It is well known that rational numbers are distributed on the number line everywhere compactly. If we consider a 'square' a parallelogram to be precise, formed by natural numbers p and q, i.e. coordinates $(p,0), (0,q)$.
Within this lattice, we assume ONLY rational points $ \frac{p}{q}$, excluding all other points.
1) How many rational numbers do we have in this lattice?
2) What is the density defined as the number of rational numbers inside it divided by the number of all possible pairs of natural numbers in the lattice. Thank you for your help.
I saw an answer being $ \frac{6}{\pi^2}$ as N tends to infinity. but I don't know how to prove it.