Legendary test question - π is less than 22/7

Happy #PiDay! When two of the hardest tests in the world cover the same problem, you know it's a big deal.

References
Wikipedia article
Putnam exam 1968 A1
JEE Advanced 2010 Paper Solutions Part-1 | IIT-JEE | Strategy, Tips, & Tricks | Paper Discussion (see around 55:30)
Proving 22/7 is greater than PI using Definite Integrals.
Why is pi less than 22/7? - Week 14 - Lecture 9 - Mooculus
2010 IIT-JEE Advanced paper 1 question 41 direct link

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Press

[PepsoP]

"Pause the video if you'd like to give this problem a try..."
No thanks, I am good.

[georgecarr]

The crazy thing is I literally knew all the math to solve the problem, but I don't think I would have come away with a correct answer had I attempted it myself.

[tyler]

This turned out to be a lot more do-able than I thought it would be.

Kind of bummed I elected not to try it on my own.

[chozen]

Me, an intellectual:
22/7=3.142857143 or 3.143
pi=3.141592654 or 3.142
therefore; pi<22/7

[_nines]

I love how they managed to hide the derivative of arctan in that mess

[iamvivektron]

Well, think about the person who came up with the idea to draft such a beautiful problem.

[lukeb]

Me, an engineer: "Nice, so I can use 22/7 instead of Pi"

[DeltaCommander]

I feel like an epic bait and switch has taken place here. 🧐

Thumbnail: “Test question: pi < 22/7”
Me: “Oooh, oooh, I know that one!!” *clicks video*
Video: “Solve for the integral of this 8-term polynomial division and use it to prove pi < 22/7”
Me: “WAT”

[usmle]

It's always interesting how very complex problems are resolved with them being broken down to simple math.

[LesleLeBang]

-Take the first three odd integers: 1, 3, 5
-Double them thusly: 113355
-Divide the last three by the first three thusly: 355/113
There ya go, Pi accurate to 6 decimal places!

[dhrubasarkar]

In Putnam, you are given 18 minutes to solve this question, while in JEE advanced, you are given 3 minutes.

[andrewmalesiadas]

Maths in school : 2+2=4
Maths in college : look! there's a number in here!

[Skeepers]

Me who hasn’t done math since Grade 10:
YouTube: Ah yes this will be perfect

[themliciousne]

“Give this problem a tr—“

“I’m gonna stop you right there”

[SenseiCoops]

I'm four minutes in and still trying to figure out why I'm watching something that makes me feel about as intelligent as a potato.

[arai_music]

If you didn't even think about pressing pause from 0:36 to 0:57 you know what silent shame feels like

[parasdahia]

"And that's the Answer", i like his tone than the actual answer..

[hitwalkhook]

Me knowing that pi is 3.1416
*"My time has come!"*

[pwmiles]

Brilliant! I confess, I just did the substitution x=tan(u) and bashed it out the hard way using integrals of tan(u)^n, n=4 to 8 which conveniently MATLAB knows. This is far more elegant, one for the locker

[MMLauritsen]

Honestly quite straightforward if you can do polynomial division. Everything falls nicely into place without the need of any creative solutions.