Talk:Squaring the square

How trivial is this?

"Squaring the square is a trivial task unless additional conditions are set." Has this been completely described? Given a square of sides 2.5 units, s-t-s is not trivial. Put a 2 square in, then what? You can have 42 angle in a circle .5 squares as they are non-integral. Am I missing something? Mr. Jones 19:14, 4 Jul 2004 (UTC)

Well, it's assumed that the square to be tiled itself has integral sides.....

"Squaring the square": problem?

Squaring the square problem would be the right title if this article were about squaring something called the "square problem". But it is not. It is about the problem of squaring the square. Hence Squaring-the-square problem, with hyphens, could be appropriate. But I think this simpler title is better because of its simplicity. As Einstein said, things should be as simple as possible, but not simpler. Michael Hardy 22:53 Mar 15, 2003 (UTC)

Squaring the plane

Quote: "It is still an unsolved problem, however, whether the plane can be tiled with a set of integral tiles such that each natural number is used exactly once as size of a square tile." This is not true: see http://maven.smith.edu/~jhenle/stp/stp.pdf

Integral squares

I would add that any set of squares tiling a larger square can be taken to have integral sides because the squares are lined up parallel to the square's sides (otherwise they would form triangles between themselves and adjacent squares) and the sum of their lengths adds up to an integer, therefore their lengths are rational numbers even for tiling a unit square, and multiplied by their greatest common denominator they are integers. If the length of at least one square were an irrational number, the difference between the length of a square needed to make the sum rational would form an incommensurable irrational number and so the number of squares tiling the plane rises to infinity. Am I wrong? You could add that to the main article, if you don't think it's too complicated. 24.184.234.24 (talk) 00:00, 23 October 2009 (UTC)LeucineZipper

Integral squares

I would add that any set of squares tiling a larger square can be taken to have integral sides because the squares are lined up parallel to the square's sides (otherwise they would form triangles between themselves and adjacent squares) and the sum of their lengths adds up to an integer, therefore their lengths are rational numbers even for tiling a unit square, and multiplied by their greatest common denominator they are integers. If the length of at least one square were an irrational number, the difference between the length of a square needed to make the sum rational would form an incommensurable irrational number and so the number of squares tiling the plane rises to infinity. Am I wrong? You could add that to the main article, if you don't think it's too complicated. 24.184.234.24 (talk) 00:00, 23 October 2009 (UTC)LeucineZipper