Plimpton 322: Old Babylonian Trigonometry via Pythagorean Triples and Base-60 — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian clay tablet (c. 1800 BCE) listing 15 rows of Pythagorean triples, likely representing the world's earliest known trigonometric table, based on base-60 (sexagesimal) arithmetic. MATH: - Pythagorean triples: \ (a² + b² = c²\), with \ (a < b\). - Tablet entries correspond to normalized ratios: \ (b/a\) and \ (c/a\), specifically \ (ba = 12 (x - 1x) \) and \ (ca = 12 (x + 1x) \) for rational \ (x = p/q\) in base-60. - Key constants: sexagesimal fractions like 0;30 (1/2), 0;45 (3/4), 0;50 (5/6), etc. - The tablet yields values of \ (² = (b/a) ²\) and \ (² = (c/a) ²\), effectively a table of secants. CONNECTION: - Ratios on Plimpton 322 approximate \ (2\), \ (3\), and the golden ratio \ (= 1. 618. . . \) (e. g. , row 11 gives \ (b/a 0. 618\), the reciprocal of \ (\) ). - Base-60 arithmetic naturally generates regular numbers (2, 3, 5) linked to crystallog Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com