Turn a Pentagon into a Square
You can cut up a pentagon and rearrange the pieces into a perfect square. Below is one way to cut a pentagon into six pieces that can be rearranged into a square.
- Cut out the pieces from the pattern. You can cut them from card stock, cardboard or Foamies™. You might want to somehow mark the back of the pieces to help you reassemble them.
- Rearrange the pieces into a square without flipping them over.
- Solution: here is how you can rearrange the pieces to make a square.
- This solution is by Henry Ernest Dudeney, a great English inventor of puzzles. Before he found his solution, the simplest solution known took seven cuts.
- David Hilbert proved that any polygon can be turned into any other by cutting it into a finite number of pieces.
- MathWorld showcases many more interesting dissections