Hi, sorry for the waste of bandwidth...
The error in your "proof" occurs in the next to the last step, when you
say that as the number of semicircles approaches infinity, the curve
formed by all the little semicircles turns into the diameter of the
original circle. You see, when you have n semicircles, each of length
pi/n, the total length is n * (pi/n) = pi, no matter how large n is.
The issue you have raised in this paradox is related to the subject of
fractals; i.e. curves which have fractional dimension.
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
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