Haberdasher's problem puzzle plan

The Haberdasher’s problem created Henry Dudeney. The essence of haberdasher’s problem is how to cut an equilateral triangle into four pieces that could make a square.

Haberdasher's problem puzzle plan

Although the Haberdasher's problem is a very interesting geometric task, it is also one quite an interesting puzzle, which can be made quite fast.

Haberdasher’s problem puzzle is not one of the difficult puzzles, but its solution is geometrically quite interesting.

If we imagine the pieces hinged together into 3 vertices, all the 4 pieces can be transformed by rotation into either the square or the original triangle.
 
Haberdasher's problem puzzle - Cutting diagram

You can make a haberdasher's problem puzzle according to our cutting diagram, and if you want to make the puzzle with different dimensions, you can easily draw cutting diagram in one of these two ways:


VERSION 1
 
  Haberdasher's problem puzzle plan - Drawing cutting diagram 1

1. Draw an equilateral triangle with points A, B and C
2. Bisect AB at D and BC at E.
3. Extend AE to F so that EF=EB.
4. Bisect AF at G, then, with G as the centre, describe the arc AHF.
5. Extend EB to H.
6. With E as the centre, draw the arc HI.
7. Make IJ=BE
8. Draw line IE
9. From D and J draw perpendiculars on IE to obtain points K and L.
This way, we made 4 pieces of equilateral triangle that can be rearranged into square.


VERSION 2
 
Haberdasher's problem puzzle plan - Drawing cutting diagram 2

1. Draw an equilateral triangle with points A, B and C
2. Bisect AB at D and BC at E.
3. Draw the perpendicular lines from D and E on the side AC.
4. Determine the intersection points F and G on the side AC
5. Draw the line EF.
6. Draw the perpendiculars from D and G to this segment and determine the intersection points H and I.