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Subject: "Proof number 27"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #395
Reading Topic #395
Teja Ravivarapu
Apr-29-10, 07:47 PM (EST)
"Proof number 27"
   I want to understand proof number 27 in the amazing list of pythagorean theorem proofs. But unlike some of the other proofs this proof doesn't explain the proof. I would love it if someone could exlain proof 27 to me.


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Charter Member
2496 posts
Apr-29-10, 07:58 PM (EST)
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1. "RE: Proof number 27"
In response to message #0
   I'll be referring to the colorful diagram under proof 27. There are a few things to observe.

1. The diagram consists of two parts: left and right.
2. Both on the left and on the right there are 5 colored pieces: 2 yellow, 2 red, and 1 blue. Call this square c².
3. On the left, all 5 pieces compose a square. On the right, two red pieces make a square (call it a²) while 2 yellow and the blue piece make another square (call it b²).
4. Square c² is slanted. Not to fall, it is supported by two equal right triangles with the hypotenuse exactly c.
5. On the right, those triangles are filled with colored pieces. Look carefully: again, the two triangles are equal (from the left part). On the right, one of the sides of these equal triangles is a, the other is b.
6. Since c² and a² + b² are composed of the same pieces c² = a² + b².

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