FINDING: Plimpton 322 encodes a sexagesimal geometric progression of secants (or reciprocal pairs) forming a systematic trigonometric table, not merely Pythagorean triples. MATH: - Sexagesimal base-60 system used for all entries. - Key ratios: - Column I: \ (sec² () = 1 + ² () \) in sexagesimal form (e. g. , 1;59, 15 = 1. 9875, 1;56, 56, 58 = 1. 949. . . ). - Columns II–III: \ (a = short side, \, b = long side \) of right triangles with \ (a² + b² = c² \), but normalized so \ (b \) is a regular sexagesimal number (smooth integer in base-60). - Implicit constant: \ (sec () = c/b \), with \ (\) decreasing in regular steps (approx. 45° to 30°). - No explicit π or φ, but the progression of secants follows a geometric pattern: each row's secant ratio decreases by a factor near \ (3/2 \) or \ (1/ \) in angle. CONNECTION: - Geometric harmony: The secant values approximate ratios linked to the golden ratio (\ (Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Mon,) studied this question.