The (Nearly) Perfect Pi Approximation
ฝัง
- เผยแพร่เมื่อ 13 ม.ค. 2022
- We can't write out every digit of Pi every time we use it, but we've got to represent it somehow. And you were probably taught that 22/7 was a great option. Well... it's an okay option. It's not bad, but it's not amazing.
355/113 is so close to the real value of Pi that you don't encounter a better approximation until you hit 52163/16604. #shorts
Why do I feel like this whole short is an excuse to say "this is a great slice of pi"
Nice pun u got there
I guess he's a genius for making puns, not for explaining about pi hahaha
Because it is
I wouldn't mind at all.
Wow, I’m surprised to randomly come across someone with a Yuuri profile pic. Kudos to you, fellow GLT enjoyer
Engineers watching be like: Isn’t pi supposed to be 3?
Its close enough for many calculations.
Let π be equal to 5...
Well in Actual Practice, Engineers use 355/113 as the approximation of π in most Cases
Dam I didn’t get the memo. We done shitting on the medical profession now we onto the engineers thanks for the heads up
3 Point something.
π/1 : I'm 4 parallel universes ahead of you.
he said using 3 digit numbers
@@user-hd2xe1ds1n 100pi/100
@@bloopletank2491 thats 4 digits. 100 is 3, putting a π is 4
@@drenz1523 pi isnt a digit
@@bloopletank2491 what if it is
My calc teacher just said, "leave it as pi, if there is pi in the question there should be pi in the answer."
My engineering profs would have loved it, if I gave them volumetric flows through a pipe in: x*Pi m³/s
@@JainZar1that would make sense tho, if you need to use it irl most computer software will have a hardcoded value for pi that's more precise than what you're gonna ise
@@hil449really depends on your problem. Simulations or something like that, sure. If you told a machinist your cut needs to have a length of c*pi*ns tho, he isn't going to be able to make your part! That's why one of the most important disciplines in engineering is working out reasonable approximations and tolerances.
My math teacher does too.
When I was in school, we had some contest to see who could best estimate Pi by measuring circles. I decided to use a string and chalk to draw the biggest circle I could, and it just so happened that the diameter of that circle rounded out to around 113 cm. Needless to say, I won the competition.
Needles.
@@Nulono you got a point! 😂
And there is me who wouldnt be avle to participate because I know 30 digits by memory
@@paulvorderegger1522 doesn't matter how many digits you know if they asked you for a fraction
@@afkaralp What if you just say (all the digits you know) × 10^(how many digits you know) over 10^(how many digits you know)
So like 3141592653589793238462643383279502884197169399375105820974944592307816/1000000000000000000000000000000000000000000000000000000000000000000000
And it's easy to remember. From bottom to top it would be 113355.
Exactly, your trick is brilliant.
I don't think now I will ever forget the fraction
You'll end up writing 553/311
@@hittingyouoverthehead he means bottom to top AND left to right
@@keyboardegg931 I understood that. I'm just saying there's potential to confuse yourself and it's easy to misremember it and hence go wrong.
Did anybody notice 52163/16604 fading in just before the end of the video? That's an even better slice of pie!
oh
my
god
Look
at
As a STEMs geek, I love a good math joke, but y=mx+b is where I draw the line.
I get it, that’s the slope formula, used in I think like graphs. I like your thinking
line* not like
My god... That accursed equation....
Oh come on using slope intercept as a line this were the joke is
@@crimsonplague1slope intercept is nice, probably, maybe, not really
tbh, I can’t think of a practical application of it (outside of plotting a slope exactly on the y axis)
I think some of you are missing the point. If you were to list every rational approximation of pi in its simplest form (3/1, 13/4, 16/5, etc.) 355/113 is significantly better than the one before it (333/106) and a lot smaller than the next biggest approximation that is better 52163/16604. (That's right there is no fraction better than 355/113 in the 4 digit range) If you were to graph the numerators of these fractions, there is a general trend, then a major anomaly at 355/113.
You are missing 7/2 and 10/3, btw.
If we list just the denominators of successive best approximations, we get 1, 2, 3, 4, 5, 6, 7, 57, 64, 71, 78, 85, 92, 99, 106, 113, 16604, 16717, 16830, .... Clearly 7 and 113 are outliers. Those are the most famous approximations of pi, 22/7 and 355/113. The next outlier is 104348/33215, though not as remarkable as 355/113. If you go further, 21053343141/6701487259 is excellent, with no better approximation with a denominator smaller than 286200632530. That's still not as exceptional as 355/113 though (in the sense that the ratio of denominators of successive best approximations is smaller). You would have to go past 10^18 before you found something similar.
@@EebstertheGreat 6/2 is closer than 7/2, and is equal to 3/1, so is not included . same thing with 10/3, 9/3 is closer, and is equal to 3/1 so is not included
FWIW, the continued fraction expansion of pi is [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, ...], so you can see the 15 and 292 stand out. These correspond to 22/7 and 355/113. The 20th convergent right before the 84 corresponds to the next best approximation above. The 433rd convergent, right before a 20776, must be spectacularly accurate.
Rather than missing the point, I would say that the point was never made in the video
@@EebstertheGreat as always, the real content is in the comments. Thanks for showing this!
He talks and writes so quickly, ill just believe him.
Writes with his left hand too
🤣🤣sure, why not
"Everyone talks about pi bu-"
"No Kevin, no they don't"
Depends on which pi(e)
In my circles they do, sounds like you need better friends
Kevin is right. You're wrong! You unbeliever! What's wrong with you why don't you "talks about Pi?" 😭😭 did you go thru childhood trauma? 😢. Talksing about Pi can heal you my friend.
@@nataliemulby7808 ?
@@eygii!
Imagine using 355/113 everytime you calculate an area of the circle.
Imagine not having a calculator with pi as an option. TI-84 laughing I’m superiority
@@stupid_name3169 imagine having maths
@@ryugafandom630 Imagine.
@@Luffy_wastakenI
@@ghost3d497 ㅤ
That's six digits to remember and more accurate than 3.14159, but if 3.14 is already in your head remembering an additional six digits brings you to 3.14159265 which just wins out and sounds just so much more impressive (or ridiculous depending on context.)
That does not sound impressive
I’ve memorised the first 1000 (;
@@Noba46688 wow the best i could do is like 85
@@zachary7996 you - and pretty much anyone else - could do it, too, if only you had a spare endless amount of spare time at home for a VERY long time. Also during recess and lunch breaks. If you really wanted to, you could, too, but one must take one’s time (it has taken me ~1.5 years of on-and-off practise: sometimes I don’t learn any new numbers for months; and other times I memorise 100 in 3-4 days ish). Also, I’d you want to learn more, I’d recommend groups of ten, stopping at 100 new ones each time. Anyway, thx for the praise ish, and have a good life (:
@@Noba46688 thanks for the advice! i really only got that far because my school was having a competition and the prize was an actual pie, but i think it would be fun to go higher if im bored someday. and np, you have a good life too!
You should have mentioned how 355/113 is just the first 3 odd numbers written twice and split up
11 33 55
113 355
355/113
Easy way to remember it
Yeh i also saw that pattern lol.
Thanks
Me a 8 IQ human
OMG it's Albert Einstein
OMG
@@anakinskywalker7915 me when you: 🤣🤣🤣🤣🤣🤣🤣🤣
@@No_king1143 me when you: 🤣 🤣 🤣 🤣 🤣 🤣 🤣 🤣
I’ve never been a huge fan of this guy for long-form, but his energy translates extremely well to short-form. I’d love to see more of these!
Where I thought it was going: *”Everyone always talks about what pi is, but they never talk about who pi is”*
Whassup
I 100% agree with you that it's a FAR better approximation, but it's not gonna happen because of two reasons:
1. because 355/113 is much harder to remember than 22/7 and
2. it's extremely rare to NEED that many digits of pi; most only need 3.14 for accurate results
Disagree, in industrial applications like 4th axis CNC milling, or dead reckonning in the guidance in planes and spaceships, you need way more than just hundredths in terms of precision.
@@chrismofer in those cases you wouldn't be using either of these approximations
@@JohnDCrafton Honestly in those cases you probably just have a floating point value saved somewhere as a constant and use that.
@@MrZoolook How many did you expect him to give? If he had 10 in mind, would he list out all 10? So just because he listed 2 just "proves" that those are the only 2? There are probably much more that he didn't list, but as already answered, most of them wouldn't use 355/113, either.
NASA uses 15, you need ~40 to be atomically accurate. You wouldn't use an estimation, you just use pi rounded to the digit you're using.
0:49 Because doing long-division to calculate 355/113 by hand is a lot more work than calculating 22/7 by hand, and gives more precision than people who _had_ to do long-division by hand usually needed (and a lot more work than just memorizing 10 or so digits). That's why.
didnt take me long to memorise 3.141592654
@@MrLembnau decimal are icky tho
@@LightPink decimal is the truth.
@@MrLembnau
Can use that decimal itself instead of some prime fractions
You had written the value of pi exactly till where I had remembered in my free time. Damn
“A great slice of pi!”
*Sir you only left a couple millionths of the pi left*
Cool video, although I would have thought that perhaps you could go into the continued fraction form of pi, since it generates things like 22/7 and 355/113, and is probably slightly more interesting than just noticing that 355/113 is considerably closer to pi.
The description mentions that "355/113 is so close to the real value of Pi that you don't encounter a better approximation until you hit 52163/16604" -- and that's the remarkable thing here about 355/113. You have to use 10 digits to do better, so it's an excellent approximation considering how small the numerator and denominator are.
@@Vsauce2 Yes, but you could also mention why, too, which is explained through the continued fraction. 355/113 is generated from [3; 7, 15, 1], the start of pi's continued fraction form (and 22/7 and 333/106 are too), but the next number in the continued fraction of pi is 292, which means that the next number that will be more accurate than 355/113 will be expressed by a very large fraction, like 52163/16604, which is arguably a more interesting piece of content that one could probably condense into 60 seconds, and it supports your main message in the video.
@@xnossisx5950 he could've done that, making the video too long to be a short tho
@@xnossisx5950 great information
Why approximate when you can just write pi as a fraction?
τ/2 = π
nah just write pi and you won't even need to find out how to write π on your keyboard
It looks so wrong because 2 taus next to each other resembles pi (ττ), but you need 2 pi to get tau...
@@everdale8920 yeah it should've said 2τ = π
@ just to suffer
genius
I once tried to rationalize pi and found 355/113 almost by accident
I literally just started learning this today and got so confused with the 22/7 thing. This is 10 times better. 👍
I've always figured the goal in school is not to calculate exact values, rather use the simplest approximation (but not too simple that it doesn't feel like it is "special" e.g. 3). Using 22/7 gives the school curriculum the opportunity to use multiples of 11 or 7 in practice problems to make calculations neat and simple. 113 on the other hand is a prime number so it can't have factors while its multiples will get too large (and often unnecessary given the goal is just to teach basic concepts)
You used fractional approximations of pi in schools?
Why?
@@martinhawes5647 because it's easy to plug into equations and get nice round numbers for answers. Accuracy was never a priority in school since a majority of students wouldn't go into a career that'd require them to deal with pi on a regular basis. Once people got into more specialised courses like engineering we stopped using fractional approximation.
@@martinhawes5647 because of ease of calculations
When did you go to school?
We just had a standard pi button on calculators for remembering the exact value
@@martinhawes5647 we didn't have calculators in school
Yes, that's nice. Just remember those 6 digits, divide those every time and you will have rough estimation of PI. I will stick with remembering 3,141592
I will stick with using the π button on my calculator
this person made pi 1000000x times bigger
I love your shorts…..and I’m not ashamed to compliment you on them.
Mathematicians be like: Isn't pi 180
No, pi is not the same thing as 180. pi radians is the same thing as 180 degrees, but pi is not 180 if units aren't specified or implied.
@@carultch we know dude. It's supposed to be a joke
We actually never really covered pi in much detail in high school before I had to choose a certain direction in math class and I chose the direction that didn't have stuff like pi in it. So the first time I'd ever heard of 22/7 was in a meme on the internet.
I am sort of ashamed, I'm not going to lie.
But isn't Pi approximated as 22/7 also used in Physics?
Or 3.14
@@anshumanagrawal346 I dropped physics.
@@Thoomas2001 Oh Ok
@@anshumanagrawal346 in physics you just use 3
Kevin! I love these short bite videos!
My brain stopped braining.
Nct always at the crime scene
The answer is simple: significant digits. Using a “more accurate” number for pi is meaningless if the number of decimal points exceeds any other numbers in your calculation.
More than that too. Uncertainty in measurement or calculation will eclipse the uncertainty from cutting off pi early.
It is not very useful to use SIX digits to approximate the first six decimal places, since you could just learn those digits and save yourself the hassle of having to divide every time
absolutely true!
Well I rather do math with a fraction than a decimal if I don’t have a calculator to hand.
@@olivers.7821 But then it‘s much easier with 22/7
@@olivers.7821 When do you find yourself calculating things involving pi without a calculator? But a pen and paper on hand? If it's an exam, they'll give you an approximation to work with.
@@itsnottimetostop4462 still it is basically useless to know pi by hearth since if you need it for some unknown reason the decimals just dont help at all. The fraction at least makes it easier to make math with it and if I need the decimal version I can just do the math and get enough digits after the comma through the fraction.
As a computer engineer I'll be using this to make the smoothest circles
This is a great slice of piE
Ok bye..
Lmao
An engineer and a physicist were working together on a free-fall mechanics problem. The engineer had messy handwriting, so the physicist commented, “your g looks kind of like a 9”. The engineer looked confused and asked, “what’s the difference?”
Good one
The first 10^314 digits of pi, multiplied by 10^314, and divided by 10^314, gives an approssimation of pi precise up to the 10^314th digit. Isn't math amazing?
Wow
Yeah but you need 10^314 digits in the numerator to actually write that down. For this you only need 3 digits in the numerator and it gives you 7 digits of accuracy.
It's something called the continued fraction expansion, it gives you the "best possible" approximation to any irrational number for a given size of denominator.
@@ericvilas I would say you missed the joke, but you are probably missing the joke as a joke and I am the one missing the joke, so now I don't know who missed who
@@giannipiccioni8411 oh lol I did miss the joke, I thought it was a sort of sarcastic reply to the video
@@IshanShah lmao u didn't get the joke?
I will never get that minute back…
Great content. Even better delivery 😊
22/7 is still slightly better than 3.14 though. Thus 22/7 should be Pi Day for non-US countries.
3.14 is closer to pi than 22/7.
Why all this fuss about pi when it's equal to 3?
like e
Its actually equal to square root of 10.
@@onradioactivewaves not even close
g = π^2
π = 3 = e
Because it isn't. If it were, we would've never assigned a name to it. No one ever assigned a letter to represent a square's ratio of perimeter to side length, because that's exactly 4.
I was eating some pie and this showed up
Dude your f-ing brilliant!
The waffle House has found it's new host
The Waffle House had found it‘s new host.
The Waffle House has found it’s new host
The Waffle House has found it's new host
no it hasn't
Folks, Waffle House don't have hosts. You just go in.
22/7 is the second covergent of the pi continued fraction expansion. 355/113 is the fourth and therefore better. The next is 103993/33102
Kevin got so much better since his beginnings with vsauce. Great job
missed opportunity to swipe everything with a towel and loop the video
When I was in nuclear power school my Math instructor was an aeronautical engineer and he made the jokes about Pi being "about 3." One day he asks a question and the correct answer is 18, but I can't explain *why* it's 18. Mind you, I was pretty terrible in this class. So naturally he calls on me, and I said, "I don't know... It's about six times pi." The class erupted in laughter and he did that drop his head, frown and sigh, head-bob thing and said, "OK, I get it... I'll stop calling on you" And I was happy.
It is now tasty...
What a knowledge
_”Everybody_ talks about pi…”
I must be hanging around with clones then.
Nice, you snuck in a slightly better approximation at the end
I know im not the only one that heard Micky in the beginning
I understood absolutely nothing of the video, yet I still enjoyed it, this guy atitude and passion just off the charts.
Mrs. Glubernutz was STILL way more accurate than my high school teacher.
Everyone talks about pi, but not pie
Earlier Mathematicians too approximated the 'Nearly' perfect Pi value😂
I like your funny words, magic man!
I ain't doing no middle school mensuration with 355/113💀
Sir listen!, My life is already pretty much disturbed because of maths and now you're give examples for pi. There's no need. I'm happy with 22/7
This dude never talked with an engineer...
all fun and games until you use this for a rocket trajectory and you accidentally land on the sun.
Friendship ends with 3. 355/113 is my new friend now
elementary schoolers bout to count 355/113 × 14 × 14 to find the area of a circle
Lol
meanwhile my physics teacher rounding the number of seconds in a year with π*10^7
This can be very handy in certain circumstances. For example, to calculate Earth's orbital velocity: Earth is 150 million km from the sun, so in a year, it travels a distance of 2π*(150 million km) = 3π*10^8 km. Since a year is π*10^7 seconds, it must be moving at about 30 km/s. The real answer (averaged, because the orbit isn't a perfect circle) is 29.78 km/s, so that's _very_ close.
Engineer:"Nah, its 5."
Curse you, Miss Glubbernuts
Good explanation
SOMEONE FINALLY DISCUSSED MY FAV FRACTION.
Don't forget 104348 ÷ 33215, it's a longer approximation of π which is 3.141592653.
I've been trying to memorize as much of pi as i can, im currently 20 digits in.
Mrs. Glovernuts is never wrong.
This is amazing
This man’s about to snap 😂
This guy is excited about pi.
ive been subbed for so long and never see your videos.
From counting 123 to this..
Man humanity has evolved...
Jokes on you I like solving my circles with headache and trauma with my 100 digits of pi memorized
Yo saw your community post, hope it works out!!
"hey you ate all the pie!"
"no, i left you a 10 millionth of it"
Mathematicians and Some Physicists: Wait... you guys are using a value for pi?
Let me answer that. Because 113 is a freaking prime number. Do you know the relief we felt in school when we got a multiple of 7 to be multiplied with pi. Now imagine if we had to do the math a denominator of 113
Best pun I heard in my day
I'm sure Mrs Glover, your maths teacher would be very proud of you 😂
And then there is me who memorise the whole asap sciense pie song.
astrophysics be like “isn’t pi 10?
Engineers be like: most I can do is 3
remebering six digits in a fraction to remember pi to six decimal places
"Mrs. Glubbernuts" 💀💀💀💀💀💀💀💀
Misses glubbernuts 💀
finally, the good stuff
No you didn't listen to her. She certainly told you it was an approximation. I still remember when my 5th grade teacher did the same to me decades ago.
Ramanujan: I am four parallel universes ahead of you
I'm going to abuse this on tests.
Broski gonna try to make pi rational
Engineers: yeah 3.15 will do
Super impressive writing left handed on a white board and didn't smudge anything
Great and not messed up at all board!
His teacher was called Mrs Gluvernuts 💀