1

Can anyone explain what's wrong with this?

enter image description here

MarnixKlooster ReinstateMonica
  • 5,576
user3628041
  • 307

1 Answers1

3

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
  • 123,496
  • 6
  • 128
  • 204
  • 1
    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