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What do Euclid, 12-year-old Einstein, and American President James Garfield have in common? They all came up with elegant proofs for the famous Pythagorean theorem, one of the most fundamental rules of geometry and the basis for practical applications like constructing stable buildings and triangulating GPS coordinates. Betty Fei details these three famous proofs.

Lesson by Betty Fei, directed by Nick Hilditch.

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How many ways are there to prove the Pythagorean theorem? – Betty Fei

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## 37 comments

My proof:

Trust me I'm a mathematician

No one believes me but I discovered this theorem before ever being taught it in school. In 5th grade I was drawing doodles with right triangles and that’s when I found the proof by rearrangement, or in my opinion the easiest way to prove this theorem

《周髀算经》原名《周髀》，算经的十书之一，是中国最古老的天文学和数学著作，约成书于公元前1世纪，主要阐明当时的盖天说和四分历法。唐初规定它为国子监明算科的教材之一，故改名《周髀算经》。 1100 BC

4:42 amazing!

I liked the volume method

Please any onw help me, how to make this animation in mathematics

Wow!!!!!! I never knew that much!!!!!!!!!! BUT WAIT a second! Einstein came up with a proof of the pythagorem theorem at the age of 12????? WOW that is to show how smart he was.

JUST LIKE EINSTEIN ALWAYS SAID; "I am not intelligent I just stay with the problem longer than other people but imagination is more POWERFUL than knowledge. Saturday 27th November, 2021 20:27 pm

Neat. I love this theorem.

Thank you

yo thats cray-cary in a good way

you can prove it by the cosine rule a^2 = b^2 +c^2 -2bc*cos(A)

where a is the hypotenuse and b + c are short sides so (the corresponding angle to a) A=90 and cos(90)=0 so

a^2=b^2+c^2-2bc*cos(90)

a^2= b^2+c^2-2bc*0

a^2=b^2+c^2

Pythagoras stole credit for this theory

Why not chose peace

Indonesian subtitle😐?

Proof Is not Scientific demonstration.

^^

Ηere's my proof (I'm sure it has been found by others many times before, altough I am not sure by whom exactly). I found it accidentally:

For any right triangle, the trigonometric identity (sinθ)^2 + (cosθ)^2 = 1 holds true for any angle.

Let "a" and "b" be the adjacent sides and "c" the hypotenus. By expanding the definition of the trigonometric numbers in the identity we get:

(a/c)^2 + (b/c)^2 = 1 <=>

(a^2/c^2) + (b^2/c^2) = 1

Multiplying by c^2:

a^2 + b^2 = c^2 Q.E.D.

It's definetly not much. But I was super proud when I came across it.

Nice 👍👍

my teacher actually sent me this lol

I would like to understand why so many proofs. In any time, can someone come with some disproof of it?

3:38 I don’t understand

For me 2:15

Bro just use a ruler

because square for A is defined by change over X, and the square for B is defined by change over Y, C has as much change over X as A, and as much change over Y as B, that is why it holds half of the total.

With that many proofs we should just call it the Pythagorean fact

yes

Proof:

Let n=2,

Then it follows from the Fermat’s Last Theorem.

Qed

Aha but what was President Garfield's proof?

I'm coming here from the Godel video so excuse my reluctance to believe you.

i was curious about the proof of this theory but couldn't solve it although i was supposing myself clever. however the solution was really simple and i am ashamed now 🤕😔

2021 Oct 11

Uh just use trigonometry TBH lol y do soo much

Here is my proof in 50 sec.

https://youtu.be/q8ptdeAaViE

My Math teacher's proof :

" TRUST ME BRO"

Here's my proof: I shat, therefore I flushed

Why does Einstein look depressed in the video?

Congrats for 15 million subs without any gaming uploads it's awesome