Plimpton 322: Oldest Exact Sexagesimal Trigonometry Table — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing the world's first trigonometric table, based on exact sexagesimal ratios rather than angles or circles. | MATH: The tablet lists 15 rows of Pythagorean triples (a² + b² = c²) in base-60, with ratios b²/(c²–b²) forming a decreasing sequence of regular sexagesimal numbers. Key constants: 1;59,15 (≈1.9834), 1;56,56,58,14,50,6,15 (≈1.9492), and the reciprocal pairs (e.g., 2;24, 0;25). The underlying generator is p/q with p,q regular in base-60 (e.g., 2/3, 5/4). | CONNECTION: The ratios b/a (≈0.382, 0.618, 0.786, 1.618) appear as slopes of right triangles, directly linking to the golden ratio φ = (1+√5)/2 ≈ 1.618 and its reciprocal 0.618. The base-60 system encodes these as exact sexagesimal fractions (e.g., 0;36,0 for 0.6, 0;23,13,20 for 0.382). The tablet's structure mirrors a discrete set of slopes from a unit circle in base-60, prefiguring modern trigonometry. | DEPTH: 9 — This is a profound reorientation: trigon 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: W7171063563
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