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At a workshop it was suggested that it likely remains an open problem whether or not there is a 3- or 2 -piece dissection of a square to an equilateral triangle. Can anyone confirm that this is unresolved?

Four-piece dissections are known, the most famous being Henry Dudeney's century-old gem:

                [Maple animation from this link.]

And here is a 5-piece dissection.

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2 is not possible because the side length of the triangle is more than the diagonal of the square. –  Ken Fan Nov 5 '11 at 2:18
I just want to tell that applet to "hold still, dammit"! –  Todd Trimble Nov 5 '11 at 13:07
@Todd: Added a stable image (in a different orientation). –  Joseph O'Rourke Nov 5 '11 at 13:40
Wow, ask and ye shall receive! Thank you, Joseph! –  Todd Trimble Nov 5 '11 at 14:30
A 3-piece dissection of the equilateral triangle would have to create 4 right angles to serve as corners of the square, and there are just a few ways this can be done. At first glance, none of them recombine as a square (though you can get a rectangle). It should be pretty easy to run through the options and rule them all out. –  Anton Lukyanenko Nov 6 '11 at 18:34
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