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Is value of $\pi = 4$?

In this question we discussed why the fake proof is wrong.

But, what about the area?

The process converges to the same area of the circle ($\frac{\pi}{4}$)?

What's the area when the process repeats infinitely?

How we can prove, using calculus and limits the result?

Pi is equal to 4

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    This question just ask about the area. Not about the problem in the proof.2012-04-17
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    have you tried to figure it out?2012-04-17
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    It is an interesting fact that intuition about area (in two dimensions) seems to be much more useful than intuition about arclength.2012-04-17
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    Doesn't this result follow from the one showing that $\sqrt{2} = 2$ by (a) going from $(0,0)$ to $(1,1)$ in a straight line and (b) along a path that is alternately parallel to the $x$ axis and the $y$ axis in ever decreasing segments?2012-04-17
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    @Andre: I don't think that's quite the problem: I think it's more an issue that the victim of such an argument doesn't have the knowledge or appreciation for rigor to be able to confidently reject the assertion that the jagged line converges to the circle in a suitable sense.2012-04-17
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    @AndréNicolas, I agree.2012-04-17
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    @DilipSarwate, well, I didn't understand at all what you're saying.2012-04-17
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    @johnw., I tried a little, but a limit to became $\pi$ looks hiden.2012-04-17
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    How this is a exaclty duplicate of another question? Well, I really hope this question didn't end because of this missunderstood.2012-04-18

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