Calculating π by hand
ฝัง
- เผยแพร่เมื่อ 12 มี.ค. 2016
- 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/ - บันเทิง
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.
+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.
+FlyingPiper13 No, it's not
And he only passed by relying on the age-old method, "Just memorize the formulas and substitute, don't think".
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.
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.
You have to go down to -1/1583 to get as good an approximation as 22/7.
How fascinating, the calculation of pi starts at 3:14
Ashay Dwivedi my mind is blown
Yeah, mine was too
It is in base 60 though.
This comment was sponsored by Jane Street and SIXTY. It’s a cool number.
Call 1-60S-IXT-YSIX
This comes on after the British weather forecast.
perfect for my pi memorization contest i could just calculate it on the spot
@Viktor Magnusson you would be surprised some people can especially if you look at your memory as a piece of paper and pen
all you need is the list of all known prime numbers
@@Sora_Halomon please explain
@@Sora_Halomon just use the nth term for the prime numbers
Might be easier to use a faster series
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.
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.
+Sam Fisk It'd be easier to just remember the digits.
Each to his own. I'd just use Google...
The purpose of an approximation like 553/113 is for use in longhand calculations.
77gravity And sometimes physicists use fractions, like when using the fine-structure constant, a~1/137.
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.
+chinareds54 I am 25; when I was in grade school, this method was taught under the name "short division".
+chinareds54 lol yeah this way is much more convenient i have no idea why they dont teach it instead
+Brenden Patch that explains why there's a long division and not a short division
that is called short division fyi
wait what? this is the only way i've ever seen long division done. what is this other method?
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.
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
Archimedes: approximates pi to the second digit with a 96 sided polygon
*Zu Chongzhi: laughs in 24576 sided polygon and 7th digit of pi*
you're aware that was 800 years afterwards?
@@peorakef Yes. That doesn't mean it's less of an extraordinary feat though.
@@kurumi394 Yes. That doesn't mean you have a point.
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
@@j.moonstorm3158 I'll disagree in one word, Euclid.
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
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.
Already the Greek mathematician Archimedes did this up to an amazing 96 sided inner and outer
polygon.
en.wikipedia.org/wiki/Archimedes#Mathematics
But then you need to know the trig functions to a high accuracy ;-)
+ 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.
ffggddss Yes, I know, but did the Greeks know that and how to do that?
Uploaded on March 13, not the 14th...classic Parker Square.
Its pi, classic parker circle
No, it was 3/14/16
Correct to 4 decimal places.
@@Jivvi technically it's 3.14159... but I guess yeah, 3.1416
@@OpRaven-62correct to 4
@niraj panakhaniya someone ruined it niraj, we must find them
The best way to find pi is the equation:
1π
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
xX GojiCrafter Xx lmao
@@goji_crafter forgot the sign change
@@goji_crafter underrated comment
ik this was a year ago
that's not an equation, that's an expression. You can tell because an equation typically has an equal sign.
This really highlights how amazingly precise 22/7 actually is
This also highlights how well you can do just by measuring a circle with a piece of string.
I have no idea why, but I could watch this man do basic math for hours. Honestly... it's odd.
+Kevin Octacok glad to hear i'm not alone with that feeling :)
yeah I could literally watch him do the whole thing with no cuts
+Kevin Octacok It's like a meditation. It's simple, but it's so beautiful in its perfection.
+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?
Reivivus
The original research is that man's beautiful face and charming wit.
I wonder how many pieces of chalk went into making this video...
+TheOneManGeekArmy I guess 3.14159
Yes.
+kVI Aak *3.04
+kVI Aak you mean 3.04183
+Summy99 *3.04184
2:34 POV: you enter an empty classroom and there's a man randomly shouting "chalkboard"
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.
i did it on a calculator, still got 3.041...
"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!!!"
What do you do with witches?
burn them?
@@jackmack1061 gooooooooooooooooooooooooooood
@@jackmack1061 and what do you burn aside from witches?
lol, that movie terrified me as a child. Nightmares...
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!
+Eric Pratt but prime numbers tho
14:17 The full answer of Pi is revealed right here.
my favourite part was 3:14
Actually, thats the part that the video really starts. I wonder if that was a coincidence
Thiago Morais probably not
no way. on a separate note i love when people spell favorite with a u
lol
@@prakharsingh9089 xd
Python one-liner:
4*sum([(-1.0)**(k)/(2*k+1) for k in range(0,10,1)])
John McKeown step is 1 by default
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))
@@beckles103 good point.
this is wrong
i got 3.0418396189294032
xD
@@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.
You could multiply it by 2 and get tau. :)
I love finding one of my favorite youtubers commenting on loads of the science/maths youtube videos i watch :)
+Cody'sLab But I was trying to calculate the circle constant… :]
+standupmaths Roasted!
+Cody'sLab Holy crap, Cody!
+standupmaths Nice one
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
I had completely forgotten how to divide numbers like this.
was this like a secret 'learning how to divide' video? lol
+EpicUltraKingSmizzy my thoughts exactly.
this is actually where i learned to divide in my head, they didnt teach me that on school, they legit said "just divide"
I learned how to divide long ago but forgot, now I know again.
same here i entirely forgot to divide by hand due to calculators^^
MegaMGstudios that is really sad ._.
Well if nothing else at least I learned the British way to divide
Cole Vohs British way? I thought it was common knowledge
he's Australian
The way to multiply too !
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...
That’s the way everyone did it before pocket calculators were invented! “Never throw away your last pencil.”-me
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.
One of my favorite videos you've ever made. I've learned SO MUCH from this video. I could never thank you enough.
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
14:08 - as we all know, four threes are twenty-eight.
+Dixavd That was just a speech error. He was pointing to a seven as he said three and the product of 28 is correct.
kdmq
Oh I know, I just thought it was funny.
4+[3×(4+4)] is 28.
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.
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.
i fell asleep on a vans gaming video and woke up to this
The magic of TH-cam
3:14 It's amazing... He starts calculating pi at pi time value.
Oh my god
The French translator in the captions captured Matt Parker's speaking style quite well.
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.
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.
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.
+Shantanu Modak NICE! .... ;)
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.
+sebamc4 Listen, it's not an Easter Egg, ok? Do it with any other number and you'll see.
Ju-In Hum yes, i had math in high school. I was playin the joke along... thats why i put the ";)"
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.
He wrote 1.0000000... Like 1•0000000..
GamerGeek like multiplication.
UK thing
Well that's how we do it in grade school, but the dot is used to avoid confusion with x as a variable.
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.
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.
I'm here for Parker Pi references.
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.
why do I suddenly understand how to do division by hand after watching this?
Me too 😊
+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.
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
I want this guy as my math teacher he's cool
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!
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" :)
I'm sorry but you draw your decimal points way too high and they look like dot products or something XD
I'm saving money with cheap low-density decimal points. But they do tend to drift off.
+standupmaths Haha that made it better XD
+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.
+byalexandr You draw your decimal points way too low and they look like full stops.
Correctrix periods and decimal points are the same character
..
I love the way you divide, the way I was taught takes up so much space. Nice to know.
This is the most ridiculously wonderful thing I've ever seen. Thank you TH-cam for suggesting this.
Damn, we are 10 days late in celebrating pie day!
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!!
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.
Don't forget that he used only ten fractions out of a literal infinite pool, ...
He made the mistake at 1/13
@@SGAMaddin It would be incorrect he didn't use all the numbers, and adding rational numbers give a rational result, unless added infinitely
here after finding out this is *actually* the value of pi
I finally understand how the digits of Pi can be seemingly all over the place. Thank you Matt Parker.
no smurfs were hurt in the making of this video :P
Your video is obviously 10 days late! Pi day should be March 4th
+Sam Auciello sorry, but wouldn't it be March 14th? at say... 15 hours? :)
+Eli Kübler-Ross Well obviously Π is 3.04
+Eli Kübler-Ross It's a joke from the video.
What is a chanber and how do I find one to go die in?
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.
I love math and among all the videos I've seen in TH-cam YOURS IS THE MOST INCREDIBLE OF ALL. Thank you for almost going mad with all these calculations. I surely going to subscribe to your channel e watch all videos about π.
To be very frank….you are the reason why i m happy right now
Really liking the consistent uploads. you're doing a good job man!
14:09 Four threes are twenty eight!
At least that was a seven.
+warpcore05 Wow! He was lucky that was a seven...
I've been waiting for this channel to exist
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
"Doing a Third the Long Way" should be your biography's title.
Never mind "Smurf Fingers" would be better.
"One man's battle with recurring digits."
+Eric Loesch Are you sure? I think "Smurf Murderer" is a lot better
+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.
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.
I love how happy he gets over dividing 1/17 in his head :D
I love the working out. Just an awesome example of getting results through hard work and persistence
I was looking for something like this really long time. Thank you for this video! :)
A real parker square that was. :)
+LarlemMagic I was about to comment this lol
GO FOR THE EYES, BOO!
Nice Rebecca Black reference in the first 5 seconds.
+Josh Hansen lol even he was cringing at it.
The editing absolutely makes this video XD
I’m excited to see what he does this year!
Next year's video: calculating pi while skydiving.
Calculating pi while eating lunch.
I eat kids Souls Calculating pi while putting out a grease fire.
+John Reynolds Calculating pi while defeating the foundation...
17:07 _"... admittedly using an actual computer..."_
what're you talking about, Matt, you _are_ an actual computer. you did the computation, you were the agent. you computed. you're a computer!
+ThoperSought oh yes!~ :P
we are all computers!~ ;-)
Gary Ferrão
indeed!
although, I feel like some of us are just calculators...
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.
Matt is so awesome i'd watch him divide and substract all day and not sleep in class
Remind me: March 4, 2018. The REAL Pi day.
+Nicholas Wright (Toothpick Nick) April 3rd...
+Josh O'fortune 22nd of July
Woah, I saw the 3.04 and thought "wait". Then I recalled that this is a slow series. I did not realize how slow though till I decided to try it. Between the fractions 1/173 and 1/175 it starts oscillating between 3.13 and 3.15, but it is quite awhile (around 1/579) before the digits actually round to 3.14, but it is still oscillating between 3.14..... (rounding down) and 3.13..... (rounding up).
+David Scott A properly weighted average of the last three terms gives a result of 3.14091... with only 10 terms (-1/19)
His excitement and sense of wonder are beautiful
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
You could call this attempt a "Parker square" of Pi
:P
No its just "Parker Pi"
+bob mike
I didn't even know she had one!
+nman rman DAMMIT YOU BEAT ME TO IT.
*malicious grin*
A Classic Parker Pie
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.
This guy is awesome, I wish he was my teacher. Thanks you for the content.
I totally forgot how long or short division worked after years and years of not using it. Thanks for the refresh.
1/19 the struggle is real lol
3:22 Why would you draw the "point" there? It looks like a multiplication symbol.
Iorveth AFAIK this is a thing in the UK
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?
It's not normal anywhere. Nothing is normal in Brexitannia.
Yeah, it's their thing. With a bit of discernment, you can translate it to the American way. Cheers.
Sorry, who uses a point as a multiplication sign? X has always been the sign that I've known... Or * for computers
just have to say i love your delivery
Great video, was never in my life so close to understand dividing :D
Sorry, but your first calculation is wrong. 1/1 = 0.999999999....
Actually it is. 0,9999999999999... = 1
it was a joke, pal
+jeromesnail Difference?
Except that he's rounding up after 20 digits, so 0.999999... would be rounded up to 1.000000... etc anyway
+verne ment no difference, I just misunderstood the comment. My bad!
14:28, "I should tell someone."
I'm dying.
Instructions Unclear...
...I ended up with Euler's Number.
This video single-handedly taught me short division. In my country we don't use this kind of division so that's why I hadn't known this version.
"Four threes are twenty eight"
You have been broken xD
Dan Dart parker multiplication
"Six times nine is forty-two."
Anyone else think he'd be a fantastic Doctor? As in Doctor Who...not just like a doctor
+DraconianDragon hmmmm
+DraconianDragon MATH DOCTOR
+DraconianDragon
In fact he has neither confirmed nor denied that he will be the next doctor. So there is hope!
Its sort of a Schrodinger box of the Doctor.
+mr_os a Schrodinger Tardis?
i was literally just thinking this. something about his speach patterns.
For some reason watching you divide fractions made me happy
i love how he said, "and we carry the nothing"
The sound of chalk legit sent a shiver up my spine.
+Lunar Dancer On the TH-cams, people seem to call that ASMR
+Jacob Wakefield Chalk on board is normally not associated with a GOOD shiver up ones spine
I love how you keep doing things that make you get the real circle constant, pi/4, and then insist on multiplying it to get the weird culturally significant value of pi.
Amazing. Never knew you can get Pi out of prime numbers. Thanks for great video.
It's fun to watch someone so passionate about mathematics.
You were inconsistent with your little jump on the first subtraction. Earlier on, you said that you would round up 6's, but then you failed to do so for 2/3. Of course, that's what the subtraction would have given you, but still.
Well spotted! I should not have been inconsistent; I reckless added the rounding policy partway through the calculation.
+standupmaths You also recklessly replied to that comment and forgot to transform "reckless" into an adverb. But hey, this isn't Stand Up English!
I love how he didn't even respond to your comment.
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.
No you're wrong
@@zoellazayce6796 compelling argument
@@Supertimegamingify I must agree
Ye, he forgot to round the 20th digit, i think in all of them
@@henriquemesquita5692 no
You do what i have always wanted to do since i was a kid, having fun doing math. I love math, algebra more like it, and would love to be a mathematician one day
here to find the full answer to pi. thanks matt!