Have fun exploring Pythagoras 1A mathematician named Henry Perigal discovered how to cut the middle size square into four quadrilaterals and use them to demonstrate Pythagoras' Theorem. He wasn't a professional mathematician like a university professor or a computer programmer. Mathematics was his hobby. He did it in his spare time because he liked the challenges. But he is famous because of his discovery. In Questions 1, 2 & 3 you used the Perigal Pieces to prove Pythagoras' Theorem for one triangle. You showed that the four piece square together with the small square piece have the same area as the square built on the hypotenuse of a right angle triangle.
You have checked Perigal's Proof of Pythagoras' Theorem for three different triangles. It took a lot of time and it still doesn't prove that it works for every right angle triangle. Perigal proved it for A mathematician would also have to check what happens if the triangle doesn't have a right angle. ## Playing with PerigalWe know the four quadrilaterals can make the four square or the five square with a space in the centre. In these puzzles you will learn to make them using rotation. However it is better if your quadrilaterals have some thickness to hold onto. Glue them to a piece of card and cut around them carefully.
Turning a square into a square - Make the five piece with the space in the middle.
- It
*is*possible to use rotation only to transform the five piece with the gap into the four piece.
Hint:When you figure it out, practise it until you can do it smoothly. It feels really good to do.
Turning a stack into a square - Stack up the four pieces so the edges all match.
- Leave the bottom one on the table.
- Pick up the top three in the stack.
- Rotate them 90°.
- Slide and place the bottom one.
- Rotate the remaining two another 90°.
- Slide and place the bottom one.
- Rotate the remaining one another 90°.
- Slide and place it.
- You only have to start again and do one thing a different way each time and you will make the other square.
Note: Answers to these rotation puzzles are in the link below. ## Just Before You Finish- Search the web to find out five things about Henry Perigal's life.
- Make sure you have a recorded Pythagoras' Theorem in your journal and can explain it to someone else.
These notes were originally written for teachers. We have included them to support parents to help their child learn from Pythagoras 1. - Notes for Pythagoras 1.
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