Plimpton 322: Oldest Trigonometric Table Using Ratios, Not Angles — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian clay tablet (c. 1800 BCE) listing 15 rows of Pythagorean triples, likely generated by a systematic method using reciprocal pairs in base-60, and now interpreted as the world's oldest known trigonometric table based on ratios, not angles. MATH: - Each row corresponds to a Pythagorean triple (a, b, c) satisfying \( a^2 + b^2 = c^2 \), with a < b. - The tablet lists values of \( b^2 / a^2 \) (or equivalently \( (c/a)^2 \)) in descending order, forming a sequence of decreasing ratios. - Generation method: For regular sexagesimal numbers \( p \) and \( q \) (with \( p > q \)), set \( a = p^2 - q^2 \), \( b = 2pq \), \( c = p^2 + q^2 \). - Key constants: base-60 (sexagesimal) system; regular numbers (only prime factors 2,3,5). - The tablet's first column gives \( (b/a)^2 \) or \( (c/a)^2 \), with values like 1.9834027... (sexagesimal 1;59,0,15) down to 1.38716... (sexagesimal 1;23,13,46). CONNECTION: - The ratios \( b/a \) from the tri Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com