At a workshop it was suggested that it likely remains an open problem
whether or not there is a 3- <strike>or 2</strike> -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="https://i.sstatic.net/BHW7F.gif" />
<img src="https://i.sstatic.net/Bpbrv.gif" />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<sub>
[Maple animation from this
<a href="http://www.maplesoft.com/applications/view.aspx?SID=6499">link</a>.]
</sub>
<br />

_______________

*Update* (6Dec2024). Now proved impossible.
"Dudeney's Dissection is Optimal."
Erik D. Demaine, Tonan Kamata, Ryuhei Uehara.
[arXiv abs](https://arxiv.org/abs/2412.03865).


  [1]: http://www.markus-goetz.de/puzzle/0041.html