At a workshop it was suggested that it likely remains an open problem whether or not there is a 3- or 2-piece <a href="http://mathworld.wolfram.com/Dissection.html">dissection</a> 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: <br /> <img src="http://cs.smith.edu/~orourke/MathOverflow/Dudeney.gif" /> <br /> <sub> [Image from this <a href="http://www.maplesoft.com/applications/view.aspx?SID=6499">link</a>.] </sub> <br />