**Discovery: YBC 7289 and the Sexagesimal Precision of √2** **1. Mathematical Knowledge Contained** YBC 7289 (Yale Babylonian Collection), a small round tablet from the Old Babylonian period (c. 1800–1600 BCE), contains the earliest known high-precision approximation of the square root of 2. It demonstrates that Babylonian scribes possessed a theoretical understanding of the Pythagorean theorem—specifically, that the diagonal of a square relates to its side by a constant factor—over a millennium before Pythagoras. The tablet functions as a geometric reference standard, likely used for surveying or architectural layout, proving the *diagonal rule* was a calculated constant, not merely a measured estimate. **2. Specific Numbers and Calculations** The obverse depicts a square with its two diagonals. Cuneiform inscriptions label the side as **30** (written as a single vertical wedge for 30, or arguably 1/2 in floating-point sexagesimal) and the diagonal as **1,24,51,10** (sexagesimal). T Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Andrew Stewart Caldin (Sun,) studied this question.