Cuneiform Discovery: Babylonian reciprocal tables sexagesimal mathematics — E8 Intelligence Research

**Discovery: The Algebraic Architecture of Babylonian Reciprocal Tables** The Old Babylonian (OB) scribal curriculum (c. 1900–1600 BCE) treated reciprocals not as arithmetic curiosities but as the operational core of their floating-point, base-60 algebra. The standard table text **BM 80150** (British Museum) lists the *igī* (reciprocals) of all regular sexagesimal numbers—integers whose prime factors are limited to 2, 3, and 5—up to 1,21 (81 decimal). Because only regular numbers possess finite sexagesimal reciprocals, division was executed as multiplication by *igī*: *a ÷ b = a × igī.b*. Tablet **YBC 7243** (Yale Babylonian Collection) demonstrates this principle geometrically. The scribe inscribed a square with side 30 (½) and computed its diagonal as 42;25,35. This value is the sexagesimal approximation of 30 × √2. The calculation relies on the reciprocal relationship: the diagonal *d* = side × √2. The scribe used the standard OB constant for √2 ≈ 1;24,51,10 (1.41421296 decimal), Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com