Sumerian Base-60 System: A Highly Composite Radix for Exact Division — E8 Intelligence Research

FINDING: The Sumerian sexagesimal (base-60) system is a positional numeral system with a radix of 60, enabling exact division by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 — a highly composite radix that minimizes fractional error in practical arithmetic. | MATH: Radix \( b = 60 = 2^2 \cdot 3 \cdot 5 \). Divisors of 60: {1,2,3,4,5,6,10,12,15,20,30,60}. In base-60, the reciprocal of any divisor \( d \) of 60 terminates exactly: \( 1/d = k \cdot 60^{-1} \) for integer \( k \). The system encodes fractions as \( \sum_{i} a_i 60^{-i} \), \( a_i \in \{0,\dots,59\} \). Key ratio: \( 60/360 = 1/6 \), \( 360/60 = 6 \). | CONNECTION: Base-60 directly links to angular measure (360° = 6×60) and time (60 s/min, 60 min/hr). The divisors of 60 include 3 and 5, enabling exact trisection and quintisection — foundational for constructing regular polygons (triangle, pentagon) and thus crystallographic point groups (3-fold, 5-fold symmetry). The ratio \( 1/60 = 0.016666\ldots \) is the seed for the sexagesima Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com