The Haberdasher's Puzzle

1.- Introduction

This puzzle was introduced by Henry Ernest Dudeney. Some of his most famous innovations were in solving the Haberdasher's Puzzle that says: Cut an equilateral triangle into four pieces that can be rearranged to make a square.

Can you solve it? (Level: Easy)

Update 2023-Mar-11: An additional version was uploaded which is only 18mm tall instead of the original version which is 40mm tall. Select the one that suits you more :)

2.- Printing the Model

There are two versions of this model, one normal (height ~40mm) and a slim one (height ~18mm), pick the one that is suitable for you. (Files are in two different directories)

Both versions can be printed without any special care, all pieces can be printed together with the same color, or printed one piece at a time having different colors for making it more attractive. (In short, it is up to you)

The printer settings I suggest are:
 

2.1.- Normal Version

2.2.- Slim Version

(*)Material and time is cumulative for all pieces.

3.- How the model was built:

The model consists of an extruded triangle with its parts already cut.

The boxes have an additional 0.4mm of tolerance, so the pieces can fit well easily. 

The following sketch was used in Fusion 360 for preparing the 4 parts out of the equilateral triangle, it illustrates the solution given by Henry Ernest Dudeney:

1. Draw an equilateral triangle ABC. I opted to have it 40mm inscribed triangle.
2. Bisect AB in D.
3. Bisect BC in E.
4. Extend the line AE to F when EF is equal in length to EB.
5. Bisect AF in G (G becomes the center of a circle tangent to A and F).
6. Extend the line EB to H when H is tangent to the circle from center G.
7. The length of EH will be the side of the required square.
8. Create a circle with the center in E that tangents point H.
9. Name J the point the above circle cuts AC.
10. Create a point K in AC where JK is equal to BE.
11. From D drop a perpendicular on EJ at point L.
12. From K drop a perpendicular on EJ at point M.

If you followed the drawing, you have all the information you need:

• The equilateral triangle size is the size of AB or BC or AC.
• The size of the target square is EH or EJ.
• Part A is constructed by extruding the polygon AJLD.
• Part B is constructed by extruding the triangle the JMK.
• Part C is constructed by extruding the polygon BELD.
• Part D is constructed by extruding the polygon CKME.
   

4.- Change Log

• Updated 2023-Apr-11 - Adding slim version.
• Uploaded 2023-Apr-10 - Initial version.

5.- Last Words

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Happy printing & Greetings from the Galilee.

Hope it was not TL;DR