3-piece dissection of square to equilateral triangle?

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.]

• 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