The problem is to cut a regular hexagon into parts that can be put together (without overlaps or wasting any parts) to make an equilateral triangle using only a ruler and compass (and scissors).

What is the smallest number of parts that will still let you achieve this?

http://mathworld.wolfram.com/Dissection.html shows a picture of a solution that uses 5 parts but I don't know if this can be done with a ruler and compass. I also have no idea how to prove that you can't do it in 4 parts.

The problem is to cut a regular hexagon into parts that can be put together (without overlaps or wasting any parts) to make an equilateral triangle using only a ruler and compass (and scissors).

What is the smallest number of parts that will still let you achieve this?

http://mathworld.wolfram.com/Dissection.html shows a picture of a solution that uses 5 parts but I don't know if this can be done with a ruler and compass. I also have no idea how to prove that you can't do it in 4 parts.

Update. It seems that a solution by Harry Lindgren (1961) that uses only 5 pieces can indeed be done using ruler and compass. The question remains how to show it can't be done in 4 pieces. I am also interested to know if Lindgren's solution is unique in some sense.

The problem is to cut a regular hexagon into parts that can be put together (without overlaps or wasting any parts) to make an equilateral triangle using only a ruler and compass (and scissors).

What is the smallest number of parts that will still let you achieve this?

There is a semi-spoiler below showing what I know so far about this problem.

http://mathworld.wolfram.com/Dissection.html shows a picture of a solution that uses 5 parts but I don't know if this can be done with a ruler and compass. I also have no idea how to prove that you can't do it in 4 parts.

The problem is to cut a regular hexagon into parts that can be put together (without overlaps or wasting any parts) to make an equilateral triangle using only a ruler and compass (and scissors).

What is the smallest number of parts that will still let you achieve this?

http://mathworld.wolfram.com/Dissection.html shows a picture of a solution that uses 5 parts but I don't know if this can be done with a ruler and compass. I also have no idea how to prove that you can't do it in 4 parts.