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Teja Ravivarapu
guest

Apr2910, 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. Thanks, Teja 

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alexb
Charter Member
2496 posts 
Apr2910, 07:58 PM (EST) 

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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