Visual Pythagorean Theorem Proof

[@thetruthfulchannel6348]

Why aren't kids taught this in school instead of just being asked to memorize the formula?

[@floridmonkey2723]

We were taught this.

[@canman5060]

Because they haven't yet learn factorizing.

[@allenli4513]

The Truthful Channel

[@HDitzzDH]

That might be taught after learning some basic arithmetic, what factorization, simplifying and area means.

[@kittymeowski]

Because nobody has time for this.

[@Ensign_Cthulhu]

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.

[@JesseMaurais]

@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.

[@Dannyisgreatful]

@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 :)

[@parahjapheth7920]

This is lovely in to me in 2021😁. Just what i needed. Thank you.

[@injusticeanywherethreatens4810]

Teach children this in school please

[@Arikg94il]

This is a really good proof. Thanks making this video!

[@kessosow1757]

you help so much! Thanks

[@sunnyjoseph558]

This is a short and meaningful lecture ! Thanks sir.

[@Dalton1294]

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

[@GlaceGamingYT]

+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?

[@Dalton1294]

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

[@GlaceGamingYT]

Dalton G i already searched it up, thanks though :)

[@michaeljordan9484]

+Dalton G Thanks a LOT for clearing that up. I was actually confused about that, too.

[@arunlakshmanan211]

Woah, everything adds up😪👍🏻

[@EdgeRetro]

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.

[@Romis008]

I would love to see you do a video on the "windmill proof" of the pythagorean theorem

[@seb_fair8531]

Thanks this helped a lot, now I perfectly understand the Pythagorean

[@zdog46]

OH MY GOSH THANK YOU SO DAMN MUCH

[@MadhavanRSI]

8:23 area of d inside CIRCLE?!

[@uy-ge3dm]

lol

[@Ian_randomwordsforthehandle]

i just realized that

[@vanonm1]

its amazing when someone shows you how they arrived to that formula.

[@jockellis]

If I were you I’d study English.

[@michaeljordan9484]

ALL HAIL MR. KHAN! You are awesome!

[@abhishekarvind]

Magically easy proof. Thanks!

[@kinraade]

@kapztheman i read that book too and saw the documentary on BBC

[@spyler1565]

The best lecture I ever watched

[@clint4Now]

Excellent mathematical and visual proof, thanks!!!!

[@sovietmain8256]

All thanks to you sir , I just passed an Exam because of you!

[@euclid9492]

That was really good. Thanks for really explaining the details.

[@Daski69]

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

[@Vanimamidi7582]

Very nice approach

[@fantellerhur]

Thank you so much for this *-*

[@catastrophis]

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....

[@Dannyisgreatful]

*diagonal of a square = length x radical 2 So in your case it'd be 1 x 1.41 whatever

[@eeelgaaatttoooo]

8:24 i'm pretty sure thats a square not a circle

[@alpajoshi7926]

Excellent explanation

[@5abdoabdo]

aaaah.>>>now i can solve those problems understanding what i'm doing

[@MrPraise88]

thats how the late of phytagoras come out the theory.....thnks this is so helpful....

[@MyMindTank]

Ingenious! :)

[@Ian_randomwordsforthehandle]

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

[@TRINI123A]

Nice! They should really teach this in school. They make it sound like witchcraft but it is really simple.

[@michaellewis7861]

Hmm.. what connection does this imply between the binomial theorem and geometry..

[@mikeleatbg]

Is this proof from "Wisdom of the west" from Bertrand Russell ?

[@boxerek123]

mindblown.

[@stephenjones6472]

Great job!

[@the_actual_lauren]

8:25 "inside circle" lol

[@valeriegosselin4580]

Either of you guys notice that spelt is not a word and that the past tense of "to spell" is "spelled" :P

[@viktor1098]

Jump to 6:00

[@thineshasutharsan9454]

This is the gao-gou theorem rite? It's in the 9 chapters of the mathematical art.

[@gbonfil]

brilliant! I love Math

[@starwarfan8342]

That was really cool

[@nguyentony6872]

Thanks, It's really help :D

[@EasternMerchant]

@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!

[@zyfos8402]

This just blew my mind :D

[@NXTstorms]

The beauty of mathematics.

[@EasternMerchant]

@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!

[@PartVIII]

i LOVE proofs

[@159FlatroN]

Don't get it, why is it 4*(1/2*AB)?

[@missswiss6498]

Honestly, my teacher taught me this and it never got in my head. This seems very different...are there other methods of this!?

[@jubjubj7311]

There are about 350 or maybe 360 other ways to proof the pythagorean thereom. :)

[@mikeleatbg]

Who dont know geometry don't come in Academy - Platon

[@Funney14096]

Thanks :D

[@EasternMerchant]

@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.

[@TheJohnnyFJ]

cool, thanks man

[@graysonjenkins6977]

I can't believe how little this video is liked

[@5abdoabdo]

thaaaaaks brooo...... ^.^

[@stereotypeyou]

In the beginning, you spelt "beginning" rong.

[@junguo1782]

Well you spelt wrong wrong

[@starithm]

FUN. :)

[@grndragon7777777]

i have their app

[@cobble2851]

I just watched this because it’s cool hehe

[@stereotypeyou]

I'm glad you got my joke. XD

[@Mihirskates]

they dont teach this stuff in school

[@MountinChicken]

+ana xuzmiashvili Aye thats what im doing rn CX

[@steel55able]

1 person is really wierd :P What is there to dislike???

[@athenarose533]

Please do a face reveal 😖

[@steel55able]

Yeah, and you spelt "wrong" wrong. :)

[@al4381]

it was first proven by babylonians in 3000 B.C

[@Niggaawatupp]

I hate it because i can't say it! xD

[@steel55able]

In the beggening, you spelt hypotnuse wrong ^^'

[@steel55able]

Hahahhahahahaaha xD

[@jaad590]

l

[@grassywaters]

Hypotenuse? no H. but this is math not English. who cares.

[@Qbabxtra]

Not sure if joking, or stupid.

[@kyraleia8090]

Not sure if you took English or decided to skip it