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Topic: Pythagorean dissection (Read 571 times) 

JocK
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Pythagorean dissection
« on: Feb 6^{th}, 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 a^{2} into four equal pieces such that when a square of area b^{2} is added as a fifth piece, the five pieces together can be rearranged into a square of area a^{2}+b^{2}. For arbitrary a > b, what is the shape of the four identical pieces that you have to construct?

« Last Edit: Feb 6^{th}, 2005, 11:59am by JocK » 
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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.
x^{y}  y = x^{5}  y^{4}  y^{3} = 20; x>0, y>0.



Barukh
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Note that this can be done as a pivot puzzle.


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JocK
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Well done Barukh. Perhaps an even better educational tool originates when dissecting below Lshape 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?


IP Logged 
solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
x^{y}  y = x^{5}  y^{4}  y^{3} = 20; x>0, y>0.



