View Single Post
2017-02-27, 22:27   #10
Dr Sardonicus

Feb 2017
Nowhere

136B16 Posts

Quote:
 Originally Posted by mickfrancis Having given some thought to this, I realise that what I really want is a way to find integer values for m such that $ (ceil(mr))^2- (mr)^2 < (mr)^s $ where s <= 1. I'm guessing this is a different kettle of fish...
This would appear to mean something like

| N/m - r| < c/m^(2 - s)

(c = positive constant), which is more easily achievable than having the exponent 2 in the denominator.

There is a notion of "best rational approximations," i.e. fractional approximations which are closer than any fraction with a smaller denominator. These consist of the "intermediate convergents" for the SCF. I know it's somewhere in Chrystal's Textbook of Algebra, but I'm sure something can be found on line.