Calculating π by hand

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Stand-up Maths

Stand-up Maths

Күн бұрын

For Pi Day 2016 I tried to calculate π by hand, using an infinite series. It goes ok.
Before you even start:
- Yes, I know π Day requites writing the date MM/DD. By objective measures: the wrong way. I don't care. My love of π is stronger.
- My opinion of Tau is a matter of public record: • Tau vs Pi Smackdown - ...
CORRECTIONS:
- At 17:23 it should be π/4 not 1/π. That was contamination from the next graphic. (First spotted by Najeeb Sheikh and Jake Trookman.)
Check out y-cruncher:
www.numberworld.org/y-cruncher...
Calculating pi by weighing a circle:
• Calculating pi by weig...
Calculating pi with a pendulum:
• Calculating pi with a ...
Music by Howard Carter
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
New book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/

Пікірлер: 3 100
@FourthDerivative
@FourthDerivative 8 жыл бұрын
This is what I thought mathematicians did for a living when I was a kid. Just adding and subtracting giant lists of numbers all day long.
@FlyingPiper13
@FlyingPiper13 8 жыл бұрын
+FourthDerivative Haha, yeah, I used to think math was something like that too. But it's a heck of a lot more beautiful than that, isn't it.
@remo4644
@remo4644 8 жыл бұрын
+FlyingPiper13 No, it's not
@nightangel7239
@nightangel7239 7 жыл бұрын
And he only passed by relying on the age-old method, "Just memorize the formulas and substitute, don't think".
@Kupkaik
@Kupkaik 7 жыл бұрын
Can't say I blame him. That's the method that's taught in school, and lets be honest, for the average person it isn't very enticing. I absolutely hated math in school! I never passed a test, infact I had to repeat algebra 3 times! It was stressful. It wasn't interesting, it wasn't fun, it wasn't intriguing. However, now that I've graduated from high school, I've seen the prettier side of math that, if I had learned and saw back then, would have been very interesting and more stimulating to learn! But now we're getting into psychology a bit, and for the average everyday person, if you're failing at things, you lose interest. I still do not like the way math is taught in school, because of what you said IS what happens. They don't show us interesting things! but now I'm just getting repetitive.
@nightangel7239
@nightangel7239 7 жыл бұрын
Ellie The Snow Fairy The issue is that the interesting things have a lot of math going into them, so teaching the interesting things off the bat will either be useless (You won't explain the math) or difficult (Hard math). Examples include all the popsci channels on youtube. How many channels are there, exactly, like VSauce? Numberphile? Honestly, even Standup Maths to a very small extent, where they teach you really cool ideas, and you get a sense of "Now I know more", but in the end you're still just as bad at math and science as before? It's easy to get people interested in black holes, rocketry, quantum physics, and to tell them things like "The sun is like a big nuclear reactor! And it's like nuclear bombs are going off in the center constantly! Computer chips are so small, electrons can jump from one circuit to another by chance because of quantum mechanics!", but at the end of the day they don't understand a thing of how it works. They can't even tell you how fast a ball will roll down a ramp, even if they memorized the analogy for the double-slit experiment. All that happens is they feel smart and then they comment "OMG, why doesn't anyone else like this stuff? Is it because I'm smarter than everyone around me?". Then they make idiots of themselves by taking analogies seriously. "If a human doesn't look at a particle, then it doesn't exist! Uncertainty! Schrodinger!". To summarize: Education is a hell of a bitch to handle. People who are good at it seriously deserve to be more distinguished.
@eddiegaltek
@eddiegaltek 8 жыл бұрын
You have to go down to -1/1583 to get as good an approximation as 22/7.
@timyang2996
@timyang2996 4 жыл бұрын
perfect for my pi memorization contest i could just calculate it on the spot
@patrickboner
@patrickboner 4 жыл бұрын
@Viktor Magnusson you would be surprised some people can especially if you look at your memory as a piece of paper and pen
@Sora_Halomon
@Sora_Halomon 4 жыл бұрын
all you need is the list of all known prime numbers
@patrickboner
@patrickboner 4 жыл бұрын
@@Sora_Halomon please explain
@efdbjon2114
@efdbjon2114 3 жыл бұрын
@@Sora_Halomon just use the nth term for the prime numbers
@JohnDoe-eu2vv
@JohnDoe-eu2vv 3 жыл бұрын
Might be easier to use a faster series
@ashaydwivedi420
@ashaydwivedi420 6 жыл бұрын
How fascinating, the calculation of pi starts at 3:14
@claygregory7513
@claygregory7513 6 жыл бұрын
Ashay Dwivedi my mind is blown
@ashaydwivedi420
@ashaydwivedi420 6 жыл бұрын
Yeah, mine was too
@thatssomethingthathappened9823
@thatssomethingthathappened9823 3 жыл бұрын
It is in base 60 though. This comment was sponsored by Jane Street and SIXTY. It’s a cool number.
@thatssomethingthathappened9823
@thatssomethingthathappened9823 3 жыл бұрын
Call 1-60S-IXT-YSIX
@loc1k
@loc1k 2 жыл бұрын
This comes on after the British weather forecast.
@karlmuster263
@karlmuster263 7 жыл бұрын
My favorite representation is 355/113 = 3.1415929203... It's easy to remember. You start with the first three odd numbers: 135. You double them up: 113355. You split it in the middle: 113/355. Then you take the inverse: 355/113. And there you have it, pi correct to 7 digits.
@SamFisk
@SamFisk 7 жыл бұрын
Having seen the final result I think I agree that this is better. Another commenter has pointed out that this is accurate to a 1/3748629th; good enough and much easier to calculate.
@derrickbonsell
@derrickbonsell 7 жыл бұрын
+Sam Fisk It'd be easier to just remember the digits.
@SamFisk
@SamFisk 7 жыл бұрын
Each to his own. I'd just use Google...
@77gravity
@77gravity 7 жыл бұрын
The purpose of an approximation like 553/113 is for use in longhand calculations.
@karlmuster263
@karlmuster263 7 жыл бұрын
77gravity And sometimes physicists use fractions, like when using the fine-structure constant, a~1/137.
@servalerror
@servalerror 8 жыл бұрын
Uploaded on March 13, not the 14th...classic Parker Square.
@wallonice
@wallonice 5 жыл бұрын
Its pi, classic parker circle
@Jivvi
@Jivvi 4 жыл бұрын
No, it was 3/14/16 Correct to 4 decimal places.
@mongoose.official
@mongoose.official 4 жыл бұрын
@@Jivvi technically it's 3.14159... but I guess yeah, 3.1416
@david-li3mn
@david-li3mn 4 жыл бұрын
@@mongoose.officialcorrect to 4
@DrKaii
@DrKaii 3 жыл бұрын
@niraj panakhaniya someone ruined it niraj, we must find them
@kaazmodan
@kaazmodan 6 жыл бұрын
I really love the idea of a student randomly walking in on this happening, seeing Matt talk to himself and writing on the chalkboard, and then just saying "He's just having one of his "special" days", then walking out without saying anything.
@JiMwB
@JiMwB 3 жыл бұрын
One of those days where you 1st try to find π 2nd start turning into a Smurf 3rd murder a Smurf 4th fail at finding π
@braylordian5541
@braylordian5541 6 жыл бұрын
The best way to find pi is the equation: 1π
@goji_crafter
@goji_crafter 5 жыл бұрын
Here, ill solve it for you: Let pi = x 1pi=x Divide both sides by pi 1=x/pi Now we can find the real value. So if I hit backspace three times on the last step, we find that: 1=x, so pi=1
@Aspiracy
@Aspiracy 4 жыл бұрын
xX GojiCrafter Xx lmao
@patrickboner
@patrickboner 4 жыл бұрын
@@goji_crafter forgot the sign change
@kerbalpanda3592
@kerbalpanda3592 4 жыл бұрын
@@goji_crafter underrated comment ik this was a year ago
@phatkin
@phatkin 3 жыл бұрын
that's not an equation, that's an expression. You can tell because an equation typically has an equal sign.
@TazPessle
@TazPessle 7 жыл бұрын
When i was 6 i thought they made bigger and bigger circles and measured with better and better rulers to find the digits of Pi. XD
@htmlguy88
@htmlguy88 7 жыл бұрын
you can use trig functions to estimate it using polygons with more and more sides it's been done up to millions of sides in the past I think.
@Bjowolf2
@Bjowolf2 7 жыл бұрын
Already the Greek mathematician Archimedes did this up to an amazing 96 sided inner and outer polygon. en.wikipedia.org/wiki/Archimedes#Mathematics
@Bjowolf2
@Bjowolf2 7 жыл бұрын
But then you need to know the trig functions to a high accuracy ;-)
@ffggddss
@ffggddss 7 жыл бұрын
+ Bjowolf2 All you need to know about the trig functions to use Archimedes' method is: sin30º = ½ tan30º = 1/√3 and the half-angle formulas for both sin and tan. Which in turn, means that you have to know how to extract square roots.
@Bjowolf2
@Bjowolf2 7 жыл бұрын
ffggddss Yes, I know, but did the Greeks know that and how to do that?
@chinareds54
@chinareds54 8 жыл бұрын
I'm 37 years old, and this is the first time I've ever seen long division done on one line rather than taking up a whole damn page. Wow.
@Jiggerjaw
@Jiggerjaw 8 жыл бұрын
+chinareds54 I am 25; when I was in grade school, this method was taught under the name "short division".
@dolantremp
@dolantremp 8 жыл бұрын
+chinareds54 lol yeah this way is much more convenient i have no idea why they dont teach it instead
@SomeRandomFellow
@SomeRandomFellow 8 жыл бұрын
+Brenden Patch that explains why there's a long division and not a short division
@rhythmic700
@rhythmic700 7 жыл бұрын
that is called short division fyi
@squidbait1396
@squidbait1396 7 жыл бұрын
wait what? this is the only way i've ever seen long division done. what is this other method?
@kurumi394
@kurumi394 4 жыл бұрын
Archimedes: approximates pi to the second digit with a 96 sided polygon *Zu Chongzhi: laughs in 24576 sided polygon and 7th digit of pi*
@peorakef
@peorakef 3 жыл бұрын
you're aware that was 800 years afterwards?
@kurumi394
@kurumi394 3 жыл бұрын
@@peorakef Yes. That doesn't mean it's less of an extraordinary feat though.
@peorakef
@peorakef 3 жыл бұрын
@@kurumi394 Yes. That doesn't mean you have a point.
@j.moonstorm3158
@j.moonstorm3158 3 жыл бұрын
Archimedes also invented calculus in his lost magnum opus "The Method" a feat not replicated for a few thousand years after a number of mathematic advances were made that archimedes didn't have access to so...he's arguably the most brilliant mathematician to ever live
@eleSDSU
@eleSDSU 3 жыл бұрын
@@j.moonstorm3158 I'll disagree in one word, Euclid.
@alejrandom6592
@alejrandom6592 3 жыл бұрын
2:34 POV: you enter an empty classroom and there's a man randomly shouting "chalkboard"
@theCodyReeder
@theCodyReeder 8 жыл бұрын
You could multiply it by 2 and get tau. :)
@Talt9999
@Talt9999 8 жыл бұрын
I love finding one of my favorite youtubers commenting on loads of the science/maths youtube videos i watch :)
@standupmaths
@standupmaths 8 жыл бұрын
+Cody'sLab But I was trying to calculate the circle constant… :]
@Kylanto
@Kylanto 8 жыл бұрын
+standupmaths Roasted!
@newgoredan303
@newgoredan303 8 жыл бұрын
+Cody'sLab Holy crap, Cody!
@hughmongusfungusamongus2439
@hughmongusfungusamongus2439 8 жыл бұрын
+standupmaths Nice one
@kevinocta9716
@kevinocta9716 8 жыл бұрын
I have no idea why, but I could watch this man do basic math for hours. Honestly... it's odd.
@Jbenneballe
@Jbenneballe 8 жыл бұрын
+Kevin Octacok glad to hear i'm not alone with that feeling :)
@Summy_99
@Summy_99 8 жыл бұрын
yeah I could literally watch him do the whole thing with no cuts
@kyleserrecchia7234
@kyleserrecchia7234 8 жыл бұрын
+Kevin Octacok It's like a meditation. It's simple, but it's so beautiful in its perfection.
@Reivivus
@Reivivus 8 жыл бұрын
+Kevin Octacok, most of what he is talking about I already know so it's not like I'm being educated. Where is the original research?
@kevinocta9716
@kevinocta9716 8 жыл бұрын
Reivivus The original research is that man's beautiful face and charming wit.
@bungalo50
@bungalo50 2 жыл бұрын
This really highlights how amazingly precise 22/7 actually is
@carultch
@carultch Жыл бұрын
This also highlights how well you can do just by measuring a circle with a piece of string.
@TomStorey96
@TomStorey96 4 жыл бұрын
I had completely forgotten how to divide numbers like this.
@Toost914
@Toost914 8 жыл бұрын
I wonder how many pieces of chalk went into making this video...
@kviaak7979
@kviaak7979 8 жыл бұрын
+TheOneManGeekArmy I guess 3.14159
@Toost914
@Toost914 8 жыл бұрын
Yes.
@Remember939393
@Remember939393 8 жыл бұрын
+kVI Aak *3.04
@Summy_99
@Summy_99 8 жыл бұрын
+kVI Aak you mean 3.04183
@Summy_99
@Summy_99 8 жыл бұрын
+Summy99 *3.04184
@EpicUltraKingSmizzy
@EpicUltraKingSmizzy 8 жыл бұрын
was this like a secret 'learning how to divide' video? lol
@Regular-Sized
@Regular-Sized 8 жыл бұрын
+EpicUltraKingSmizzy my thoughts exactly.
@MegaMGstudios
@MegaMGstudios 6 жыл бұрын
this is actually where i learned to divide in my head, they didnt teach me that on school, they legit said "just divide"
@Berniebud
@Berniebud 6 жыл бұрын
I learned how to divide long ago but forgot, now I know again.
@Metalhammer1993
@Metalhammer1993 6 жыл бұрын
same here i entirely forgot to divide by hand due to calculators^^
@azestical6566
@azestical6566 6 жыл бұрын
MegaMGstudios that is really sad ._.
@DhananjayDhole-DD
@DhananjayDhole-DD 6 жыл бұрын
I got curious by how slowly the series converges to PI/4 and started running calculations. I was observing the absolute error for PI at each step and found a bit of interesting pattern. Below are the first 11 values of (2n + 1) at which the absolute error falls further by a factor of 10. 63, 637, 6367, 63661, 636619, 6366197, 63660819, 636485221, 6334383829, 61037411473 Found it fascinating 1) How the 63....... pattern holds from for the first few elements 2) How 63 is about 20xPI (62.832), thus 637 is ~200xPI and so on. It's a convenient factor of 10 if we use Tau over PI, but lets not go there :-). I prefer PI as anyway
@brandonmonroe9822
@brandonmonroe9822 2 жыл бұрын
One of my favorite videos you've ever made. I've learned SO MUCH from this video. I could never thank you enough.
@jackeown
@jackeown 7 жыл бұрын
Python one-liner: 4*sum([(-1.0)**(k)/(2*k+1) for k in range(0,10,1)])
@beckles103
@beckles103 4 жыл бұрын
John McKeown step is 1 by default
@RoyBrush
@RoyBrush 4 жыл бұрын
In case people want to run this in their browser in place, here is a roughly equivalent one-liner in javascript: ((t)=> 4*(new Array(t)).fill(0).map((_,i)=>Math.pow(-1,i)/(2*i+1)).reduce((a, v)=> a+v))(10) You might also want to explicitly console.log the result of the above expression and/or change the precision like so: console.log(((t)=> 4*(new Array(t)).fill(0).map((_,i)=>Math.pow(-1,i)/(2*i+1)).reduce((a, v)=> a+v))(10000000))
@jackeown
@jackeown 4 жыл бұрын
@@beckles103 good point.
@x_star6100
@x_star6100 3 жыл бұрын
this is wrong i got 3.0418396189294032 xD
@jackeown
@jackeown 3 жыл бұрын
@@x_star6100 It's an approximation. Replace the 10 with a much higher number and you will get a better approximation. try 10000 or higher and you'll see it gets a little better. Convergence is very slow though.
@leocorn58
@leocorn58 7 жыл бұрын
"Oh that's neat. I wonder how that works." "Woah cool, he knows his stuff." "Okay, can't wait to see how he knows this." "HE'S A WITCH!!!"
@tonksdude
@tonksdude 5 жыл бұрын
What do you do with witches?
@jackmack1061
@jackmack1061 5 жыл бұрын
burn them?
@tonksdude
@tonksdude 5 жыл бұрын
@@jackmack1061 gooooooooooooooooooooooooooood
@tonksdude
@tonksdude 5 жыл бұрын
@@jackmack1061 and what do you burn aside from witches?
@jackmack1061
@jackmack1061 5 жыл бұрын
lol, that movie terrified me as a child. Nightmares...
@topdog8035
@topdog8035 7 жыл бұрын
my favourite part was 3:14
@cyberfalcon2872
@cyberfalcon2872 6 жыл бұрын
Actually, thats the part that the video really starts. I wonder if that was a coincidence
@fanq_
@fanq_ 6 жыл бұрын
Thiago Morais probably not
@Boonda-p
@Boonda-p 6 жыл бұрын
no way. on a separate note i love when people spell favorite with a u
@prakharsingh9089
@prakharsingh9089 5 жыл бұрын
lol
@GerassimosOfficial
@GerassimosOfficial 5 жыл бұрын
@@prakharsingh9089 xd
@Mdibah
@Mdibah 7 жыл бұрын
Mistake #1 (fixed during montage at 13:08): incorrect number of decimal places written for 1/17 Mistake #2 (@ 12:00): The difference of the decimal expansions given for 1 and 1/3 should be 0.66...667. This throws off the 20th decimal place for the rest (meh). Mistake #3 (visible @13:03): After adding the decimal for 1/13, the partial sum should be 0.820 934 620 934 620 934 62 (vicinity of 7th decimal place on is wrong). This throws off the rest of the calculation. The ending tally should be 0.760 459 904 732 350 552 78, which gives 3.041 839 618 929 402 211 12 after multiplying by 4. Again, very close---just issues around the 7th and 8th decimal places. Mad props for carrying out this masochism by hand; I needed to break out a calculator to track down the arithmetic error.
@squarerootof-1307
@squarerootof-1307 2 жыл бұрын
i did it on a calculator, still got 3.041...
@codebroker_
@codebroker_ 8 жыл бұрын
Well if nothing else at least I learned the British way to divide
@inserttheemailyouusehere1480
@inserttheemailyouusehere1480 6 жыл бұрын
Cole Vohs British way? I thought it was common knowledge
@diamonddave2622
@diamonddave2622 6 жыл бұрын
he's Australian
@micrapop_6390
@micrapop_6390 6 жыл бұрын
The way to multiply too !
@silkwesir1444
@silkwesir1444 6 жыл бұрын
I don't like it, because it looks a lot like a square root symbol. I tend to dislike any notation which could be confused for being something else...
@franciscodanconia45
@franciscodanconia45 6 жыл бұрын
That’s the way everyone did it before pocket calculators were invented! “Never throw away your last pencil.”-me
@criotene
@criotene 8 жыл бұрын
i fell asleep on a vans gaming video and woke up to this
@mason26392
@mason26392 8 жыл бұрын
The magic of KZfaq
@MichaelWilliams-ow9ue
@MichaelWilliams-ow9ue 5 жыл бұрын
I’m genuinely inspired and impressed an an adult professional mathematician who has spent years learning advanced mathematics can still enjoy this so much. I am a musician and this would be the equivalent of me being excited by playing a scale or Mary had a little lamb, which just doesn’t happen.
@shadowpod13
@shadowpod13 6 жыл бұрын
I like that you're calculating pi without using any Sin stuffs. Makes it easier to follow. Also, at the same time you are explaining what happens when I put a fraction into a calculator. Real cool.
@12tone
@12tone 8 жыл бұрын
I know this probably didn't affect the outcome very much, but your value for 1-1/3 should've ended in a 7, not a 6, right? Like, if you're doing it by approximating 2/3 then it needs to end there because the next digit is a 6 so it should round up, and if you're doing it by subtracting a truncated series of threes from a truncated series of 0s, I'm fairly certain that 10-3=7.
@zoellazayce6796
@zoellazayce6796 3 жыл бұрын
No you're wrong
@Supertimegamingify
@Supertimegamingify 2 жыл бұрын
@@zoellazayce6796 compelling argument
@0ijrc
@0ijrc 2 жыл бұрын
@@Supertimegamingify I must agree
@henriquemesquita5692
@henriquemesquita5692 2 жыл бұрын
Ye, he forgot to round the 20th digit, i think in all of them
@milestailsprower4555
@milestailsprower4555 Жыл бұрын
@@henriquemesquita5692 no
@kocajj
@kocajj 7 жыл бұрын
I love how excited you were doing the long division. It actually made me remember my days in 3rd grade when I was learning more complex long division and thinking of how your enthusiasm would have made the process much more enjoyable; more of a game, rather than a chore. I will make sure to pass that on to my son when he gets older.
@georgew.9663
@georgew.9663 6 жыл бұрын
Holy crap that transition to the chalkboard was seriously amazing, I've never seen a transition like that anywhere near as good as you did that, Jesus Christ.
@bryankurniawan5397
@bryankurniawan5397 5 жыл бұрын
OMG THIS GUY IS SO GOOD AT MAKING ME FALL ASLEEP IM NOT BORED BUT HIS VOICE MAKES ME SOO SLEEPY IDK WHY BEST VIDEO SO FAR.
@Dixavd
@Dixavd 8 жыл бұрын
14:08 - as we all know, four threes are twenty-eight.
@kdmq
@kdmq 8 жыл бұрын
+Dixavd That was just a speech error. He was pointing to a seven as he said three and the product of 28 is correct.
@Dixavd
@Dixavd 8 жыл бұрын
kdmq Oh I know, I just thought it was funny.
@birthsonbluebell3654
@birthsonbluebell3654 6 жыл бұрын
4+[3×(4+4)] is 28.
@timothy9958
@timothy9958 8 жыл бұрын
Really liking the consistent uploads. you're doing a good job man!
@jraqn
@jraqn 4 жыл бұрын
I want this guy as my math teacher he's cool
@liliacfury
@liliacfury 5 жыл бұрын
I love the way you divide, the way I was taught takes up so much space. Nice to know.
@terryendicott2939
@terryendicott2939 8 жыл бұрын
At 13:14 you said, "The trouble with using red chalk after blue chalk is now it looks like I murdered a smurf." in a tone that sounded like you thought that murdering a smurf might be a bad thing.
@alexchulzhanov
@alexchulzhanov 8 жыл бұрын
I'm sorry but you draw your decimal points way too high and they look like dot products or something XD
@standupmaths
@standupmaths 8 жыл бұрын
I'm saving money with cheap low-density decimal points. But they do tend to drift off.
@alexchulzhanov
@alexchulzhanov 8 жыл бұрын
+standupmaths Haha that made it better XD
@lapk78
@lapk78 8 жыл бұрын
+standupmaths That's one of the best retorts I've ever seen in a comment thread. Beautiful. But why not splurge a bit for PiDay? Get the good stuff.
@Correctrix
@Correctrix 8 жыл бұрын
+byalexandr You draw your decimal points way too low and they look like full stops.
@__nog642
@__nog642 8 жыл бұрын
Correctrix periods and decimal points are the same character ..
@JosiahDouglas
@JosiahDouglas 5 жыл бұрын
This is the most ridiculously wonderful thing I've ever seen. Thank you KZfaq for suggesting this.
@lollycopter
@lollycopter 2 жыл бұрын
14:17 The full answer of Pi is revealed right here.
@asp-uwu
@asp-uwu 8 жыл бұрын
Another way you can find π: π=3+(4/[2*3*4])-(4/[4*5*6])+(4/[6*7*8]) I wrote a program to calculate π using both the method you did in this video, and the one above, and it turns out the one above gets much closer with many fewer iterations. Great video sir!
@chainezo
@chainezo 8 жыл бұрын
+Eric Pratt but prime numbers tho
@putinstea
@putinstea 7 жыл бұрын
3:22 Why would you draw the "point" there? It looks like a multiplication symbol.
@SJN3000
@SJN3000 7 жыл бұрын
Iorveth AFAIK this is a thing in the UK
@entropyzero5588
@entropyzero5588 7 жыл бұрын
I've also seen people on this channel drawing the multiplication symbol where the rest of us would place the decimal point and was quite confused - apparently this is normal somewhere?
@Pteromandias
@Pteromandias 6 жыл бұрын
It's not normal anywhere. Nothing is normal in Brexitannia.
@danjbundrick
@danjbundrick 6 жыл бұрын
Yeah, it's their thing. With a bit of discernment, you can translate it to the American way. Cheers.
@sp00kiestchannelevah76
@sp00kiestchannelevah76 6 жыл бұрын
Sorry, who uses a point as a multiplication sign? X has always been the sign that I've known... Or * for computers
@thebenevolentsun6575
@thebenevolentsun6575 6 жыл бұрын
I've been waiting for this channel to exist
@DanielRBW
@DanielRBW 6 жыл бұрын
I've discovered (through excessive use of excel), that the number of iterations is equal to the degree of accuracy. So at the 10000th iteration, the value is equal to pi to 5 s.f. At 1 million iterations, the value is equal to 3.141592 (rounded), which means it is accurate to 1 part in every million. Either way, I thought that was pretty interesting, although it maybe should have been more obvious, looking at it in hindsight.
@anarcho.pacifist
@anarcho.pacifist 8 жыл бұрын
The 8th digit after the decimal point should be 0, instead of 9, at 13:12 The correct results are: 0.76045990473235055278398931649706 and 3.04183961892940221113595726598823
@TommiHimberg
@TommiHimberg 8 жыл бұрын
Damn, we are 10 days late in celebrating pie day!
@jdat
@jdat 6 жыл бұрын
I seriously learned multiple tricks from the video! Thanks for teaching me some easy techniques! I'm currently taking algebra 1 in 8th grade (US) so I'm sure these will be used a LOT!
@popcet224
@popcet224 6 жыл бұрын
Matt is so awesome i'd watch him divide and substract all day and not sleep in class
@modakshantanu
@modakshantanu 8 жыл бұрын
This video is 1119 second long. If you make a circle with diameter 1119m, it's circumference is 3515 m. 3515/1119 =3.14. Nice Easter egg.
@ju-inhum7896
@ju-inhum7896 8 жыл бұрын
Sorry to burst your bubble, but that is no Easter Egg... Diameter is (2 * radius) and circumference is (2 * pi * radius). Therefore, by dividing circumference by diameter, regardless of the value, will always return pi.
@sebamc4
@sebamc4 8 жыл бұрын
+Shantanu Modak NICE! .... ;)
@ju-inhum7896
@ju-inhum7896 8 жыл бұрын
Also, you used the wrong "its/it's". Although the apostrophe is usually used for the possessive form, in this case, it is used to contract "it" and "is" into a single word. Additionally, I'm pretending to be smart by being fancy.
@ju-inhum7896
@ju-inhum7896 8 жыл бұрын
+sebamc4 Listen, it's not an Easter Egg, ok? Do it with any other number and you'll see.
@sebamc4
@sebamc4 8 жыл бұрын
Ju-In Hum yes, i had math in high school. I was playin the joke along... thats why i put the ";)"
@jordansmith2520
@jordansmith2520 7 жыл бұрын
3:14 It's amazing... He starts calculating pi at pi time value.
@questionable2140
@questionable2140 2 жыл бұрын
Oh my god
@Sacorian
@Sacorian 7 жыл бұрын
I finally understand how the digits of Pi can be seemingly all over the place. Thank you Matt Parker.
@MattMcIrvin
@MattMcIrvin 6 жыл бұрын
The French translator in the captions captured Matt Parker's speaking style quite well.
@NikolajLepka
@NikolajLepka 8 жыл бұрын
why do I suddenly understand how to do division by hand after watching this?
@cupcakearmy
@cupcakearmy 8 жыл бұрын
Me too 😊
@S4R1N
@S4R1N 8 жыл бұрын
+Nikolaj Lepka Yup, I'm watching this while procrastinating/finding motivation to study for a math exam (albeit a very basic one). I can now to division by hand magnitudes easier than what I was originally taught.
@NikolajLepka
@NikolajLepka 8 жыл бұрын
S4R1N We were taught long division at school, and it was so cumbersome and confusing I never really bothered to learn it. Now, I'm a programmer, so I deal with integer division and modulo operations all the time, so short division just seems so much more natural, because all it deals with is remainders
@sezylrin4138
@sezylrin4138 8 жыл бұрын
no smurfs were hurt in the making of this video :P
@leighhurley9410
@leighhurley9410 5 жыл бұрын
The editing absolutely makes this video XD
@mgsquared5204
@mgsquared5204 7 жыл бұрын
He wrote 1.0000000... Like 1•0000000..
@mgsquared5204
@mgsquared5204 7 жыл бұрын
GamerGeek like multiplication.
@ffaiq
@ffaiq 7 жыл бұрын
UK thing
@jaythatch7295
@jaythatch7295 6 жыл бұрын
Well that's how we do it in grade school, but the dot is used to avoid confusion with x as a variable.
@matthewbertrand4139
@matthewbertrand4139 6 жыл бұрын
CubeMania We do any of three things. We could write that as: 6 × 2 6 * 2 6 • 2 My preferred method is the dot. It's quickest to write and avoids confusions with any variables named x.
@markdallen4018
@markdallen4018 6 жыл бұрын
The letter x and multiplication symbol are very different in UK mathematics, so it's easy to distinguish between them. The x is curly, and the multiplication symbol is too straight lines crossing.
@legofan431
@legofan431 7 жыл бұрын
I love how happy he gets over dividing 1/17 in his head :D
@patrickwienhoft7987
@patrickwienhoft7987 8 жыл бұрын
The series up to n = 19 is actually 3.041839 (here you get wrong) 61893... Not sure where the error is tho. edit: got it! (assuming its the only mistake). 13:03 1-1/3+1/5-1/7+1/9-1/11+1/13 is 0.82093462093..., not 0.82093471093... edit2: yes, with that result I get your "pi" :)
@thermitebanana
@thermitebanana 6 жыл бұрын
I love the working out. Just an awesome example of getting results through hard work and persistence
@andrewmartin3671
@andrewmartin3671 2 жыл бұрын
I'm here for Parker Pi references.
@lasagnahog7695
@lasagnahog7695 8 жыл бұрын
"Doing a Third the Long Way" should be your biography's title.
@lasagnahog7695
@lasagnahog7695 8 жыл бұрын
Never mind "Smurf Fingers" would be better.
@standupmaths
@standupmaths 8 жыл бұрын
"One man's battle with recurring digits."
@marsamet128
@marsamet128 8 жыл бұрын
+Eric Loesch Are you sure? I think "Smurf Murderer" is a lot better
@IrizarryBrandon
@IrizarryBrandon 8 жыл бұрын
+dopplegänger_01 Yes, I was initially more fascinated by that han the actual discussion of pi itself. I guess that shows the real level of my mathematical understanding! Oh well, you have to learn to crawl before you can learn to walk, as they say.
@IrizarryBrandon
@IrizarryBrandon 8 жыл бұрын
Yes, same here, actually (sorry if my comments mislead). It seems like a pretty practical method. Who knows? I may use it in the future.
@olleicua
@olleicua 8 жыл бұрын
Your video is obviously 10 days late! Pi day should be March 4th
@elikubler-ross5997
@elikubler-ross5997 8 жыл бұрын
+Sam Auciello sorry, but wouldn't it be March 14th? at say... 15 hours? :)
@amarpersaud2950
@amarpersaud2950 8 жыл бұрын
+Eli Kübler-Ross Well obviously Π is 3.04
@JamieDenAdel
@JamieDenAdel 8 жыл бұрын
+Eli Kübler-Ross It's a joke from the video.
@olleicua
@olleicua 7 жыл бұрын
What is a chanber and how do I find one to go die in?
@MrSpookersMcGeeThe1st
@MrSpookersMcGeeThe1st 7 жыл бұрын
Dude, does your town not have a local chanber? I feel so bad for you, man. That's my favorite place to die! I do it once a month to relax. Yes. I die once a month, intentionally. Apparently.
@d4m4s74
@d4m4s74 7 жыл бұрын
I totally forgot how long or short division worked after years and years of not using it. Thanks for the refresh.
@mrchel2525
@mrchel2525 6 жыл бұрын
I was looking for something like this really long time. Thank you for this video! :)
@circular17
@circular17 7 жыл бұрын
The correct result would be 3.0418396189294022111359572659882 so Matt got the first 7 digits right and then, well, not correct. But anyway, the correct result is still way off Pi!!
@SGAMaddin
@SGAMaddin 7 жыл бұрын
The result given by you is the one i got too; I think he made a typo when adding the numbers; his result for pi/4 is correct apart from the eighth digit where it should read 0 instead of 9; pi/4 = 0.7604599 0 47323505528. But still very impressive doing it by hand that well. I did it with Mathematica.
@klobiforpresident2254
@klobiforpresident2254 7 жыл бұрын
Don't forget that he used only ten fractions out of a literal infinite pool, ...
@SPACKlick
@SPACKlick 7 жыл бұрын
He made the mistake at 1/13
@ashortguy24
@ashortguy24 3 жыл бұрын
@@SGAMaddin It would be incorrect he didn't use all the numbers, and adding rational numbers give a rational result, unless added infinitely
@sasukesuite1
@sasukesuite1 8 жыл бұрын
Sorry, but your first calculation is wrong. 1/1 = 0.999999999....
@jeromesnail
@jeromesnail 8 жыл бұрын
Actually it is. 0,9999999999999... = 1
@epicfailtackular
@epicfailtackular 8 жыл бұрын
it was a joke, pal
@vernement4752
@vernement4752 8 жыл бұрын
+jeromesnail Difference?
@Pattonator14
@Pattonator14 8 жыл бұрын
Except that he's rounding up after 20 digits, so 0.999999... would be rounded up to 1.000000... etc anyway
@jeromesnail
@jeromesnail 8 жыл бұрын
+verne ment no difference, I just misunderstood the comment. My bad!
@Zachdancer1
@Zachdancer1 3 жыл бұрын
I’m excited to see what he does this year!
@billyrobertson3170
@billyrobertson3170 7 жыл бұрын
If anybody's looking for a way to calculate Pi by hand that's actually pretty efficient, I recommend the following: (Found by Nilakantha in the 1400s) Pi = 3 + 4/(2*3*4) - 4/(4*5*6) + 4(6*7*8) - 4/(8*9*10) + ... I got quite a few correct digits after just 5 terms and it's relatively easy to compute (I recommend using decimals like how Matt did it)
@nmanrman911
@nmanrman911 8 жыл бұрын
You could call this attempt a "Parker square" of Pi :P
@bobmike2373
@bobmike2373 8 жыл бұрын
No its just "Parker Pi"
@ffggddss
@ffggddss 8 жыл бұрын
+bob mike I didn't even know she had one!
@NoriMori1992
@NoriMori1992 8 жыл бұрын
+nman rman DAMMIT YOU BEAT ME TO IT.
@bobmike2373
@bobmike2373 8 жыл бұрын
*malicious grin*
@jakob_z
@jakob_z 8 жыл бұрын
A Classic Parker Pie
@8ytan
@8ytan 8 жыл бұрын
Next year's video: calculating pi while skydiving.
@bendover8738
@bendover8738 8 жыл бұрын
Calculating pi while eating lunch.
@8ytan
@8ytan 8 жыл бұрын
I eat kids Souls Calculating pi while putting out a grease fire.
@theatomixgaming5520
@theatomixgaming5520 8 жыл бұрын
+John Reynolds Calculating pi while defeating the foundation...
@Veptis
@Veptis 2 жыл бұрын
Also a good indicator as to how long the periodic bit of a periodic decimal can be for any given denominator, as it's always fractions. And why some numbers can't be fractions and how they aren't rational.
@peterflom6878
@peterflom6878 4 жыл бұрын
His excitement and sense of wonder are beautiful
@WolfOfLegend
@WolfOfLegend 8 жыл бұрын
Wouldn't the 2/3 be 0.66666..67 due to rounding?
@Filmsuper95
@Filmsuper95 8 жыл бұрын
+DrPengin 1,000,000 Media 0.000...04 because he multiplies with 4
@kisaragiayami
@kisaragiayami 8 жыл бұрын
+DrPengin 1,000,000 Media That is 0
@kaytontruong2739
@kaytontruong2739 8 жыл бұрын
+WolfOfLegend No, it would not be due to rounding because there *is no rounding.* It's just like how 0.999... = 1 without "rounding" of any sort.
@ffggddss
@ffggddss 8 жыл бұрын
+Ginger Bread Yes, it IS rounding; round infinitely many sixes to 19 sixes and a seven, which is twice as close to true as rounding it to 20 sixes. And, yes, an infinite string of 9's will equal 1; but a finite string of 9's will not.
@NoriMori1992
@NoriMori1992 8 жыл бұрын
+ffggddss But Matt was obviously truncating rather than rounding.
@199NickYT
@199NickYT 8 жыл бұрын
Remind me: March 4, 2018. The REAL Pi day.
@TheJmax04
@TheJmax04 8 жыл бұрын
+Nicholas Wright (Toothpick Nick) April 3rd...
@avisian8063
@avisian8063 8 жыл бұрын
+Josh O'fortune 22nd of July
@catamountcubing4851
@catamountcubing4851 4 жыл бұрын
i love how he said, "and we carry the nothing"
@taggartm6469
@taggartm6469 7 жыл бұрын
Mathematicians: damn this needs a lot of fractions to get this accurate... Programmers: need some help? mathematicians: yea, see there is a lot of... Programmers: shut up im already done 200,000 digits
@DanDart
@DanDart 7 жыл бұрын
"Four threes are twenty eight" You have been broken xD
@oz_jones
@oz_jones 4 жыл бұрын
Dan Dart parker multiplication
@Jivvi
@Jivvi 4 жыл бұрын
"Six times nine is forty-two."
@dotMarauder
@dotMarauder 8 жыл бұрын
14:28, "I should tell someone." I'm dying.
@midwestrailroadproductions8116
@midwestrailroadproductions8116 5 жыл бұрын
Amazing, Matt. You're Matthew the Math Man.
@greature
@greature 6 жыл бұрын
"wait a minute, we're back to where we started" 😂 SURPRISE!
@IoEstasCedonta
@IoEstasCedonta 8 жыл бұрын
Since the series can also be expressed as 2/((4n+2)^2-1), you can use the integral test to show that the "tail" at this point is between 1/4 * ln(23/21) and 1/4 * ln (19/17), or between .02274 and .02781, meaning the error in pi would be between .09097 and .11123. (I used a log table. Stop looking at me like that.) So what Matt got seems about right, although I did notice that two-thirds should have ended in a seven rather than a six. A relatively easy one that converges relatively quickly would be the Maclaurin series of inverse trig functions, e.g., arcsin(1/2) = pi/6.
@LarlemMagic
@LarlemMagic 8 жыл бұрын
A real parker square that was. :)
@justinlasker6269
@justinlasker6269 8 жыл бұрын
+LarlemMagic I was about to comment this lol
@TinyRoboticPiggies
@TinyRoboticPiggies 7 жыл бұрын
GO FOR THE EYES, BOO!
@laser8389
@laser8389 3 жыл бұрын
I tuned out a bit when you were working out the individual fractions but popped back in for my favorite one: for any integer x, 0
@Makker_1
@Makker_1 4 жыл бұрын
I'm interested to know how and why this works. Because my idea to calculate pi was to write a computer program that calculates very accurate points that lay on a circle and then measure the distances and then divide that by the double of the radius.
@warpcore0541
@warpcore0541 8 жыл бұрын
14:09 Four threes are twenty eight! At least that was a seven.
@utl94
@utl94 8 жыл бұрын
+warpcore05 Wow! He was lucky that was a seven...
@NoriMori1992
@NoriMori1992 8 жыл бұрын
13:02 - Found an error at the 1/13 point, which you made really tedious for me as it's the only part you _didn't actually show_. (Damn you, Matt!) Your result was 0.8209314*71*…; it should've been 0.8209314*62*… From examining the strings, I really really don't know how you got 71 there. XD Unless you had a brain fart and added the 9 from above to get 21? I don't know if this is the only error, but it's the only one I've found. Don't know how much it affected the final result, either.
@limecyanizer4394
@limecyanizer4394 5 жыл бұрын
He put 1.00000000000000000000-0.33333333333333333333=0.6666666666666666666666666 but it's actually 0.66666666666666666667
@blueslime5855
@blueslime5855 5 жыл бұрын
@@limecyanizer4394 duh
@GerassimosOfficial
@GerassimosOfficial 5 жыл бұрын
@@limecyanizer4394 xd
@0x13a9
@0x13a9 5 жыл бұрын
This guy is awesome, I wish he was my teacher. Thanks you for the content.
@knutsletvold
@knutsletvold 7 жыл бұрын
"...carry the zero..." My math teacher would have thrown a massive fit. I love it!
@ayylmao93_12
@ayylmao93_12 7 жыл бұрын
"It's pi day, pi day, gotta get down on pi day" Sounds familiar...
@jamief415
@jamief415 8 жыл бұрын
Can you do a video on a proof of why the (1 +/- 1/(prime)) series equals 2/pi?
@felipea.barretto7503
@felipea.barretto7503 8 жыл бұрын
+Jamie F Do a matt parker explains out of this!
@decdedceeded
@decdedceeded 8 жыл бұрын
It's actually just a disguised version of the odd reciprocals, you just factorise and use geometric series (essentially)
@toasterwafflz5694
@toasterwafflz5694 5 жыл бұрын
For some reason watching you divide fractions made me happy
@mahdirostami7034
@mahdirostami7034 4 жыл бұрын
i remember i tried to calculate pi with this serie but its leaning towards pi really slowly. and it doesnt matter how much digits you calculate. even the first 2 digits wont be correct with only 10 fractions.
@axiezimmah
@axiezimmah 8 жыл бұрын
couldn't you theoretically use this in reverse to calculate prime numbers?
@michaelbauers8800
@michaelbauers8800 7 жыл бұрын
My intuition is that you would not be able to decompose PI back to primes like that. Seems intractable.
@klobiforpresident2254
@klobiforpresident2254 7 жыл бұрын
You *could* do this but it is ... impractical.
@htmlguy88
@htmlguy88 7 жыл бұрын
my guess is no simply because you need to know if they are 1 or 3 mod 4 to know if they were added or subtracted.
@joaopedroholanda4167
@joaopedroholanda4167 5 жыл бұрын
Hm. I don't see how. In order to calculate a single term of the series you would need to know the partial sums... which would require knowing the terms to calculate. Unless there's a closed formula for the partial sums, which I doubt, this doesn't seem feasible.
@jqerty
@jqerty 8 жыл бұрын
Does Tau/2 also have a special day? Didn't know that.
@Fematika
@Fematika 8 жыл бұрын
Oh you better not!
@yxlxfxf
@yxlxfxf 8 жыл бұрын
+jqerty Get out
@LLHLMHfilms
@LLHLMHfilms 8 жыл бұрын
+PiTau he did....he just did...
@BlazingMagpie
@BlazingMagpie 8 жыл бұрын
+jqerty Look at this heretic.
@volbla
@volbla 8 жыл бұрын
+jqerty Knickers twisted.
@debbieepstein6133
@debbieepstein6133 2 жыл бұрын
Would be great to hear about the actual algorithms and work methods used by the human calculators for the atomic bomb and early space travel. How did they make use of many people working side by side without waiting for a previous result. Perhaps next attempt to calculate pi will give more digits!
@ellabakker6642
@ellabakker6642 3 жыл бұрын
I have no idea why I try memorizing pi when I can't even memorize my own phone number.
@martinshoosterman
@martinshoosterman 7 жыл бұрын
Next year on pi try calculating pi using the curvature of the earth! (you could do it with a laser, a ruler and one of those meter wheels.
@willsumner6914
@willsumner6914 6 жыл бұрын
only problem is the earth isnt an exact sphere
@silentinferno2382
@silentinferno2382 5 жыл бұрын
@@willsumner6914 the Earth is a Parker sphere
@silverbladeii
@silverbladeii 4 жыл бұрын
@@willsumner6914 mas é muito próximo disso, dá pra ter uma boa noção com um baixo erro
@jackwilliams7193
@jackwilliams7193 3 жыл бұрын
you want him to walk around the circumference of the earth?
@chairwood
@chairwood 8 жыл бұрын
Why do you put the decimal point so high up :( it looks like you're multiplying.
@chairwood
@chairwood 8 жыл бұрын
***** yes. 1·0 is (1*0), not 1.0.
@chairwood
@chairwood 8 жыл бұрын
***** oh im sorry. skeletons seem to give off a sarcastic vibe for some reason.
@MoempfLP
@MoempfLP 3 жыл бұрын
In the time he calculated 1/7 i thought to myself "Hmm, every fraction gets periodically at least after so many digits as the absolute of the divisor." I was really surprised after he explained the exact same idea at 9:36 😲 I have never heard about the pidgeonhole theorie ever before.
@duncanw9901
@duncanw9901 6 жыл бұрын
Pi shows up because primes are related to the zeros of the analytic continuation of the Riemann zeta function, which is a complex continuation of a sum of an infinite series. Complex numbers are themelves related to the circle in the cos(theta)+isin(theta) notation of primes. There's your circle, Mr. Parker.
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