-60 (sexagesimal) fractions and exact ratios instead of angles or approximations. | MATH: Sexagesimal reciprocals (e.g., 1/60 = 0;1, 1/30 = 0;2, 1/20 = 0;3, 1/15 = 0;4, 1/12 = 0;5, 1/10 = 0;6, 1/6 = 0;10, 1/5 = 0;12, 1/4 = 0;15, 1/3 = 0;20, 1/2 = 0;30, 1/1 = 1;0) generate Pythagorean triples via the algorithm: take two sexagesimal reciprocals (p, q) with p > q, then sides = (p² - q², 2pq, p² + q²). The table lists 15 such triples, with the ratio (p² - q²)/(2pq) corresponding to a "trigonometric" slope (like cotangent) in exact rational form. | CONNECTION: Base-60 directly yields the golden ratio's sexagesimal approximation: φ ≈ 1;37,4,55,20 (1.618055…). The reciprocal pairs (p, q) often involve divisors of 60 (e.g., 1,2,3,4,5,6,10,12,15,20,30,60), linking to the 360° circle (6×60). The table's structure mirrors a discrete set of rational slopes, analogous to crystallographic lattice directions i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com