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:

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Update (6Dec2024). Now proved impossible. "Dudeney's Dissection is Optimal." Erik D. Demaine, Tonan Kamata, Ryuhei Uehara. arXiv abs.