Diophantus's Sum of Squares Identity I (visual proof)

[@oddlyspecificmath]

Dude. You just gave me something profoundly interesting. _Thank you._

[@MathVisualProofs]

Glad to hear it!

[@LittlePaimon]

非常好的视频！

[@cheeseburgermonkey7104]

Very elegant!

[@MathVisualProofs]

😀👍

[@HeckaS]

Beautiful

[@MathVisualProofs]

Thank you!

[@agytjax]

At 0:50, how do we know that the blue triangle is also right angled ? Do we have a proof ?

[@MathVisualProofs]

Yes. As stated the two triangles meet at complementary angles (those add to 90) so the angle between them is also 90 to get to the full 180 of a line. (The reason they meet at complementary angles is they are similar because they are scaled copies of one another)

[@pazzicuriosi6660]

Great!

[@MathVisualProofs]

Thank you!

[@innosanto]

Diophantus - father of Algebra

[@jakobthomsen1595]

Cool!

[@MathVisualProofs]

Thanks!

[@oddlyspecificmath]

Are there proofs that combine fractals to cover an area? ...Is that just reducible to your shorts proving infinite sums by recursively "fractionating(?)" polygons?

[@MathVisualProofs]

I'm not exactly sure what you mean, but perhaps it is similar to what you say?

[@oddlyspecificmath]

Well...interestingly enough, Steve Mould posted a video covering just this a few hours after I pondered it here. I haven't watched more than a minute or two, but it looks like what I'm asking...except of course that I was curious to see how you might Manim-ly approach such a proof. No worries :)

[@oker59]

how come you only take the square root of one side( the left side) and not the other side? Isn't hte algebraic rule "whatever you do on one side, you have to do to the other side?"

[@محمدالسباعي-ك1ب]

WoW

[@MathVisualProofs]

👍😀