square roots and cube roots

an idea from Martin Wilson, in Harrogate
(some of his questions slightly adapted, for ease of checking)

fraction approximations to square roots

there are patterns to be found in the fraction approximations

this work links with Heron's method for calculating square roots (which seems to have been known to the Babylonians)

see also the very helpful CTK (Cut the Knot) insights blog where the use of the 'Regula Falsi' method is explored