Talk:Squaring the square

Missing reference
"The first perfect squared square was found by Roland Sprague in 1939." Although the Scientific American: '97 July, p86 indicates a slightly earlier discovery (1938, by Cambridge mathematicians), the "Sprague" page has been deleted without visible explanation nor removal of the reference: The deletion and move log for the page are missing:
 * 09:28, 21 March 2005 RickK (talk | contribs) deleted "Roland Sprague" ‎ (content was: 'squaring the square')Wikidity (talk) 17:01, 1 August 2010 (UTC)

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.....
 * 'Pluperfect square' is classically defined as using only integers for all measurements. Otherwise, it would be trivial, unless a limit is also placed on the number of sub-squares, which would usually approach infinity.Wikidity (talk) 17:01, 1 August 2010 (UTC)

"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)
 * I recommend "Filling Integer Squares" or "Pluperfect squares"Wikidity (talk) 17:06, 1 August 2010 (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
 * No non-infinite combination of orthogonal filling squares can form a triangle. That does not mean they are inherently integral, or even rational, since irrational numbers can add up to an integer (integer-irrational=irrational).  It does make sense that one non-integer squares requires more (all?), to add up to an integer in both directions.Wikidity (talk) 17:47, 1 August 2010 (UTC)

Cubing the cube
There's something wrong with the argument (at 2010-01-06) which refers to contradicting the minimal S when there has been no statement about S being minimal. The argument is, IMO, correct as far as it goes, but a step or two have been omitted. Can anyone clear this up? -- SGBailey (talk) 07:36, 7 January 2010 (UTC)
 * I found where it had been edited from a more complete argument, so I undid the edit. Happy now... -- SGBailey (talk) 23:06, 7 January 2010 (UTC)

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