I learned an interesting Pythagoras proof today. Note that the yellow subtriangles are congruent tot the main yellow triangle.pic.twitter.com/HnQTje1RDt
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Mathematical physicist and mentor to mathematically talented youth. Talent is that which bridges the gap between what can be taught and what must be learned.
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I learned an interesting Pythagoras proof today. Note that the yellow subtriangles are congruent tot the main yellow triangle.pic.twitter.com/HnQTje1RDt
This is a deduction from the Pythagoras theorem, but not a proof. How do you know the rectangular areas are equal to a^2 and b"2? Also the triangles are "similar" rather than congruent.
You can easilly prove the areas of the rectangles are a2 and b2.
The easiest way to prove it is to start from the Pythagoras theorem. But another way is needed if you are trying to prove Pythagoras is true.
Right, see the reply from @MathPrinceps for how to see the areas of the rectangles and the squares are equal, and from there you get Pythagoras!
I can't see anything from @MathPrinceps in the thread.
The hypotenuse of the main yellow triangle is c, so the two yellow subtriangles result from scaling it down by a/c and b/c. The main yellow triangle's hypotenuse is divided into pieces of lengths (a^2)/c and (b^2)/c, so the rectangles on these segments have areas a^2 and b^2.
Thanks. I suppose the (a^2)/c comes from a.(a/c) and (b^2)/c from b.(b/c).
Yes, that's right.
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