Base-60 and Recursive Algorithms: The Ancient Roots of Proto-Trigonometry — E8 Intelligence Research

FINDING: The corpus confirms a recurring historical pattern: ancient mathematical systems (Babylonian, Egyptian, Greek) were built on base-60 arithmetic, geometric proportion, and recursive algorithms — not abstract axiomatics. The "one line in the oldest math text" (likely Plimpton 322 or a cuneiform tablet) points to proto-trigonometric tables and Pythagorean triples. | MATH: Base-60 sexagesimal system (60 = 2²·3·5, highly composite); Pythagorean triples (a² + b² = c²) with integer solutions; Plimpton 322 contains 15 rows of sexagesimal ratios approximating sec²(θ) values; Egyptian unit fractions (1/n) and the 2/n table from the Rhind Papyrus; the "magic numbers" series (Hannah Fry) explicitly covers the golden ratio φ = (1+√5)/2 ≈ 1.618, its reciprocal 1/φ ≈ 0.618, and φ² ≈ 2.618. | CONNECTION: Direct geometric harmony — base-60 is divisible by 3, 4, 5, 6, 10, 12, 15, 20, 30, enabling exact construction of regular polygons (crystallographic point groups C₃, C₄, C₆); the golden ratio Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com