# Is $\pi = 4$ really? [duplicate]

The problem is that you think that if a sequence of curves $\gamma_1,\gamma_2,\dots$ approaches the curve $\gamma$, the lenghts of $\gamma_i$ should converge to the length of $\gamma$. This is not true.
• Also, it's got nothing to do with $\pi$ per se. You could use the same reasoning to argue that the distance from (0, 0) to (1, 0) is $\sqrt{2}$. – StumpyLeg Jun 2 '14 at 19:12