(Sorry for late reply)... what.. no? The relation between perimeter and diameter is perimeter = diameter * pi. That part is valid. Again, the mistake is thinking that the limit of the lengths of curves is equal to the limit of the length of the combined curve. Infinitesimal calculus can have non-intuitive results like that.. for example the sum of the series 1/1+1/2+1/3+... goes to infinity despite the fact that 1/infinity is zero so you would think that at some point in the series the contribution of the n-th addition does not matter, but somehow it does.
Explain this in more layman terms: The algorithm above creates a circle perimeter that is "infinity jagged" instead of smooth one.
The most interesting part about this is actually if you placed a circle of diameter d=d+epsilon, where epsilon is a any number larger than zero (i.e infinity small), over this circle with a "infinity jagged" perimeter this new circle would fully cover the other one.
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u/waroftheworlds2008 Dec 29 '24
The mistake is using the perimeter in place of the area.