I asked this question on MSE here.
Given a continuous function $f :[a,b]\to\mathbb{R}$, what is the least number of closed circles with fixed radius $r$ required to cover the graph of $f$?
It is easy to prove (by using the extreme value theorem) that only finitely many circles are required to cover the graph of $f$, but how can I find the least number of circles? I don't think a closed form exists , but is there a solution, like an indefinite integral? If there isn't, is there an algorithm that can solve this problem?
