FINDING: Old Babylonian base-60 system enabled efficient generation of regular numbers and primitive Pythagorean triples, with Plimpton 322 revealing advanced trigonometric or ratio-based computation. MATH: - Base-60 (sexagesimal) place-value system: digits 0–59, positional notation. - Regular numbers: integers of form \ (2ᵃ 3ᵇ 5ᶜ\) (a, b, c integers ≥0), reciprocals have finite sexagesimal expansions. - Primitive Pythagorean triple generation (Dickson method): find integers \ (r, s, t\) such that \ (r² = 2st\), then triple = \ ( (r+s, r+t, r+s+t) \). Equivalent to Euclid's formula: \ (a = m² - n²\), \ (b = 2mn\), \ (c = m² + n²\) with \ (m>n\), coprime, opposite parity. - Plimpton 322 table: columns of \ ( (b², a, c) \) or \ ( (b/a, c/a) \) for 15 triples, likely computed via regular numbers and reciprocals. CONNECTION: - Base-60 directly links to geometric harmony ratios: 1/60 = 0. 01666. . . , but more critically, regular numbers produce ratios like 0. 618 (≈ 1/φ) via \ (2^-13^-15^ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Wed,) studied this question.