Can we calculate 100 digits of π by hand? The William Shanks method.
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- Опубліковано 31 тра 2024
- For Pi Day 2022 I used the same method as William Shanks and we got π = 3.14159265358... you know, etc etc.
Huge thanks to my patreon supporters who make this video possible. Join in and you can also help enable my ridiculous ideas: / standupmaths
And if you are a patreon supporter and would like a piece of my working out: let me know! forms.gle/RsuU3dY1ZxG7hKEJ7
Volunteer to help out next time here: forms.gle/ypGENWgivE1WMTZZA
See more letters that Shanks sent the Royal Society over on Objectivity:
The Mathematical Spammer - • The Mathematical Spamm...
And I do some more maths about Shanks's other work on Numberphile.
Reciprocals of Prime Numbers - • The Reciprocals of Pri...
Thanks to Kepier School for letting us use their hall. kepier.com/
The human calculator volunteers were:
Anitej Banerjee
Sam Basak
Thomas Beauchamp
Diana Bergerova
Lauren Billett
Sophie Bleau
Jasmine Burgess
Nick Campen
Hannah Charman
Matt Clough
Kelsey Hewitt
Max Hughes
Ben Hughes
Deanna Judd
Jeremy Kew
Christian Lawson-Perfect
Sophie Maclean
Max McCormick
Hazel Minty
Tilly Pitt
Matt Robinson
Matthew Scroggs
Richard Shackleton
Katie Steckles
Victoria Sun
Milosz Szymanski
Adam Townsend
Clare Wallace
Thanks specifically to the Council of Calculating Pi By Hand who helped me organise the event: James Grime, Christian Lawson-Perfect, Sophie Maclean, Matthew Scroggs, Ben Sparks and Katie Steckles.
CORRECTIONS
- We got pi wrong in the 12 decimal place. Apparently π ≠ 3.14159265358868...
- Viewer einyen1 is a true Shanks: they spotted two other mistakes in the printed version of pi. Thankfully William Shanks had them fixed back in 1873: royalsocietypublishing.org/do...
- Let me know if you spot anything else!
Filming and editing by Alex Genn-Bash
Additional filming by James Hennessy
Music by Howard Carter
Design by Simon Wright and Adam Robinson
HIDING IN THE CREDITS BY T̸̝̉H̵͘ͅĖ̸̯ ̵͕̆M̶̙̉I̴͈̅GHT̵̠̀Ẏ̷̳ ̵̘͑J̶̼̭͗Ì̸̼̘G̶̳̈́
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b... - Розваги
![The biggest hand calculation in a century! [Pi Day 2024]](http://i.ytimg.com/vi/LIg-6glbLkU/mqdefault.jpg)
![The biggest hand calculation in a century! [Pi Day 2024]](/img/tr.png)
As a kid, this is what I used to think mathematicians do, just endless long division
as long as you were a kid long, long ago, you were correct!
In Shanks time, they did
Calculus was described to me as "It's like the math you do, but with bigger equations." And I thought, "well that's not so hard, you just use order of operations to reduce it!"
Same
@@RubixB0y funnily, that's the kind of thinking that's a lot closer to what math is about!
The Parker Pi is a very fascinating number. It changes its value every year.
I laughed.
the real question is if parker pi will ever converge to pi. i suspect it won't, but its fascinating nonetheless
@@feronanthus9756 I think the goal is that, given enough data points, the Parker pi will average out to pi.
That's because the Parker circle changes how many sides it has every year
if you circle the parker square, you’ll get the parker pi
I'll be honest, Keith the Head Librarian at the Royal Society is the most librarian-looking dude I've ever seen. 1:50
That's just Tom Scott with glasses and a wig.
librarian-looking fellow**
There's a whole channel featuring him in the Numberphile universe! It's @ObjectivityVideos
I really suggest everybody to check out the Objectivity channel by Brady, really interesting stuff and Keith is a regular there.
I imagine he walked into the job interview for that position, and they took one look at him and said, "you're hired."
It is actually really amazing the proceeding ended up on page 318, as he devoted most of his life to reciprocals of primes, and the first digits of 1/π is 0.318...
Ah, so it all works out in the end!
I admit that was kind of cool
I was just wondering why the digits of 1/π were so close to the digits of π (318 vs. 314). Then I noticed that π was kind of close to the square root of 10...
@@renerpho engineer moment
@@denny141196 /r/onejoke
Matt: "A room full of people calculating!"
Me, having watched plenty of Matt's other Pi Day videos: "Have you implemented error detection this time?"
Yes, but it used the Parker method, so the results were as expected.
This needs to be properly reengineered for next time, with cascading/parallel computing and error checking built-in. The process is the fun part. I love how some teams came up with clever solutions.
Yea no offence to Matt but the huge bits of paper method that it started as looked a real mess to organise. I like the guy's method where they were passing each digit along and agree they need some error checking as they go to make sure everything is on rail. And finally the adding up and final division needs to be happening within the process if possible not a scramble at the end! And additionally it would be nice if they could get into the former boarding school for a fortnight to break the record next time! They only need to be correct to less than 600 terms to beat it.
To be fair, it's absolutely the best method he's tried yet. I'm sure the natural sciences solution next year can get to 700 digits or so.
@@jackwilliams7193 Yea it seems like being off target is part of the entertainment each year. If we had it right one year it might put a dampener on future failures!
@@kailomonkey I'm unsure it's possible at all to do the final summing up as part of the process. The issue is that for summing/subtracting you need to start with the final digits, and work your way backward to the leading ones.
I don't think there's been a lot of research into emergent parallel computations in collaborative tasks
And thus is demonstrated the original meaning of "computer": a person who performs large scale computation.
I'm pretty sure everyone knows that
Those students are hugely impressive, not just for grasping what they're doing in the first place, but for coming up with clever solutions and shortcuts and organising them into a bafflingly complex rube goldberg production line of calculation. Guessing some of these students will go on to become expert programmers
If those people were locked in a room together for enough time I think they could prove the Riemann hypothesis.
@@vigilantcosmicpenguin8721 If you lock me in a room alone for long enough, I will eventually come up with a proof of the Riemann hypothesis. The proof will be wrong, of course (incomprehensible, actually), because I went mad from being locked up.
@@vigilantcosmicpenguin8721 lmao not even close
@@pepega3344 "Given an infinite amount of time blah blah blah..."
@@pepega3344 Hello person no one talks about (we don’t talk about Bruno)
7:53 I just love how the book says "Value of PI = 3 .". As an engineer, the book could not be more right
3=pi=sqrt(10). Therefore 9=10 (approximately).
I prefer the idea that pi is 3 and a bit
All those other digits are simply decorative.
It's irrational !
@@cH3rtzb3rg 2.3 + 2.3 = 4.6
2 + 2 = 5 (approximately)
I kind of want to see the average of all of Matt's attempts at calculating pi... like to see how accurate it's gotten over the years or something.
This would be interesting
I was curious about this too… So I re-watched all of them the current average is 3.18438257025287 that is the most precision google sheets would give me, strangely it’s only that high because of last year when he “counted atoms” if you take that out it goes down to 3.12159916754859
Pi day as an excuse to learn about parallel processing is a pretty good idea. It doesn’t sound like this is where it started, but I think it was a good development. First come up with the algorithm to parallel the computations and fact checking, then come back around to workplace design and how to physically layout a workspace to enact that algorithm. Microchip design in macro, or factory design in abstraction.
It was really interesting to see that sort of algorithm being demonstrated with humans as the computers.
oh this is such a great description of the video!
It's funny how you mentioned factory design - because I had to think about Factorio.
One of the key limitations of Factorio is that it processes the game world one "chunk" at a time (Minecraft does that, too). IIRC, one chunk is 32x32 squares, and transferring resources between chunks can be a serious bottlenecks in megabases (huge bases containing 100,000s of components and millions of resource items).
Now, there's another way to compute pi, namely pi = 2 + 2(1/3) + 2(1/3)(2/5) + 2(1/3)(2/5)(3/7)+.... One of the ways to compute that is to compute 2, then multiply by 1/3, then multiply that by 2/5, etc, and to add all of those together. Another is to fill an entire array with 2's, and repeat the following steps:
- multiply each entry by 10,
- add n-1 to the (n-1)th entry if the nth is >=2n-1, subtract 2n-1, repeat this step until it isn't,
- add n-2 to the (n-2)th entry if the (n-1)th is >=2n-2, subtract 2n-2, repeat this step until it isn't,
- ...
- add one to the first entry if the second is >=3, subtract 3, repeat this step until it isn't,
- output the first entry and set it to zero.
That's essentially some carry routine working with values like 1/3, 2/5 etc. instead of 10 and outputs some numbers like 30, 13, 11, 5... which have to be carry-corrected again (this time using regular decimal carry) to 31,4,1,5, and so on, for about 0.3 decimals per array entry. All computation involves small numbers which fit inside a single CPU register, which can be seen as a "chunk" in arithmetics.
This type of reasoning was (still is?) used to design "efficient" office spaces.
@@imacds Wow I wouldn't have thought of the office space application but it makes total sense
I'd just like to reiterate that the value in this project is defined not by the precision of their final result, but by the experience and lessons learned along the way. It's easy to look at their 11 digits of accuracy and call the project a failure, but I'd hope that everyone involved would look back at the process involved and remark on the value of that experience.
I'd just like to iterate that the value in this project is exactly defined by the precision and accuracy in the final result, albeit using a different and altogether more mathematical meaning of value.
@@igrim4777 touche
@@sk8rdman Glad you took my comment good naturedly. I thoroughly agree with your original comment. Two days to get only 11 digits--but to get 11 digits at all! So much co-operation and integration of various methods and subgroups in such a fascinating and engaging experience, you're right, _there_ is the real value.
Fich dich your comment spoiled the video by telling me the ending
hello? SPOILER ALERT????
This is my 7th favorite way out of 22 to calculate Pi. Cheers!
This is my 113th favorite way to approximate pi out of 355
The feeling is reprisical.
I hope you're serious about that and you really made a list.
Christian, you are close !
Cliff86, you're closer ! LOL
This has to be the most successful pi calculation Matt has ever had. Bravo!
I much enjoyed seeing those young folks working together, and having fun with Maths.
Is there some irony on the fact that Matt didn't calculate it himself this time?
I went back through all of the pi day videos so far and counted the number of correct digits in each one. This is definitely the most successful one by a considerable margin. 2nd Place goes to 2018's video with 6 correct digits, 3rd place to 2020's video with 5 correct digits, 4th place to 2015's video with 3 correct digits. All the other videos are either 0 or 1 correct digit.
@@spatialwarp huh 2015 on that list is surprising. If I remember correctly, even years are formulas worked out by hand, and odd years are using things like probability and physics properties and physical measurements to calculate it. So you’d kinda expect the even number years to be more accurate on average (since the main sources of errors are issues working out the numbers and not like, random gusts of wind).
But, apparently using a pendulum was good enough to get into the top 5?
I tried this method a year or more ago, to compute 20 digits. I carried 4 or 5 "guard" digits, I did everything by hand, and I actually got 20 correct digits.
Having gone through that, I would definitely *not* try 100, let alone 707 digits manually by this method.
Kudos to Wm. Shanks!
And to Matt & his team!
Fred
I thought it was interesting that you had a lifeguard there. I did not realize that calculating pi by hand could be so dangerous.🙂
This would’ve been the perfect opportunity to use the term computer to refer to people doing computations.
He did so.
@@michaelsommers2356 Time stamp?
@@renerpho You can find it as easily as I can.
I rather enjoy how much this process resembles optimising computer code. Thinking about parallisation is always hard, and the idea of passing half-done terms down the chain so people could start the next term before the current one in particular is a lot like making software use pipes.
Indeed! Scroggs and I were talking a lot about how often we could fork, and started referring to the volunteers as processes
@@ChristianPerfect That's great lol :D
@@ChristianPerfect "processes" 🤣
But honestly, yeah when one does something by hand, one often get glimpses on how one can further optimize complex computations!
William Shanks was the Matt Parker of his era. Great job everyone! I got a cool history lesson and entertained while listening to a Bruce!
Does that make Matt a Parker Shanks or Shanks a Parker Parker?
@@whiskeytuesday Now, if Parker were a Shanks Shanks, that would mean that he was a Shanks, but the records got lost.
I just realized, "Oh heck today's Pi day, I bet there's a new calculating Pi by hand." Then I looked it up and here it is, thank you so much.
It would have been useful to chat about the origin of that equation for pi/4.
When I stopped teaching math I thought I wouldn’t ever hear things like this again. I never anticipate subtitles that keep writing “pie” for pi and “crimes” for primes. How fun!
A video that is 33:14 in length. Very satisfying.
Wow i just noticed it
He should do a summary of this video for 3.14 minutes length.
Why not do the divide by 25 as a division by 100, basically shifting a decimal point, and then a multiply by 4. Simpler, and while it is 2 calculations it is also a lot easier to do, plus the multiply can be easily done over the long division.
Indeed! We did this 👍
@@Alsadius Matt is just being so coy about it at 15:10
This was my intuition too.
But division you do from left to right. Multiplication from right to left. So you have to calculate your first term in full (and probably some extra digits, because the error term will multiply as well)
@@ralphvangelderen68 You can do multiplication left to right? Unless you mean exponentiation?
I just love how jazzed all these math nerds are about this project. This is fun for them.
To generate the corrected version of the table from the book in Unix, including the line length and spacing:
echo $(pi 708 | tail -c +3 | fold -w 5) | fold -w $((12*6))
It's actually the "44193" earlier on the same line that's wrong, should be 44065.
Great example of tackling multi-threading, asynchronicity and optimization. Each person is a thread and you need to figure out a system in which no one will have to wait for another person to complete their calculation. Also breaking down difficult problems into simpler (dividing 239 twice instead dividing once by 239**2 and calculating 10 digits at a time) and asynchronizing even that is just so cool.
Its also about not being able to trust outputs and making error-resistant systems.
The penmanship of those books is absolutely insane, and it's not on ruled paper, that's nuts
Hey Matt, just wanted to say that this is my second year teaching mathematics. Today I used your first method for computing pi (1 - 1/3 + 1/5 - ...) during class. My students (12 - 13 yo) loved it! Thanks for being such an inspiration, and keep up the good work!
That is awesome! I wish I had a teacher like you back when I was in school
What I could not remember (and we never did this in my class that I recall), is WHY this method gives a value for pi - I think there is a YT vid that shows where there is a relation but dont have time to find it!
@@highpath4776 if you're talking about the method I mentioned (the one with the fractions), it actually computes pi/4. I don't remember if Matt gave an explanation for the method, but I guess you could rewatch his video.
@@absantos I sort of remembered how it worked (I was never taught arctans), and worked out from first principles how the simple definition of pi can be divided into a quarter circle and then found from effectively trianganglaur segments approaching a closer approximation to an arc rather than a straight line (basically an overestimation, less a smaller overestimation , etc until the difference oscilates to the mean)
I hope you multiplied by 4 at the end!
Now I just need an explanation why Machin's formula produces pi and where does 1/5 and 1/239 come from!
because the infinite sums are related
The wikipedia article Alsadius linked explains it very well. The TL;DR is that it's an algebraic combination of the following two formulas: arctan(1) = pi/4 and arctan(a/b) + arctan(c/d) = arctan((ad+bc)/(cd-ab))
@@Alsadius so it is because arctan are segments of a circle ? as in a large number of triangular 'wedges' so you add a large triangle( which is too big, so take away a smaller one to correct the error, then back and forth each time , to get the curve from a number of straight edges ?)
@@Alsadius It's all about optimizing the algorithm. You could call that Machin learning.
With i^2 = -1, note that (239 - i) * (5 + i)^4 = k(1+i) for a real positive k. Take the arg of both sides: the arg of the right-hand side is pi/4. Then use arg(x*y) = arg(x) + arg(y) on the left-hand side to get 4 atan(1/5) - atan(1/239).
I'm sure William Shanks would be proud of the work y'all did.
Yes! And I'm sure he'd have a few tips too... 😁
You didn't get the whole pi, but damn it all if you didn't try! I'm very impressed by the commitment and honesty of these young mathematicians. The way I see it, it's not about being right all the time, but how you handle being wrong, to measure the caliber of a mathematician. Amazing sportsmanship to you all. The future is brighter with people like you!
Happy pi day!
I would imagine the time frame to undertake this must be a function of the accuracy achieved ,
9:18 The fact that digits after the error clearly show that the error was in his original hand calculated work. If the error was only in the typesetting, it would have been just a single erraneous digit in the print and the rest of the digits on the same page would have been fine.
707 digits! (okay well 500 or so then) Shanks was so close to the 6 9's in a row at digit 762. That would have blown his mind.
He probably would have stood there and said, "We've made a horrible mistake some where!"
Probably even after seeing the first two 9's of the set of six that were about to emerge,
@@peterkelley6344 Nah, you'd expect to have seen seven pairs of consecutive 9s in the first 700 digits - on average it'll come up once in every hundred digits (give or take a fencepost error).
@@rmsgrey 3 in a row sure. But 6 in a row is very unlikely. The next 6 in a row (also 9's) is at digit 193,034.
@LIES
Would he have generated those six nines?
Shanks made an error at digit 528. Doesn't this mean that every succeeding digit was also wrong? If so, the likelihood of the six nines appearing is very small.
🍌🙂
It appears that the first person who would have stumbled upon that coincidence would be D.F. Ferguson in 1947. At that point he was using a desk calculator, so the discovery may have been a bit less astonishing.
Happy π-day, Matt! This amazing way of working together reminded me of Gaspard de Prony’s « Manufacture à logarithmes ». If you want to give it another go for a future π-day, I suggest you do it in the circular « Salle π » at the Palais de la Découverte in Paris. For the World’s Fair in 1937, the walls were covered with William Shanks’s 707 digits. After the mistake of the 528th digit was discovered, they corrected the 180 wrong digits in 1950.
Wow, an entire room dedicated to pi. That's got to be an amazing place.
i've been waiting for that "well, we've got it with error less than 10%!"
Happy π-day everyone! 🥧
n day
If I like this comment it will no longer have 42 likes so I wont like it
Congrats on 1M subscribers Matt!
I think it's perfect how you got enough digits for it to be the best you've ever gotten while still being disappointing. Just means you'll have to break the record next year.
This is my 1st pi day since I discovered this channel. I was really excited for the video, and I enjoyed it a lot.
I presume that organizing everything and keeping everyone on task while maintaining maximum efficiency would be FAR more difficult than doing the actual arithmetic. This was an outstanding effort, and it’s fascinating to watch!
Such a wonderfully loopy way to spend a weekend. Brilliant organization and oodles of cheerful hard work by the dedicated teams of human computers. Well done to all!
What a cool video! As always, the happiness of math on your voice is clear... and that is awesome too.
William Shanks DID NOT uses the Gregory/Taylor Series for Arctan. He used Euler's suggested accelerated version of Arctan where m = x^2 +1 : arctan(1/x) = 1/sqrt(m) * (1 + (1/2 * 1/3m)+((1*3)/(2*4)*(1/5m^2))+((1*3*5)/(2*4*6)*(1/7m^3)) +... ) , Believe Me , The Indefinite Man.
Google search serves up the (1/5,1/239) tale. Can you provide a reference to the other?
@@DouglasKubler Hi Douglas. The general tale is correct. He did use Machin's formula, 4 x atan(1/5)- atan(1/239). But, rather than compute the arctan of each of those with the Taylor series, he used the accelerated version that Euler devised. You still need an inhuman amount of terms with Machin to get Shanks' decimals if done with the Taylor series - one must accelerate. Shank's books all talk about the acceleration methods he used. There is an acceleration method named after Shanks I use everyday. Shanks was an accelerator, and definitely didn't plug values into the Taylor series like a pleb :) (all of Shanks books, especially rectifying the circle, talk about it.)
And to think I memorised more digits of Pi for a competition at school than there was ever known at the time, and more than they’d painstakingly calculated over years of hard work
Pi is like dinosaurs. People hardly knew anything about the subject but then all of a sudden the interest in the topic grew exponentially.
What a wonderful effort and I think it was worthwhile for everyone involved. For myself I learned something new which is worthy of my time, and your group's of course. What was most interesting out of this is the possibility of working out how Shanks did the original calculations to begin with. Good show everyone. Cheers from Canada.
I've recently been cutting a bunch of my Patreon subs for financial reasons, but honestly this made my day and I will happily continue giving my money to this channel. :) xxxxx
Love to see the ways people were parrallelising their tasks! Very satisfying.
The closed captioning does a different interpretation of Houghton-le-Spring every time he says it. In a video focusing so heavily on transcription pedantry, it's always refreshing to get a look at the opposing perspective.
I am truly impressed at how very much the cc is unrelated to the words being spoken at times
This is always the highlight of my year! :-p
With this method, it’s not really clear (to me!!!) what you’re calculating, exactly, and how this relates to Pi.
Your other Pi-Day videos do a great job at that. Hopefully that’ll still be possible with a follow up video.
All the best, Matt!
This is probably the most wholesome video I've seen in a long time. Love the entire atmosphere and would've loven to be there :P Being in a super competitive environment right now, whenever you get people together to do recreational maths it restores my faith in humanity ;)
The sheer number of calculations, even if each individual one is likely to be correct, means that getting the whole thing right takes a miracle.
Speaking of which, Shanks' consistency in getting multiple hundred correct digits is all the more impressive in light of how painstaking this process is...
Seeing all these young people having fun with maths fills me with joy and optimism for the future in this world. Sorely needed cheer up, thanks for this. Happy Pi Day!
So great. I just got obsessed with Objectivity and Keith in particular and here on my favorite way to celebrate pi day he features heavily :)
Would be very interesting to have each piece inputted into a program running the process in parallel with both the actual numbers and the given numbers to see exactly where things went wrong next time, such a great video! Always had so much respect for those old mathematicians
It's nice to see you again on half-τ day. Really wish you'd celebrate the actual day in June, but I do understand how important the halfway mark is to some.
Celebrating the half way mark, and failing, is a very Parker thing to do.
C=2 π r = π D
Released at 3:14pm. Nice! happy pi day!
Not just that! 33:14 minutes long
@@rq4740 didn't catch that. Just going to take it in now, didn't have time earlier.
Here's my paper on the calculation of e.
"I have calculated e to be 2.718281828... obviously it must continue 18281828 ad infinitum. QED."
Ah, nice and definitely irrational.
2718281828 is just a sequence somewhere in the tail of pie, can't fool us :)
You have to admire these young mathematicians, their hearts are pure, their reasoning unclouded. I would be happy to call anyone here brother or sister. They are just starting their lives, but have already discovered that teamwork feels awesome. Love to all, William
Glad to see that a splinter team managed to modularize the calculations, dealing with them in groups of ten digits at a time. That's the correct way to handle large computations like these.
I have a slight desire to program this so that the algorithm does exactly what a human would working it by hand. Like, do the long division IN CODE and store the result in a string to the first 100 digits. iterate over x number of terms... then add the strings together as if doing adding on paper... It'd be basically doing everything using BIGINT, but I'd have to code it up..... could be fun and generate a lot of heat.
Even easier than bignums, it sounds like you can keep an accumulator for each division, multiplication, etc. operation in progress; and just cycle between them, bringing in the next digit from the dividend, caching multiples of the divisor, and putting out the next digit of the quotient as you go.
Bonus points for doing it on an arbitrarily simple machine e.g. AVR, Z80, 6502, ENIAC, etc.! :P
Excellent idea!
@@T3sl4 Extra bonus points for doing it on the digital camera they used to film the video - proving that the camera was Turing complete, and thus that that they were breaking their own rules.
(Concept by fellow commentator Benny Blue, but I had to add it here because it fits that idea nicely.)
We did it in school as one of the assignments in our programming classes, only with 10000 digits. We even used the exact same formula. No extra libraries, just explicit arithmetic on long arrays of digits.
Of course, the teacher also asked to estimate the number of digits we should actually use to make sure the first 10000 are exact (after all, it was thousands of operations with finite precision).
Update. I have "Long Multiplication" done. It's programmed in code the exact same way I would do it by hand. in testing, I have basically unlimited numbers to multiply and steps. I was getting 200 digit products out of the code that matched results from Wolfram Alpha. I think long division is going to be a bit harder to implement, but it's actually very fun.
2:25 Keith's refusal to tuck the tail of the tie into the keeper loop is so on brand
It might be an older tie that doesn't have such a loop.
Really adds to the whole aesthetic.
A very happy Pi Day to you all. Fantastic video and attempt as always Mr Parker. What a beautiful constant.
It’s like an automaton of people working in perfect sync, crunching numbers in analog, it’s amazing to see.
This is how I'm reminded that its Pi Day
This whole day, at the back of my mind, I knew March 14 was special. Is a birthday? No. An appointment on my calender? No...
Every year
I never forget it because it's my birthday. And in fact it was Albert Einsteins Birthday too^^
@@job3rg It's also the day Krabs fries
I always look forward to the annual redefinition of Parker Pi. If in future you wanted to *actually* get 100 accurate digits of pi, maybe try the chudnovsky algorithm you used a few years ago as it converges really quickly. In the meantime, keep making these funny, educational videos I love a lot.
You would be lying if you say your heart didn't skip a beat at the smile at 21:39
I really appreciate referring to William Shanks as they in your description! Thank you Matt!
What an inspiring group of people!
Would it be easier to figure out one of the very far terms of the sequence and then multiply your way back up by x^2 to the first term? I would expect that multiplication is less prone to errors than long division. One problem with this method could be determining how far is a far enough term (and of course division by a huge number might be cause more errors too).
The problem with that might be figuring out to how many digits that far back number is needed, because you will definitely need more than 100 digits when multiplying back up. But maybe just going for a little more than 100 _significant_ digits will already assure full precision to the end.
We did try something like this but found that a single long division by a huge number takes hours and is extremely error prone!
Yeah, we tried repeatedly squaring 239 to jump ahead a few steps and set off another branch of the process, but either multiplying or dividing by a large number of digits is way slower. So that's why we tried the table of people just dividing by 239
@@adamtownsend3744 I guess that's why they call it long division and not short division.
The fact that it was division was power on 5s that would be useful from the fact that 1/5 is precisely known. So multiplications can be done accurately.
Awesome! Your Pi day videos never dissapoint me!!
Such a nice collaborative effort! Maybe we can learn from it that it is often best to go for a smaller problem and try to make sure it is correct and then expand on it. Starting right away going to 100 digits is really very ambitious. Pretty good that you got more than 40 digit for the second term.
Love that it's presented as a failure but realistically when would you ever need more than 11 digits of Pi lmao
To impress your friends by knowing that pi is roughly equal to 3.14159265358979323
That's how much I know
@@silvervaliant I know one digit more, get wrecked
@@CK-ceekay didn't post, doesn't count.
The guy with the neater method, and include the adding up in the people machine throughout if possible, and I think you'll nail 100 and then some next time.
"Your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should."
This channel content is amazing, congratulations for the quality
Wouldn't it be great if this is the video that pops Matt over 1M subscribers?
Edit : How about that! Congrats!
Little question: How do you know the precision of pi that you're going to end up with, assuming perfect calculation? As in, how many terms for these series do you need to compute in order to ensure you can get 100 digits of pi out the other end? and how do you find that number?
If you were trying to find pi to 5 digits, you could compute terms until you got a number that starts off with, .00000[stuff]…. The actual stuff no longer matters as it won’t influence the first 5 digits. As for knowing when that occurs you can use some guesstimating and number theory tricks to narrow down your search.
I don’t know how they did it initially but I’d guess they did the first 102 digits of each term and stopped when they were all zeros. Then, he explained at 23:10 how they did it more efficiently at the end. They calculated the first ten digits of the first term, then the first ten digits of the second term and so on until they had only zeros. Then they did the same thing with the next ten digits.
I wondered this too.
If you imagine each number they are generating, it's x/(x^a), and the 'a' (in the divisor) increases over and over, making the number smaller and smaller.
Let's use the 239 example.
If it was just 100 _instead_ of 239, then the calculation would be straight forward with some standard arithmetic of exponents:
100^(X) = 10^(2*X) = 10^100, where its now easy to see you need 2*x=100, or x=50. That would be 50 factors necessary.
We're actually dealing with 239, not 100, but 239 ~= 100^2.39, so:
239^(X) = 100^(2.39*X) = 10^(2*2.39*X) = 10^100, thus 2*2.39*x = 100, or x = 20.92. Thinking of the 4 in the numerator, we may need to bump that up from 21 to 22; however, 4/239^2 is less than 10^-4, so our answer shouldn't change until after, or maybe at, the 4th significant digit, meaning you shouldn't need to go above 21.
It's worse for the number 5, tho, because log(5)=0.7, so x=100/0.7/2 = 71.4. And then there is a 16 in the top, so that's another factor of 5^5, maybe 2 factors to be safe.
Anyone else reading this? Does this look right? It makes sense to me....
EDIT: Edited for clarity.
@@kindlin you indeed nailed it. I initially wanted to go into more detail in my former post but I was at work and on mobile so I simplified it in order to show the general concept.
Great work!
Gods I love this. Never change Matt, you make every Pi day as special as the number itself.
Love seeing so many people passionate about maths working together, it really is amazing and its wonderful knowning so many people love numbers.
Another great pi day video, love seeing them every year !!
Watching in the early hours of 15/03/2022 in Australia. It just hits different the day after. Matt how could you do this to your own people? Parker Pi Day 🤷♂️
I'm pretty sure he's from WA where it is still the 14th
You’re right, he is from Perth. Still wish I could experience the Pi day video on Pi day. Very WA though, perfectly timed to exclude east coast Aussies. No hate.
he uploaded it at 3:14 pm GMT
Same!
@@emilchandran546 I don't know much about Australian rivalries, but it'd be hilarious if that was done on purpose as a slight to the easterners.
Only a mathematician could spend a weekend with people from Houghton without finding out how to say Houghton. Or caring.
"you're going to make a number joke now aren't you?" (6:56) I still can't tell if this was said in hope or in fear 😂
Matt, you're absolutely crazy but watching your videos is so much fun! Cheers from germany!
damn this looks fun as hell! My heart SANK when I got to the result part :(
Congrats on being within 1% of 1 million subscribers, I know Steve Mould got it first, but you always did the long hard work and deserved it more 😁✌️
I have always wanted to do the calculations by hand, I am not sure about your method, but I loved the video!
The Parker π, almost most but not quite, just like the Parker square. At least there's consistency in Matt's videos, consistently entertaining.
Amazing effort by all of the volunteers 👏
I have about Pi number of Matt videos posted at the same time in my feed. I see what you did there.
An amazing effort. Well done!
Interesting to see this calculation workflow evolve between 2022 and the 2024 effort.
_Me, who knows the 20 first digits of pi, looking at the description during the video_ : Oh no...
Another entry for the second book of 'When Maths Goes Wrong'. 😀👍
Fascinating how people adapted the process specifically to include better error-checking. Mr Parker, in your great video with Dr Fry at the Shard there was a bit of dialogue, almost aside, about how trig tables were first calculated. It got me thinking about Ptolemy and I wondered whether he enlisted his students in crowd-calculation just as you've done here. It would be great to reproduce some of that process. A tough realistic version would have a no-zeroes rule and no Arabic numerals but it wouldn't have to be so extreme. I think the basics are inscribed polygons and the formulas for half / double angles and then something about interpolation which I don't yet understand. Could be fun. Anyway, thanks for your great inspiring videos.
I just love those automated subtitles: "we have the reciprocals of crimes"...
The Parker-square value of Pi
4
Parktan?
Hi Matt. Is the tree and untested code coming soon? Based on last year it’s the highlight of my post Christmas spiral.
Great video. I love this sort of thing. Just for fun I wrote a little 10 line program in Python to calculate pi to arbitrary precision (essentially just keeps spitting out the next digit of pi until you lose interest) using a continued fraction method. Running on a raspberry pi (naturally) it calculates 5000 digits in about 1.2 seconds.
Classics Parker PI calculation.
Where the effort matters more that the result.
But this was cool... Really shows how difficult it is to calculate PI to over 500 ditties.