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   Pythagorean dissection
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   Author  Topic: Pythagorean dissection  (Read 571 times)
JocK
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Pythagorean dissection  
« on: Feb 6th, 2005, 11:27am »
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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?
 
« Last Edit: Feb 6th, 2005, 11:59am by JocK » IP Logged

solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.

xy - y = x5 - y4 - y3 = 20; x>0, y>0.
Barukh
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Re: Pythagorean dissection   Pythagorean_Dissection.zip
« Reply #1 on: Feb 7th, 2005, 11:17am »
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Note that this can be done as a pivot puzzle.
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JocK
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Re: Pythagorean dissection   pythagorean_dissection.JPG
« Reply #2 on: Feb 7th, 2005, 2:33pm »
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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?
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.

xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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