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        riddles >> medium >> Pythagorean dissection
        
(Message started by: JocK on Feb 6^th, 2005, 11:27am)

Title: Pythagorean dissection
Post by JocK on Feb 6^th, 2005, 11:27am

You have to teach a class Pythagoras' theorem. You decide to make a puzzle to help them understand this theorem.
Someone told you that one can dissect a square of area a² into four equal pieces such that when a square of area b² is added as a fifth piece, the five pieces together can be rearranged into a square of area a²+b².

For arbitrary a > b, what is the shape of the four identical pieces that you have to construct?

Title: Re: Pythagorean dissection
Post by Barukh on Feb 7^th, 2005, 11:17am

Note that this can be done as a pivot puzzle.

Title: Re: Pythagorean dissection
Post by JocK on Feb 7^th, 2005, 2:33pm

Well done Barukh.

Perhaps an even better educational tool originates when dissecting below L-shape into 4 equal triangles and a square such that the five pieces can be put together in the form of a square.

What is the shape of the triangles, and what is the size of the square?