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# What Is The Most Elegant Proof Of Pythagoras?

ToraToraTora | 22:30 Wed 28th Feb 2024 | Science

I love the Euclidian one of course but I'd love to hear about others, possibly Algebraic.....?

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If you're not capable of giving serious answers to this type of question please dont bother wasting time by posting flippant responses.This is in Science, not CB.
23:53 Wed 28th Feb 2024
Question Author

did I put this is the wrong category?

As good as any I suppose.

Question Author

would anyone like to have a go at the OP?

I've always been a big fan of proof by contradiction for any mathematical theorem:
https://www.cut-the-knot.org/pythagoras/proof122.shtml

Question Author

yep chico, I also love PBCs, such a great way to look it things.

Elliemay1:
That joke has been doing the rounds since it was first published in the Sheffield University Rag Mag in the early 1970s.

I should know because I was the one who contributed it!

Yes, Chris, I remember it from my schooldays!

?si=YMmj1raWIuwtPAFH

I like this one. Hope the link works.

Question Author

Tomus I love that, thanks.

I remember this from school (a LONG time ago), quite a simple proof  :)

Here's a link to the diagram I'll be referring to:

https://i.ibb.co/rtd4Hkp/Pythagorus.png

Consider a square ABCD with a smaller square PQRS within it.

The area of the square ABCD is given by multiplying the lengths of the sides of the square together:

= AB x BC

= (a + b) x (a + b)

= a² + b² + 2ab

This area is also equal to the sum of the areas of the smaller square PQRS and the 4 triangles

= c² + 4 (1/2 x (a x b))

= c² + 2ab

These 2 areas are equal, i.e.

a² + b² + 2ab = c² + 2ab

a² + b² = c²

Q.E.D.

Question Author

cheers giz that's the well known one I was hoping for something different.

Apparently there are over 350 proofs, but many are empirical (like tomus42’s video of water filled squares).

Question Author

Indeed hymie, that's why I am looking for an elegant/amusing one. Thanks for taking time off to contribute.

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