Talk:Tarski's circle-squaring problem
From Wikipedia, the free encyclopedia
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. LambiamTalk 21:28, 2 May 2006 (UTC)
