If you don't know what trollpi is, you can see it here:(adsbygoogle = window.adsbygoogle || []).push({});

http://qntm.org/files/trollpi/piequals4.png [1]

It seems to me that the flaw in this problem is that while the shape may converge to a circle, the way you measure the perimeter is ds=dx+dy=1+(dy/dx) not ds=sqrt(1+(dy/dx)^2 )dx as usual. So I tried using this new definition of the arclength in the first quadrant with r=0.5 and integrating expecting to get 1. I put the following into mathematica:

Integrate[1 - x/Sqrt[0.25 - x^2], {x, 0, 0.5}]

This did not give me 1. Can someone explain why?

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# Don't know what trollpi is?

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