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

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Can anyone explain what's wrong with this?

## marked as duplicate by Henry Swanson, Hakim, 5xum, user91500, Git GudJun 2 '14 at 11:55

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## 1 Answer

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