Root Two is Irrational Visually

In this short, we use a similar triangle argument to prove that the square root of two is irrational by infinite descent.

#irrationalnumbers #realnumbers​ #manim​ #math​ #mtbos​ ​ #animation​ #theorem​​ #visualproof​ #proof​ #iteachmath #mathematics #irrational #carpetstheorem #proofbycontradiction #root2 #algebra #infinitedescent

To learn more about animating with manim, check out:

[ethanyap]

Good proof, but a little fast for a short

[joesmith]

My brain =error- malfunctions does not compute. Error..

[fahrenheit]

The geometry was a little fast, but I trusted you on it. The argument's lovely - I love infinite descent arguments.

[aclearlight]

Your skill with these visual proofs is extraordinary. I hope they gain you some serious recognition and a great job in math education if you wish it. Academic pay is a bit thin, but the work can be very rewarding!

[wyboo]

this is a very nice proof! ive always only been shown the algebraic proof where we show that we cant create a fraction in reduced form, so this is a nice change of proof

[TheMarineIguanaStudios]

*Cubert* : That's impossible. You can't have an infinite descent of positive integers!
*Farnsworth* : Of course not. That's why mathematicians increased the number of positive integers between zero and one in 2208.

[jhgvvetyjj]

Visual proof that circle cannot be represented with only quadratic bezier curves

[philb]

I'm going to watch that again *really slowly.*

[Shreyas_Jaiswal]

I like how all the proofs are contradiction-based.

[anhaihanane]

You should really do a video about how you came up with those idea when it comes to visualising you are

[Player_is_I]

But tan45 = 1
Which means perpendicular = base
Let perpendicular and base be b
And hypotenuse be a
Another isosceles right angled triangle 📐
where b² + b² = a²

[MichaelRothwell]

Nice! Fermat's method of infinite descent.

[MidnightStorm]

Wowow never knew you could do it visually thats pretty cool

[edwardblair]

I am missing what steps you use to prove how the second triangle is also an issocolese(sp?) triangle. All he says is "using the consyruction shown" but I don't see how the construction shown proves the assertion.

[PerfectArmonic]

In the end, when you claim that process can be repeated indefinitely is a little bit forced. In math there is a positive acceptance for breaking paradoxes regarding the recurrent processes (or fractalic). The proof is not consistent because we observe that (2a -b)^2 = 2(a-b)^2 => 2a -b = k*a and a-b =k* b meaning that a = k (a-b) and b = (a-b)/k. Therefore sqr(2) = a/b = k(a-b)/((a-b)/k) = k*k. Where k = c/d, c and d belonging to natural numbers. Therefore sqrt(2) = a/b = c*c/d*d But if we accept that sqrt(2) is a rational number then sqrt(a) and sqrt(b) are rationals as well. Meaning that c*c/d*d is rational. Is a circular reasoning which simply is equivalent with “a=b because b=a and b=a because a=b”, unfortunately unaccepted as proof.

[mowestsacc]

@mathsvisualproof what is the background music in the first half of the video? Raymar football also uses it and I would love to find out what piece it is.

[spectralanalysis]

It was a great proof, but yeah I do think you can condense the information. Maybe instead of showing the circular arc stuff, you could show the fractal like descent and focus on the conclusion of the proof? It might take away from some of the magic, but it gives the general idea? It felt like you were speed running a formal proof when maybe some details could be excised

[abdulrazik]

Maths is my lovely subject and you make it more interesting for me.. thankyou so much sir❤❤ though I didn't understand this one hope you wil make it more easy for us.. keep going sir.😊 Love from India.❤❤❤

[steveclark]

Smells a little like 1.4142 with a hint of the Golden ratio lingering 😮

[KT_]

a and b with b and a gives a-b and b+a and this is that, that means that is this.
Therefore root 2 in irrational 🙂🙂🙂