Turn an Equilateral Triangle into a Square II

In a classic puzzle, you are asked to chop up a triangle into pieces and rearrange them into a square. These dissection puzzles lead to fascinating and ingenious solutions like this one from Frederickson. Not only can the pieces be rearranged to form a square, but if you connect the pieces with hinges, you can swing all the pieces into place.

Steps

1. Cut out the piece from the pattern
   
2. Cut along the solid lines in the interior of the triangle. Notice that you cut through the tabs in only a few places. Where the tab isn't cut through, the tab will act as a hinge.
   
3. Fold the tabs up perpendicular to the piece.
   
4. Swing the pieces from their original position to their new location to form a square.
   

Notes

• One technique for designing dissections like this is to superimpose your target shape onto you original shape. If you line up the figures just right, the superposition will show how you can cut the pieces. In this case, the midpoint of one side of the square meets the triangle at the midpoint of its side. The midpoint of the opposite side of the square touches the base of the triangle.
  

Links

• Greg N. Frederickson has an animation of this transformation on his website.

References

• (G. N. Frederickson n.d.)