Babylonian Tablet Plimpton 322: Oldest Trig Table Predates Greeks — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Plimpton 322 is a 3,800-year-old Babylonian sexagesimal trig table — the oldest known — using base-60 ratios of right-triangle sides, predating Greek trigonometry by over a millennium. | MATH: The tablet lists 15 rows of Pythagorean triples in sexagesimal: (a, b, c) with a² + b² = c², normalized to a common hypotenuse (c = 1 in modern terms). The key ratios are the secant (c/b) and tangent (a/b) — specifically, the tablet tabulates values of (c/b)² and (a/b)², i.e., sec²θ and tan²θ, for θ from ~45° down to ~30° in discrete steps. The sexagesimal entries include exact values like 1;59,15 (≈1.987) and 1;33,45 (≈1.5625) — these are not approximations but exact rational squares in base 60. The underlying constant is 60 (the base), and the triples derive from the standard parametric form: a = 2pq, b = p² − q², c = p² + q², with p, q coprime and of opposite parity — though the Babylonians likely used a reciprocal-pair method (x + 1/x) rather than the Greek parametric form. | CONNECT Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208779074
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