Sexagesimal Reciprocals: Cuneiform Mathematics Without Zero — E8 Intelligence Research

FINDING: Cuneiform mathematics is a base-60 (sexagesimal) positional system with no true zero in early phases, using placeholder gaps and reciprocal tables rather than algebraic abstraction | MATH: Base-60 = 2²·3·5; reciprocals of regular numbers (those of form 2^a·3^b·5^c) terminate exactly; e.g. 1/2=30, 1/3=20, 1/4=15, 1/5=12, 1/6=10, 1/8=7;30, 1/9=6;40, 1/10=6, 1/12=5, 1/15=4, 1/16=3;45, 1/18=3;20, 1/20=3, 1/24=2;30, 1/25=2;24, 1/27=2;13;20, 1/30=2, 1/32=1;52;30, 1/36=1;40, 1/40=1;30, 1/45=1;20, 1/48=1;15, 1/50=1;12, 1/54=1;6;40, 1/60=1 | CONNECTION: 60 = LCM(1..6) = 2²·3·5; highly composite (12 divisors); 60° = π/3 radians = 1/6 of full rotation; 360 = 6·60; the regular-number reciprocal structure is a multiplicative lattice closed under 2,3,5 — a 3-generator monoid; connects to crystallographic 6-fold and 3-fold symmetry (hexagonal lattice, root system A₂, 60° and 120° angles) | DEPTH: 8 FINDING: Babylonian reciprocal tables and the YBC 7289 tablet demonstrate √2 ≈ 1;24,51,10 (se Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com