You can start with rotating the triangle three times, or you can construct the outer square to start and divide its length in the ratio A/B, following which it's easy to prove that the triangles thereby constructed are congruent and the internal figure is also a square. Algebra follows.
@runawaybg if a=b, it wouldn't be a 30 60 90 right triangle. That would be a perfect square on its own so the area would be 1 and the hypotenuse in this case would be the diagonal of the square :)
You can partly see this without the math you imagine rotating the center square inside the bigger one such that the inner square's vertexes are always on the perimeter of the outer square. When the vertexes are lined up, you have the same square. If you rotate it 45 degrees, you have a diamond inside a square.Draw lines to opposite vertexes of this diamond, you create 8 equal right triangles, 4 of them in the diamond, and 4 in the outer square. Wonder how you could "see" the points in between.
I did like this: Area of small sq.=c^2 Area of large sq.=(a+b)^2 Area of the triangles=4*1/2ab=2ab Area of large sq.=a^2+2ab+b^2=c^2+2ab do some algebra and subtract 2ab from both sides to get a^2+b^2=c^2
+Dalton G i know you said this a long time ago, but how did you get a^2+2ab+b^2? since (a+b)^2 or a^2 +b^2 is the area of the large square, why would you add 2ab?
so if C squared is the area, and usually the area of a square is A times B, would you be able to get it by multiplying too instead of A square times B square
jesus goddamn christ thank you for this video i swear to god if someone would just say hey flip that triangle around and make a square out of side c i woulda fuckin got it instantly. Instead most other videos use shitty animation techniques while playing chopin in the background and smash the ideas together without explanation. Thank you khan....
@07alanhahn we only have a handful of mathematicians that theorize new concepts, but we have a SH!@$!$T Load of Scientists and Engineers who utilize math as a tool for their research! I believe those who create new math are literally at the top of the hierarchy of science for they are creating the foundations of almost all disciplinary foundations!
@07alanhahn another thing I'd like to add is that.....I've yet to see a Mathematician that was even half decent as far as looks go, there are sexy scientists and engineers, but.....mathematicians? almost all of them look like aliens from outer-space!!! I suspect their knowledge is Literally otherworldly!
@07alanhahn uh......do you realize how far and few between mathematical fundamentals enter our realm of human knowledge? only a handfew of people can come up with new foundations of math every so many decades or even centuries! And the chances of them constantly coming up with novel concepts is RARE, Most are only noted for making one or two mathematical discoveries on their own.
![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](http://i.ytimg.com/vi/p6j2nZKwf20/mqdefault.jpg)
Why aren't kids taught this in school instead of just being asked to memorize the formula?
We were taught this.
Because they haven't yet learn factorizing.
The Truthful Channel
That might be taught after learning some basic arithmetic, what factorization, simplifying and area means.
Because nobody has time for this.
Teach children this in school please
You can start with rotating the triangle three times, or you can construct the outer square to start and divide its length in the ratio A/B, following which it's easy to prove that the triangles thereby constructed are congruent and the internal figure is also a square. Algebra follows.
This is a really good proof. Thanks making this video!
8:23 area of d inside CIRCLE?!
lol
i just realized that
This is lovely in to me in 2021😁. Just what i needed. Thank you.
This is a short and meaningful lecture ! Thanks sir.
Thanks this helped a lot, now I perfectly understand the Pythagorean
its amazing when someone shows you how they arrived to that formula.
If I were you I’d study English.
@EdgeRetro It's also interesting to point out that when the inner square is a diamond (ie x=y) it's area is at a minimum.
@runawaybg if a=b, it wouldn't be a 30 60 90 right triangle. That would be a perfect square on its own so the area would be 1 and the hypotenuse in this case would be the diagonal of the square :)
Woah, everything adds up😪👍🏻
All thanks to you sir , I just passed an Exam because of you!
ALL HAIL MR. KHAN! You are awesome!
you help so much! Thanks
OH MY GOSH THANK YOU SO DAMN MUCH
The best lecture I ever watched
i could now rest wouldn't i have the need to desperately study for my physics test exam. This still gave me plenty of peace of mind
all hail mr khan
I would love to see you do a video on the "windmill proof" of the pythagorean theorem
Nice! They should really teach this in school. They make it sound like witchcraft but it is really simple.
You can partly see this without the math you imagine rotating the center square inside the bigger one such that the inner square's vertexes are always on the perimeter of the outer square. When the vertexes are lined up, you have the same square. If you rotate it 45 degrees, you have a diamond inside a square.Draw lines to opposite vertexes of this diamond, you create 8 equal right triangles, 4 of them in the diamond, and 4 in the outer square. Wonder how you could "see" the points in between.
Magically easy proof. Thanks!
aaaah.>>>now i can solve those problems understanding what i'm doing
I did like this:
Area of small sq.=c^2
Area of large sq.=(a+b)^2
Area of the triangles=4*1/2ab=2ab
Area of large sq.=a^2+2ab+b^2=c^2+2ab
do some algebra and subtract 2ab from both sides to get a^2+b^2=c^2
+Dalton G i know you said this a long time ago, but how did you get a^2+2ab+b^2? since (a+b)^2 or a^2 +b^2 is the area of the large square, why would you add 2ab?
KreamDonut (a+b)^2=(a+b)(a+b)
FOIL (a+b)(a+b)=a^2+ab+ab+b^2
a^2+ab+ab+b^2=a^2+2ab+b^2
Dalton G i already searched it up, thanks though :)
+Dalton G Thanks a LOT for clearing that up. I was actually confused about that, too.
Hmm.. what connection does this imply between the binomial theorem and geometry..
so if C squared is the area, and usually the area of a square is A times B, would you be able to get it by multiplying too instead of A square times B square
Excellent mathematical and visual proof, thanks!!!!
That was really good. Thanks for really explaining the details.
8:24 i'm pretty sure thats a square not a circle
Ingenious! :)
Thank you so much for this *-*
Very nice approach
thats how the late of phytagoras come out the theory.....thnks this is so helpful....
jesus goddamn christ thank you for this video i swear to god if someone would just say hey flip that triangle around and make a square out of side c i woulda fuckin got it instantly. Instead most other videos use shitty animation techniques while playing chopin in the background and smash the ideas together without explanation. Thank you khan....
Don't get it, why is it 4*(1/2*AB)?
Is this proof from "Wisdom of the west" from Bertrand Russell ?
Excellent explanation
@kapztheman i read that book too and saw the documentary on BBC
This is the gao-gou theorem rite? It's in the 9 chapters of the mathematical art.
8:25 "inside circle" lol
mindblown.
*diagonal of a square = length x radical 2
So in your case it'd be 1 x 1.41 whatever
brilliant! I love Math
Great job!
That was really cool
Thanks, It's really help :D
The beauty of mathematics.
i LOVE proofs
This just blew my mind :D
Honestly, my teacher taught me this and it never got in my head.
This seems very different...are there other methods of this!?
There are about 350 or maybe 360 other ways to proof the pythagorean thereom. :)
Either of you guys notice that spelt is not a word and that the past tense of "to spell" is "spelled" :P
@07alanhahn we only have a handful of mathematicians that theorize new concepts, but we have a SH!@$!$T Load of Scientists and Engineers who utilize math as a tool for their research! I believe those who create new math are literally at the top of the hierarchy of science for they are creating the foundations of almost all disciplinary foundations!
@07alanhahn another thing I'd like to add is that.....I've yet to see a Mathematician that was even half decent as far as looks go, there are sexy scientists and engineers, but.....mathematicians? almost all of them look like aliens from outer-space!!! I suspect their knowledge is Literally otherworldly!
Jump to 6:00
I can't believe how little this video is liked
Thanks :D
cool, thanks man
Who dont know geometry don't come in Academy - Platon
thaaaaaks brooo...... ^.^
@07alanhahn uh......do you realize how far and few between mathematical fundamentals enter our realm of human knowledge? only a handfew of people can come up with new foundations of math every so many decades or even centuries! And the chances of them constantly coming up with novel concepts is RARE, Most are only noted for making one or two mathematical discoveries on their own.
FUN. :)
I just watched this because it’s cool hehe
In the beginning, you spelt "beginning" rong.
Well you spelt wrong wrong
I'm glad you got my joke. XD
i have their app
they dont teach this stuff in school
+ana xuzmiashvili Aye thats what im doing rn CX
Please do a face reveal 😖
1 person is really wierd :P What is there to dislike???
it was first proven by babylonians in 3000 B.C
Yeah, and you spelt "wrong" wrong. :)
In the beggening, you spelt hypotnuse wrong ^^'
I hate it because i can't say it! xD
l
Hahahhahahahaaha xD
Hypotenuse? no H. but this is math not English. who cares.
Not sure if joking, or stupid.
Not sure if you took English or decided to skip it