Approximating cube roots of integers, after Heron's Metrica III.20

Heron, in Metrica III.20-22, is concerned with the the division of solid figures - pyramids, cones and frustra of cones - to which end there is a need to extract cube roots. We report here on some of our findings on the conjecture by Taisbak in C.M.Taisbak, Cube roots of integers. A conjecture about Heron’s method in Metrika III.20. Historia Mathematica, 41 (2014), 103-104.