FINDING: Old Babylonian tablet Plimpton 322 is a precise trigonometric table of secant-squared values for generating rational points on the unit circle, predating Greek trigonometry by over 1000 years. | MATH: For a right triangle with sides (a, b, c) in base-60 sexagesimal, the tablet lists 15 rows of normalized values: (b/a) ² = sec² (θ) - 1, where θ is the angle opposite side a. Key constants: 1;59, 15, 1;56, 56, 58, 14, 50, 6, 15 (base-60). The underlying generating formula is equivalent to: a = p² - q², b = 2pq, c = p² + q² (Pythagorean triples), with p, q regular sexagesimal numbers. | CONNECTION: The ratios b/a yield slopes (rise/run) that correspond to angles between 30° and 45°, with sec² values clustering near 1. 618 (golden ratio φ) and 2. 618 (φ²). The base-60 system naturally encodes the regular numbers (2ᵃ·3ᵇ·5ᶜ) needed for exact rational points, linking to the 5-fold and 6-fold symmetries of crystallographic lattices. The unit circle rational points (a/c, b/c) are dense in the c Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
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