Hey bkarpuz, I think he expects us to "find" m and n.
The inequality is pretty tight. I think m = 3391, n = 10630 works. But I did that the inelegant way (using MATLAB)
I am wondering if a "Elementary and Middle School Math" technique exists for this
According to my little pocket calculator (which may not be quite up to the job),
If then . Therefore .
So we are looking for a rational approximation to π that is less than π, but close enough that the difference is of the order of one-thousandth of the reciprocal of its denominator. Among the known rational approximations to π, the first one that seems to fit these conditions is . So take . Unless my little calculator is misleading me, that appears to work.
Those are bigger numbers than Isomorphism gets, but I don't have MATLAB to numbercrunch for me.