Visual Pythagorean Theorem Proof

Visual Pythagorean Theorem Proof - some basic geometry required

[thetruthfulchannel]

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

[vanonm]

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

[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.

[parahjapheth]

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

[sunnyjoseph]

This is a short and meaningful lecture ! Thanks sir.

[Arikgil]

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

[seb_fair]

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

[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.

[sovietmain]

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

[TRINIA]

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

[Dalton]

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 

[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 :)

[Romis]

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

[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.

[Daski]

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

[abdoabdo]

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

[MrPraise]

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

[clintNow]

Excellent mathematical and visual proof, thanks!!!!

[euclid]

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

[Dannyisgreatful]

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