22/7 vs pi #shorts

22/7 or pi, which one is bigger and why? Watch this video to find out!

[seanshameless]

Man pulls out an integral to prove a point

[fahad-xi-a]

I could do shorter
22/7 = 3.142....
π =
22/7 > π
Q.E.D


Note: This comment is intended for humourous purposes only. It does not intend to hurt any emotions of mathematicians.

[kingbeauregard]

Personally I favor 355/113. Not only is it a freakishly good approximation for pi, it's easy to remember as "11 33 55".

[Chester]

Dr Peyam in "how to compare two numbers the easy way" :-D

[Sky-pgxy]

It turns out they’re equal and pi has been rational all along.

[DrWeselcouch]

I once approximated pi to be 3.28 which is definitely bigger than 22/7. I guess you just proved that my approximation was bad...

[bulldawg]

Yes, we need a video on the derivation of the mystery integral ...

[designtechdk]

Since pi=3 then it follows that 22/7 > pi.... just kidding

[insouciantFox]

I think that's similar to how Ramanujan would do it in conservation.

Guy: Hey Srinivasa, which is bigger, pi or 22/7?
Ramanujan: Oh it's quite trivial really. *integral*
Guy: oh. Ok.

[Kdd]

I like these type of shorts un which u speak instead of the music coz u speak fast in the shorts and it sounds like a rap

[davidbrisbane]

Notice that 1/(1 + 0^2) >= 1/(1 + x^2) >= 1/(1 + 1^2) for x between 0 and 1.
So, _integral x^4(1-x)^4/1_ from x = 0 to x = 1 > _integral x^4(1-x)^4/(1 +x^2)_ from x = 0 to x = 1 > _ integral x^4(1-x)^4/1_ from x = 0 to x = 1
So, 1/630 > 22/7 - pi > 1/1260
So, -1/1260 > pi - 22/7 > -1/630 (by multiplying everything by -1).
So 22/7 - 1/1260 > pi > 22/7 - 1/630 (by adding 22/7 everywhere).
So, 3.1421 > pi > 3.1412.

[reussunased]

Engineers be like : I see no difference

[JSSTyger]

Now, children...how to prove that 2 is greater than 1. The integral of inverse tangent from....

[martinpareegol]

the only problem of that demostration is imagine that specific integral that helps you to figure it out the answer. Nice video!

[davidbrisbane]

0 < integral from x= 0 to 1 = 355/113 - pi, So 355/133 > pi and 355/133 is closer to pi than 22/7 is :-).

In fact, if you replace 3164(1+x^2) with 3164(1+0^2) and again by 3164(1+1^2) and integrate between x= 0 to 1 and compare these results to the integral above, then we find that 3.14159274 > pi > 3.14159257. Note: pi = 3.141593 ( 6 decimal places).

[moekacchi]

there's an anime called "22/7" which has some math in it if you dive deeper into it.

[charlottedarroch]

This approach can be readily generalised. Integrating over the same range the function f(n) = 2^(-2n+2) x^(4n)(1-x)^(4n)/(1+x^2) gives inequalities of pi with approximants to pi, with the approximants alternating on either side of pi for successive integer values of n. Similarly, integrating g(n) = 2^(-2n) x^(4n+2)(1-x)^(4n+2)/(1+x^2) gives inequalities of ln(2) and ln(2) approximants, again alternating either side of ln(2).

[Nightmare-olze]

Please show this :, for 0<a<b<pi/2

[eavlongsok]

You solved this without actually solving this

[thedr]

I was trying to find 22/7 anime.... instead i got educated....nice