Sumerian Base-60 and Non-Standard Digit Expansions in Arbitrary Bases — E8 Intelligence Research

FINDING: Sumerian metrology (c. 4000 BC) is the earliest documented sexagesimal (base-60) system, and modern number-theoretic work on non-standard digit expansions formalizes the general problem of finite representation in arbitrary integer bases. | MATH: Base-60 = 2²·3·5; highly composite → 12 divisors {1,2,3,4,5,6,10,12,15,20,30,60}. Reciprocal expansions terminate for denominators dividing 60^k. Non-canonical digit-set problem: for base b with digit set D ∌ 0, existence of finite expansion for every integer n. | CONNECTION: 60 = 2·30 = 3·20 = 4·15 = 5·12 = 6·10 → maximal divisor symmetry among small integers. 60° is the interior angle of the equilateral triangle and the fundamental angular quantum of hexagonal/trigonal crystallographic systems (space groups P6, P6₃, etc.). 360° = 6·60 ties base-60 to the hexagonal lattice and to the 12-fold zodiacal division (12 = 60/5). | DEPTH: 7 FINDING: The Sumerian sexagesimal system is the historical origin of the 360° circle, the 60-minute h Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com