I won't do your homework for you, and you clearly have been asked to think about this, not to ask someone else to think about it for you.
But, no. you cannot compute the number of squares fully inside a circle merely by knowing the area of the circle. As simple a relationship as that will not happen.
You do have a simple option - just count the number of squares inside. Check each square. Is it inside or not? (Are there really that many squauares you would need to check? Of course not! Computers are fast at these things.)
So just use a loop. Actually, you don't even need an explicit loop. An implicit loop would suffice, but that would involve me writing code, telling you how to do this homework. And you are the one who needs to do the thinking here. As it is, I've probably told you more than I should by my standards, but you did make SOME effort.
Oh. what is the difference between an explicit loop and an implicit loop?
for i = 1:n
stuff
end
That is an explicit loop.
i = 1:n;
The latter is what I like to call an implicit loop, since the looping is done for you. In the latter case, operations are performed on all elements, effectively at once.
Are there direct methods? I can think of a sum that would work, but I don't know if there is an analytical expression for the summation: that starts to dive into number theoretic issues, and I just don't want to spend the mind sweat to do homework.
