(Apologies for continuing off-topic)
The problem with the reasoning is the part that goes, "At last we end up with a
You don't - it *looks* like a straight line but it is actually a series of
infinitesimally small semicircles, and the length along the curves remains 1*pi
no matter how small you get.
These ideas are treated in the fundamentals of differential calculus.
Priit Kull wrote:
> Hi list
> Of cource the Pi legislation in Alabama is a joke for the simple reason that
> they have got the wrong value for it.
> I am going to prove that the correct value for Pi is actually 2.
> The reasoning goes like this. You take a unit circle with R=1. According to
> the definition of Pi the length of such a circle's surcumference is 2Pi,
> that is half of the circle = Pi and diameter=2. Now you draw a half of a
> circle with R=0.5 on the half of the diameter and another halfcircle on the
> other half of the diameter. The length of the first halfcircle is 0.5Pi. The
> same goes for the other halfcircle. That means that the total length of the
> bent line is equal to Pi. Now we do the same trick of deviding the R and D
> by 2 and we end up with 4 halfcircles 0.25Pi length each, which once again
> totals to 1Pi. Continuing in the same line (8*0.125Pi=1Pi, 16*0.0625Pi=1Pi
> ...) we can every time prove that the total length of the bent line is equal
> to Pi. At last we end up with a straight line, which (look at the beginning
> of the paragraph) is the diameter of the original unit circle and therefore
> 2. Ergo Pi=2.
> Tell me where am I wrong. If you can not, you have to accept the truth and
> rethink your life.
> Best regards
> Priit Kull
> PS: The puzzle is not my invention, but the place where I read it did not
> give any acceptable explanation about what is wrong with the reasoning. I
> think I figured it out after four years of concentrated thinking and there
> is nothing wrong with the reasoning, the problem is with the traditional
> geometry. I also made a .STL file depicting the first four steps of the
> iteration. It is actually a quite nice trinket with neverending Yin/Yang
> pattern. I will not attach it as this is off topic and the file is 346KB.
> Anybody wanting to have a solid proof of the fact that Pi=2 switch on your
> RP machine and send me a message.
> For more information about the rp-ml, see http://ltk.hut.fi/rp-ml/
For more information about the rp-ml, see http://ltk.hut.fi/rp-ml/
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