Why does the Pythagorean Theorem Work?

Some exploration of the Pythagorean Theorem and why it works.

[@mind-blowingmath6370]

I was a bit disappointed at first when I saw it's about Pythagorean Theorem, but it's the best SoME1 entry I've seen so far: simple, but no hand-waving, just actual math with actual proofs.

[@BanCommies_Fascists]

Best explanation ever.

[@beaumaths]

One of my favourite things in math is seeing how abstract ideas can be represented as transformations (in a loose sense)! Loved what you did with this video by using the stretching transformation of multiplication to help prove/illustrate the theorem!

[@PictooMath]

Don't forget that this theorem only works on the euclidean geometry.

[@smoother4740]

This is genius! Being able to see a^2 + b^2 = c^2 with actual lines instead of squares is so satisfying, i’ve tried it myself but never figured it out. Thanks for making this video!

[@TypoKnig]

Nicely done! I hadn’t thought about the Pythagorean Theorem this way.

[@pascalbercker7487]

This is very good. But two things, after having watched hundreds of hours of math and science videos, I've noticed that just a tiny bit of additional audio production really helps: 1) add a tiny bit of background music at very low volume, so that there's never any silence in between your pauses; some sort of background but unobtrusive music; 2) maybe a better mic? There's a slight echo - and feels like you are in the bathroom talking. But the visuals are simply superb! Consider me subscribed!

[@mellan2223]

Love the vid souds like a good explanation but i will come back when im fully awake

[@elyades2480]

Nice video ! I would really like a deeper explanation as to why stretching corresponds to a multiplication. Other than that, I loved it !

[@badrunnaimal-faraby309]

For the first stretch, the scaling is actually arbitrary. The second has an additional requirement: preserving angles, (so you get a nice straight line) which requires preserving ratios, which is what multiplicative scaling does.

[@user-fl5nv7oh3z]

Can you to make a video, where those Pythagorean triples are just vectors in a 3-d space over the integers?

[@themathsdude763]

hi dude, some feedback on the fly why would stretching be a multiplication after you proposed that the relation could be logarithmic or "zetaic" haha this looked very similar to another mindblowing proof of ptolemy's theorem which implies pythagorean theorem featured on numberphile one year ago : kzbin.info/www/bejne/mHuypq2nqpiAi7M great video !

[@thehungarywaffleinc.7775]

“Somehow the universe has given us…….” 😉

[@BuleriaChk]

Godel expresses wff's in odd numbers every number is prime relative to its own base n = n(n/n)=n(1_n) (primes do not include division by other numbers) Goldbach's Conjecture "every even number is the sum of two primes" n + n = 2n Godel's expression does not include even numbers in his defintion of wff's - they are therefore "undecidable" (o + e) = o is always odd so is undecidable because of the existence of even numbers (e+e) = e (o and e are sets of numbers). Proof of Fermat"s Theorem for Village Idiots c = a + b c^n = [a^n + b^n] + f(a,b,n) (Binomial Expansion) c^n = a^n + b^n iff f(a,b,n) = 0 f(a,b,n) 0 c^n a^n + b^n QED works also for n = 2. Someone go tell the physicists (Especially Einstein and Pauli) and also for multinomials (tell the cosmetologists..) Pythagorean theorem fails because it doesn't include the areas in the four quadrants of the circle 2ab = 4(1/2(ab)) one only can generate c^2 = a^2 + b^2 by using complex numbers: c = a + ib Note that: c = a + b = 3 + 4 c^2 = 7^2 = 49 = [25] + [24] 25 = 5^2 (Hint: Wylie had to use modular functions, which are only defined on the positive half of the complex plane.) there are no negative numbers: -c= a-b, b>a iff b-c=a, a >0, a-a = 0, a=a if there are no negative numbers, there are no square roots of negative numbers. The ""complex" plane is affine to the real plane (1^2 1, sqr(1^2) = 1 2qr(1) (Russsell's Paradox; a number can't both multiply and not multiply itself). more on this on the physicsdiscussionforum (dot org)

[@rajatdogra96]

It works on complex number also ?

[@davidbrisbane7206]

Not really ... i² + 1² = 0, where i = √(-1).

[@davidbrisbane7206]

i² + 1² = 0, where i = √(-1).

[@pandabearguy1]

Because it was invented by birds

[@josefernandomanzoli8159]

That’s not the answer, that’s a demonstration