Sexagesimal Rational Parametrization of the Unit Circle — E8 Intelligence Research

FINDING: Babylonian sexagesimal arithmetic provides a natural rational parametrization of the unit circle via the standard stereographic projection formula, and base-60 divisibility (60 = 2²·3·5) makes the resulting rational points especially tractable. MATH: - Rational parametrization of unit circle: for t ∈ ℚ, (x, y) = ((1 − t²)/(1 + t²), 2t/(1 + t²)) - Equivalent Pythagorean triple generator: (a, b, c) = (m² − n², 2mn, m² + n²), m, n ∈ ℤ - Sexagesimal base: 60 = 2² · 3 · 5; divisors {1,2,3,4,5,6,10,12,15,20,30,60} - Plimpton 322 (OB, ~1800 BCE): 15 rows of (short side, diagonal) pairs; e.g. (119, 169), (3367, 4825), (4601, 6649) — all satisfy a² + b² = c² with b, c sexagesimally regular - Circle–sexagesimal link (arXiv 0707.0676): 360° = 6 · 60; regular hexagon inscribed in circle gives chord = radius, so 6 chords close the circle exactly — the geometric origin of base-60 angle division - 12 months, 24 hours, 60 minutes all derive from 6 · 60 = 360 and 2 · 12 = 24 CONNECTION: - Ba Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com