Old Babylonian Division via Reciprocal Tables of Regular Numbers — E8 Intelligence Research

FINDING: Old Babylonian division was executed as multiplication by reciprocals drawn from canonical IGI-GUB tables, restricted to *regular* numbers (those whose reciprocal terminates in base 60). | MATH: A number n is regular iff n = 2^a · 3^b · 5^c (primes dividing 60). Reciprocal terminates after at most 2 sexagesimal places. Canonical table pairs: 2↔30, 3↔20, 4↔15, 5↔12, 6↔10, 8↔7;30, 9↔6;40, 10↔6, 12↔5, 15↔4, 16↔3;45, 18↔3;20, 20↔3, 24↔2;30, 25↔2;24, 27↔2;13;20, 30↔2, 32↔1;52;30, 36↔1;40, 40↔1;30, 45↔1;20, 48↔1;15, 50↔1;12, 54↔1;6;40, 1;4↔56;15, 1;12↔50, 1;21↔44;26;40. Division a÷b = a × (1/b) only defined when b is regular; irregular divisors (7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61...) have no finite sexagesimal reciprocal. | CONNECTION: Base-60 = 2²·3·5 yields 5-smooth (Hamming) regular numbers — the same class underlying the 5-fold/icosahedral symmetry group and the 2-3-5 prime lattice. The reciprocal map n↔1/n is an involution on the multiplicative group Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com