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Can anyone explain what's wrong with this?

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MarnixKlooster ReinstateMonica
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user3628041
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1 Answers1

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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.

5xum
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    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 02 '14 at 19:12