Pythagorean Theorem XII (visual proof)

This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) following essentially Euclid's proof. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. As a bonus, we show how to use Euclid's shear and rotate proof to create a dissection proof of the Pythagorean theorem. Which of these proofs do you prefer?

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[BlackbodyEconomics]

I've never seen that one before. Pretty cool. Euclid was a mad genius!

[theoremus]

I like the sheering proof. It is Cavalieri's Principle in the manipulation of rectangles. I call it a "Cavalieri Shift". I have videos on the geometry of Cavalieri Shift as it pertains to the area and slope of ordinary curves.

[StudywithmeinPakistan]

As always. Beyond imagination. Great work. 👍

[phiarchitect]

Morphing is a great tool for understanding what is happening, however, it is not a tool in Euclid's box. He is limited to the set of operations with a straight-edge and compass. Following the chain of dependent propositions is like following function calls in code. There are no short cuts. Even constructing the squares on the sides requires many operations.

To render proposition I.47 as Euclid described requires probably hundreds of operations, all leading back to the axioms and definitions.

Another great video!

[lukakirtadze]

so good animation. do you have page on FB?

[PrintersBroadcastingCompany]

nice as always, but i don't really get it with the sheering operation. it is not intuitive to me how sheering works and why the resulting rectangles fit the lower square. could you make a vid about that please?

[specialk]

I have a question about this diagram. Forgive me if I can't see it but what's the connection/relationship between the triangle and the squares it produces from the 3 sides?

[youtubeutilis]

hye good joob ! i have a new proof to pythagore by circle how can i contact you ?

[knopfir]

i like the sheering proof, but you can just as easily lie about the area of the deformed shapes and most people wont notice. so i wouldnt recommend it