Talk:Tarski's circle-squaring problem

Older theorem?

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)

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)[reply]

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)[reply]

Number of pieces in Laczkovich's solution

89.66.70.59 recently changed "about 10⁵⁰ different pieces" to "at most 10⁵⁰ different pieces". Is there any reference for this? Laczkovich's original 1990 paper says (right at the end)

Unfortunately, each step of the proof increases the constants considerably and eventually we end up with something like 10⁵⁰.

In the absence of other information I am inclined to revert the text to about, or even roughly. Chris Thompson (talk) 13:31, 26 March 2018 (UTC)[reply]