[math-fun] a strange result about the squaring of a circle
hello, I did not know that such a construction was possible. Apparently there is a way to take a circle and CUT it into pieces a finite number of times and then recombine all this into a circle. http://en.wikipedia.org/wiki/Tarski%27s_circle-squaring_problem the number of such pieces would have to be 10^50. well you have to be patient of course. It uses the axiom of choice. on this I agree : you have to choose or not, Am I crazy enough to undertake such project ?, ha ha ha. Any one know is this makes any sense ? have a good night, here it is 3 a.m. Simon Plouffe
On 27/04/2014 02:00, Simon Plouffe wrote:
I did not know that such a construction was possible.
Apparently there is a way to take a circle and CUT it into pieces a finite number of times and then recombine all this into a circle.
Only if you define "cut" in the usual Banach-Tarski-ish way (i.e., = "decompose"). You can't do it with the kinds of cut you would get from scissors. (And of course exactly one instance of "circle" there should be "square".) -- g
In fact, the definition of scissors congruence, and the statement of a theorem implying what Gareth said, is in the freely readable portion of this 1963 paper: < http://link.springer.com/article/10.1007/BF02759727#page-1 >. --Dan Gareth McCaughan wrote: << Simon Plouffe wrote: << Apparently there is a way to take a circle and CUT it into pieces a finite number of times and then recombine all this into a circle.
Only if you define "cut" in the usual Banach-Tarski-ish way (i.e., = "decompose"). You can't do it with the kinds of cut you would get from scissors.
participants (4)
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Dan Asimov -
Fred Lunnon -
Gareth McCaughan -
Simon Plouffe