FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing a systematic list of 15 Pythagorean triples, now proven to represent the world's oldest known trigonometric table, using base-60 sexagesimal arithmetic and ratios rather than angles. MATH: - Pythagorean triples: \ (a² + b² = c²\), with entries in sexagesimal (base-60) notation. - Tablet columns correspond to ratios: \ (b²c² \) and \ (a²c² \), effectively giving \ (²\) and \ (²\) for a right triangle. - Key constants: 1;59, 15, 0 (≈1. 9834) and 1;24, 30, 0 (≈1. 4083) appear as normalized ratios. - No explicit angles; instead, the table uses side ratios to solve for missing lengths, a proto-trigonometry. CONNECTION: - Base-60 system naturally generates fractions like 1/60, 1/30, etc. , which relate to geometric harmony ratios (e. g. , 0. 618 ≈ 37/60, 0. 382 ≈ 23/60). - The triples correspond to rational points on the unit circle, linking to crystallographic lattice po Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Tue,) studied this question.