Talk:Tarski's circle-squaring problem

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The article says:

Along the way, Lacskovich also proved that any polygon in the plane can be decomposed and reassembled to form a square of equal area.

This is just a strict version of the Bolyai-Gerwien Theorem. Wasn't it proved by Banach? --Zundark 21:10 Apr 26, 2003 (UTC)

Yes, you are correct. Lacskovich proved that you only need translations, no rotations. I fixed it. AxelBoldt 02:22 May 6, 2003 (UTC)

[edit] Non sequitur?

Concerning this: In particular, it is impossible to dissect a circle and make a square using pieces that could be cut with scissors (i.e. having Jordan curve boundary). Therefore, a non-constructive proof is necessary. Does that really follow from the non Jordan-ness of the cutting boundaries? Couldn't there be a case of something that is cut along "regular" fractal boundaries and reassembled? Definitely yes if the outer boundaries are allowed to be fractal. Lambiam^Talk 21:28, 2 May 2006 (UTC)

Why do we say it is impossible to make such a transformation dividing the circle into open regular subsets? How do we know it is impossible?--Pokipsy76 (talk) 16:05, 3 June 2008 (UTC)