Take a piece of paper and do the following:
- Make it into a square (interesting discussion on best way to do this).
- Fold in half then unfold so you have created crease along a vertical line of symmetry
- Then take any corner and fold to the midpoint of the opposite edge. Press down to make a crease along the fold line
- Unfold and now investigate all the triangles you have created, i.e. can you work out their lengths?
Here are some pictures, which also give some hints, although not a complete solution. The result is very satisfying although I would love to find a way to show this that doesn’t require reams of algebra. Any takers??
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