Another Pythagorean theorem proof | Right triangles and trigonometry | Geometry | Khan Academy

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Visually proving the Pythagorean Theorem
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Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.
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[@mitchellele]

Your videos sooth me when I am stressed

[@addeleven]

Wow. Nice to see there are still things like proofs of the Pythagorean Theorem that can blow my mind.

[@natetibebu6150]

6:24 "well you see" *pun unintended

[@strangecookie111]

Who invented this proof - I am doing a project, and need the name please :)

[@imsamiha]

check out the proof using the properties of similar triangles. that one doesn't use area

[@fmakofmako]

Given that there are at least 300 distinct proofs of the pythagorean theorem you might be at this for a while.

[@SirTrollsAlot1000]

Very interesting video great stuff can you do some math videos on differential equations please it would help out a lot!!!

[@PoweredMinecart]

"Cleaning up geometric constructions!" FEATURING: Sal Khan. ;)

[@JJMMKK1997]

I suppose it would be either really difficult or impossible to skip delving into the area of the triangle(s) because the Pythagorean theory, in nature, deals with the squares of the side lengths.

[@addeleven]

Ah, I meant it was nice that there are "still" mathematical things that can blow my mind. Even if those things are related to relatively uncomplicated maths, like the Pythagorean Theorem. :)

[@MrDoraemon2100]

I believe there is some.
As I can, we can prove this formula using vectorial scalar product with jumping to the next dimension as you wanted.

[@WilbertKiemeneij]

It's only called a theorem once it's been proven. If it wasn't it would have probably been called the pythagorean conjecture, or the pythagorean hypothesis.

[@seyiojewale7907]

This mindblew my mind, Jesus Sal

[@ad2181]

All these proofs of the relationship of length of the sides of a triangle involve going the next dimension (the Area) to prove the lower dimension (the length) relationship. Why is this so? Can you show a proof of the relationship without going to Area argument? Is there a proof?
I

[@kailashrai]

keep the faith Sal, we are still working towards your goal. Just give us some time!!!

[@kailashrai]

Or pluripotent stems cells and regenerative medicine... What's your long term view?

[@user-lb2yn6pq3p]

anyone know the name of this proof? plz comment

[@kailashrai]

In fact, maybe for your own interest you should do a study on SYMBIOSIS?

[@slipperyjack007]

(grahams number)th

[@changjin1229]

wow

[@samus1225]

what trickery is this?

[@GuerrJohnn]

Second

[@MrSanZo]

clap clap clap O_O