Calculating π by hand the Isaac Newton way: Pi Day 2020
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- čas přidán 17. 06. 2024
- So it turns out that this year π = 3.141591678589793935225
Thanks to Ben Sparks, Deanna Judd, Max Hughes and Zoe Griffiths!
Huge thanks to the National Trust for letting us film at Woolsthorpe Manor and much appreciation to the on-site staff for being endlessly helpful. Next time you are near Grantham, England you can visit Newton's house for yourself: www.nationaltrust.org.uk/wool...
Thanks as always to Jane Street for being the Stand-up Maths channel principle sponsor. This would not have happened without them. www.janestreet.com/
Here is the full working out for the derivation of Newton's expression for Pi, including how to get a general expression for the sum: www.dropbox.com/s/jndc4y12f2z...
And here are the full Think Maths teacher resources, that includes this workings out, plus further notes for teachers and a worksheet for students: think-maths.co.uk/standupmaths...
Ben's method for calculating the square root of three can be seen on the second channel: • Calculating root 3 wit...
Signed copies of much of the working out (one featuring a Parker Square) are available on the Stand-up Maths eBay account. All money goes to charity. www.ebay.co.uk/usr/standupmaths
SCANS OF ALL WORKING OUT!
Any missing working out is for a term which a school did for us.
www.dropbox.com/s/0hp70cvchui...
CORRECTIONS
- Nothing yet. Let me know if you spot anything! (Or find where we went wrong, so very wrong.)
Thanks so much to all the schools who helped out! Names are below. If teachers want to find out about similar projects in the future, sign up here: www.think-maths.co.uk/sign-up
St John's-Ravenscourt School Winnipeg, Canada, Teachers: Morgan MacLennan and Lam Nguyen
Varndean College, UK, Teacher: Nicole Cozens
John Taylor High School, UK, Teacher: Simon Curzon
Cals College IJsselstein Netherlands, Teacher: Maarten Van Haaren
Whitgift School, UK, Teacher: Kathryn Coffin, Students: Paul Ajuwon, Mikaeel Toosy, Wei-Shun Fam, Ashwiyn Sekaran, Mr Lau, James Zhang, Artyom Boyorov
South Bromsgrove High School, UK, Teacher: Sue Rowing
King Edward VI Aston School, UK, Teacher: Andrew Russell, Students: Mohammed Ali Awan, Adeel Imam
Leftwich High School UK, Teacher: Sam Webster, Students: Harri Major
George Heriot’s School, Edinburgh, UK, Teacher: Gregor Dickson, Students: Judith Morrow, Euan Strachan, Isaac Browning
The Cheney School, Oxford, UK, Teacher: Padma Thealla
Thanks to my Patreon supports who do support these videos and make them possible. Here is a random subset:
Glenn Watson
Neil McGovern
John Lewis
Patrick Stover
James Hall
Kragar
Ron Hochsprung
Jordan Scales
Samuel Ytterbrink
Philippe von Bergen
Support my channel and I can make more videos:
/ standupmaths
Music by Howard Carter
Filming and editing by Alex Genn-Bash
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/products/5b9f...
Nerdy maths toys: mathsgear.co.uk/ - Zábava
The biggest error comes from the term 4, where it is 0.0000271[2]67361111...; this error is also present in the sheet (terms/Term04-02.jpg) where the term for that digit was subtracted but the digit itself was missing in the result. This term has a single recurring digit pattern, so a missing digit resulted in only a burst error in the final computation.
All other errors are in last three digits, so having this sole error corrected, the result would be 3.141592653589793 935225, not too far from the actual value of 3.141592653589793 23846264.... 15 whooping decimal digits were correct!
(By the way facial masks, if available, would have been much better way to prevent contagious diseases [EDIT: when you are working close to each other]. Stay safe everybody!)
The face masks thing should be clarified because we don't want to spread misinformation. Wearing a mask WILL NOT PROTECT YOU FROM CATCHING IT IN ANY WAY. It can however protect you from spreading it if you have already been infected
@@amandaberg6671 You are basically right, but in this particular case people were working close to each other (within a metre) and facial masks should have been worn. I should have been more specific...
EDIT: Okay I've edited the original comment to reflect this.
Yes - nice. I came to the same conclusion about the missing 2 ... but didn’t see your post before I posted. The fact that many digits after the wrong digit were correct meant that it was pretty easy to find - it had to be a term with a single recurring digit.
Good work! Thanks for spotting our mistake.
PS I’ve re-pinned your comment (edit: not tweet). If you edit it: it stops being pinned.
@@standupmaths Tweet?
“Does it start with a 5?”
“No”
I can relate
"We started to complicated. Does yours have 18 digits?"
@@kayleighlehrman9566 Matt, that's not how comparing numbers works xD
A classic Parker Moment
It bothers me a bit that Mr. Parker knew he was supposed to compare his doubling result to the calculation of a SQUARE of a previous result, viz. (2^29)^2. Yet he muffed it by reading his result for 2^59. Fifty-nine isn't just odd, it's a prime! 2^59 = A^2 has no solution for ANY integral A!
I suspect that this was a bit of "reality TV" scripting.
@@doodlegoat I love the extreme sarcasm here.
One day, matt will have made sooo many pi estimation that the most accurate method for calculating pi will be to average all of his poor estimates xD
Columini
So it would a parker square of a solution?
+
It will certainly the most precise estimate. I'm not sure about accuracy though.
Parker Pi
oh dear!!!
12:41 "Newton was a π-oneer...."
12:53 "Let's not go Matt..."
Newton was a "π... or near."
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Dangit you beat me to it
"A value that is close, but not quite"
I would call it a Parker-Pi
The π-rker.
The π-rker.
...but since it's pi by hand, I would call the parker hand over 1 foot.
Or, if you will, a Parker Approximation; correct only for an arbitrary smattering of digits.
So cool that he got integral signs built into his house as well
*Integrated* into his house.
@@crosswingrobots stop
As a reminder for the superiority of liebniz's calculus notation
Jia Ming yes.
@@jiaming5269 My thoughts exactly 😆
It's somehow comforting to know that a room full of full-time mathematicians had difficulty doing this.
Newton was inspired to calculate pi after a pineapple fell on his head.
I wish more fruit was falling on my head--
Then he said, "I'm a bit tired, I think I'll go and have a napple."
@@abdaniel487 he had such an incredible naptitude.
you mean a πapple
or a πneapple?
Or maybe someone threw a pie at his face
When you're standing on the shoulders of giants, you need to be careful going through doorways. 2:10
This is the sort of thing that drove Charles Babbage to decide 50 years of trying to build his difference engine was the easier job.
If you try a lot you will eventually make a big difference.
Fun fact: if you have 22 pies and divide them among seven people, everyone gets a bit over one pi.
*a bit over one pi pies. You forgot your units!
@@andymcl92 -90 quadrillion marks
If you have 1 pies and divide it among 2 people, everyone gets exactly a pi of a pie.
I see what you did there
22 divided by 7 divided by 32
This morning my sister mentioned to me that it's Pi day and my first thought was "Ooo, that means Matt Parker is gonna upload today!" 😂
Pi Day? I thought it was Tau/2 Day...
@@strehlow Absolutely!
Q: What was the most difficult part of this whole exercise?
A: Everyone using handwriting 3 to 4 times larger than normal so that the camera can see it!
I can relate.
The thought that a day of work makes 7 digits of pi yet an 11 year old can calculate 11 correct digits of pi in 5 minutes using the formula (square root of 2 + square root of 3)-(683499^2/10^14)-(27^2/10^11)-(7^2/10^12)-(4^2/10^12)-(17/10^11)
p.s. I discovered it
@@lemonheadgaming2378 You would have to be working very fast to do that in 5 minutes.
@@AAA-de6gt thanks i meant five hours
@@lemonheadgaming2378 how did you discover it?
This video, in the time it was filmed and posted, feels so surreal. It was close enough to the tipping point where we knew it was going to grind our world to a halt, yet the interactions of everyone is as if it was a normal day in a normal year, with people in close contact, high fives, no masks in a cramped space, etc.
Imagine Cambridge closing due to a contagious outbreak! That would never happen now
People:
High-five at 9:13
The virus:
9:19
LMAO that's great
lmao
Underrated
I saw this at 12:25
LMAO
The three stages of reaction I had to this video:
1. Ooh, a new upload by Matt!
2. Oh, it's 25 solid minutes of tedious maths...
3. Wow that was great and I thoroughly enjoyed every minute of it :)
you know how before digital computers the word "computer" refeared to a bunch of people to whom you always delegated the number crunching and whose job was to do calculations all day?
Because that is a lot of computers right there
Computer (n). Thing that computes.
You mean, before the electronic ones? I'm quite sure they also used digits, i.e. were also digital computers.
@@PauxloE you know... the good ol pre-Alan Turing days where the closest thing to a calculator was some cluster of cogs and the second best thing was some pearson with pen and paper
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Ahh, the good old days of 2020, when you could cram five mathematicians into Newton's study and have them emerge in relatively good health.
It was a Parker's Square of an attempt.
I bet he wishes he never met Brady. He’s not gonna live that one down.
Parker Pi
The *correct* calculation was just a square. The *incorrect* one was a Parker Square.
Piker math.
Thank you for posting this. I was going to be so disappointed if I had to do it myself.
Watching this 'collaborative maths' reminds me that about a hundred years ago there was a proposal to calculate a weather forecast by filling the Albert Hall with mathematicians (called 'computers') each of whom represented positions on a grid systems and passed their calculations to each other. Maybe an idea for a future video when it's possible to get enough people together!
If you had calculated the circumference of the earth based of your number you would have been roughly been 12 meters away from the right answer.
...assuming this is the only error propagating through the calculation (and this, ladies and gentlemen, is how you land in the Caribbean and call the native people Indian).
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Love the reference at 2:08. "If I have seen further it is by standing on the shoulders of giants." That is my favorite Newton quotation (even though he wasn't the first to say it).
Matt Parker, you are a treasure. The world is a much better place for your excellent, enthusiastic, hilarious math(s) outreach. Thanks!
Watching this video retaught me all of my middle school math, and actually made it all make sense. What a great video.
I was waiting for your video the whole day!
0:01 someone graffitied two integral signs onto newton's house probably one of leibniz's guys
Probably, since it was originally Leibniz's notation. Newton's notation just put a dot over a variable
@@JM-us3fr isn't that newton's derivative?
@Sai Sasank i guess that is the modern way to write, as far as I remember newton's derivative put a dot over the variable. And leibniz' derivative (this I am sure) is written as dy/dx
@Sai Sasank That notation for a derivative was invented by lagrange
@@JM-us3fr Ez integral
Absolutely amazing video. Brilliant setting, brilliant idea, brilliant (ish) execution. Great interludes to explain etc. Lovely!
I forgot about this! What a wonderful surprise.
Frodo lives!
"I forgot to carry a 1"
- Ah yes.. a classic Parker-pi
Finally. The video I've been waiting for the entire day!
One of the highlights of the year, always look forward to this vid
Never did I think that watching a load of people undertaking mathematical calculations I don't understand would be so fascinating.
Well done, and keep up the good work.
"I don't think i can salvage this- this is all- all wrong- I've gotta start over"
How do you tell if you're talking to a mathematician?
For some reason, this one (as opposed to other Pi Day videos) brought back a memory from high school robotics. We had an engineer as a mentor, and apparently he’d believed for as long as he could remember that PI is exactly equal to 22/7. I *really* hope he didn’t use that in any projects requiring high precision.
Watching you video is always a joy.
π brilliant! I love the maths commitment here. But... also, Zoe’s nails are on-point, and I feel this needs to be acknowledged.
I can’t help but watch this and hear the echoes of teachers in my head “WE DON’T DO MATHS IN INK! WE ONLY USE PENCIL!” Incorrect, dear madams and sirs, WE do maths in Sharpie!
hardcore maths in sharpie!
Wait what. We weren't allowed to use pencil at school except for graphs and stuff especially for exams because it isn't permanent
@@StrawberryLegacy We were supposed to do a pencil draft on yellow paper then copy our final answer in ink on white paper. Some of us had the confidence to skip the pencil draft and pen in answers directly.
oh. that's a Parker quarantine if I've ever seen one
I've been waiting for this video today!
Your videos are always entertaining.
i love that you calculate tau/2 by hand once a year every tau/2 day
1:00
So no one's going to point out the irony that Newton's house had the Leibniz Notation for the Integral??
I look forward to this every year.
Waiting all day for this
-Take the first three odd integers: 1,3,5
-Double them thusly: 113355
-Divide the last three by the first three thusly: 355/113
There ya go, Pi accurate to 6 decimal places!
i went to 9 and so pi is 5.099161887, accurate up to 10 decimal places
When this was uploaded we didn't realise how much we would be empathising with Isaac Newton stuck in infection lockdown and wasting time on unimportant digits.
Most solid math related high five every. Great vid
That’s great! Can’t wait for the next pi day. A yearly tradition now! :)
Newton was a πoneer
It hurts to read this as a Greek person. I read it as peeoneeer or poneer because in greek, π is read as pee and used just like p.
pure, unfiltered, and brutal cringe in the most fatherly humorous and face distorting sentence I have had the unpleasure of reading in quite some time
Pi on ear.
Back in 1975 or so, I had just found my father's university textbooks and gotten to the chapter about Taylor series. At that point I realized that I could calculate pi by hand using the Taylor series for arctan! I got to ~24 digits during a few physics lectures. :-)
A couple of years later I started university and finally got access to a computer. My first real program was a Fortran version of the same old algorithm, this time I managed 1000+ digits within my allotted cpu time.
Really a beautiful exercise, well done!
look at jane street go. well played lads! great guys, borderline geniuses there left right and centre. good to see they use it for good
I did not end up teaching maths-I got terribly close! I teach astronomy in a planetarium-and my only regret is that I cannot involve students in such wonderful things as this. Well, maybe someday.
I LOVE how he incorporates Newton’s “Standing on the shoulders of giants” quote at 2:10.
It is my absolute favorite quote of all time. Kudos.
I'm never taking calculator for granted ever again
Oh it's Ben Sparks! I loved his bit at Maths Inspiration, and it was great meeting you as well, Matt!
Thank god, i waited for this!
That‘s what happens if you allow nerds to socialize...
And i think it‘s amazing
Happy PI Day Matt!
Happy Pi Day! Hope you don’t go outside too much these days. You’re a treasure we can’t lose.
I just don't understand why everyone gets all bent out of shape when the calendar gets halfway to June 28. I mean yeah, June 28th is a very important date, but why celebrate it in such a half-assed manner in the month of March?
Phroggster We don’t take kindly to tau talk.
This post was made by tau gang
Even the anchor plates look like integral signs
no no no, the intgral sign we use today came from the facade of that very building XD
I figured that was intentional.
@@witerabid I would believe that, if Newton used the long S for integration.
@@wademarshall2364 That's why I put the "XD" at the end. ;)
'cuz Newton was graciously celebrating his rival's (Liebniz) superior notation /s
Gj Matt! :)
Finally my boy
"He had a lot of time with his hands [...] he wasted a lot of it"
Hahaha made my day
I'm rather impressed. I know for most "common" math we take it to 3.14 and they got that spot on. But I've heard for "most" math above that "common" math that people tend to take it to 3.14159 and they got at least ALL those digits right.
HAPPY PI DAY!!!
I noticed you calculated each number individually at the end. Since I'm prone to make mistakes that way I usually make easy combinations in such lists and pick pairs of numbers that make 10 like 8+2, 7+3, 9+1 ect.
This not only helped me decreasing mistakes, but also increased speed as I just have to count 1 up in the tens row for each pair.
Great video! Happy Pi Day!
I had my first participatory Pi Day today, and it was by accident.
I mean, I'm aware of Pi Day, but I always think of pies -- like dessert pies. I also didn't think 7-11 would be aware of Pi Day. Anyhow, I drove over because I wanted a pizza and it was already 9 pm, only to discover they DO care about Pi Day. A fully cooked medium pizza cost $3.14! Alas it was one per customer, but I was OK with paying the usual $7 for the second pizza.
So today was whatever the opposite of a Parker Square is. I forgot about Pi Day, and everything worked out better than expected in spite of that.
What was funny is that the store owner thought it was some sort of national pizza day. He had no idea it was in any way related to the number pi until I explained it to him.
It was the first time I participated in pi day too, other than seeing the videos the day after and realizing that I missed out on the pi day specials again. The grocery store (Krogers) had their $9, 14 inch, 41 oz., "Deli" pizzas for $3.14, and you could buy up to 5. So I got $45 in pizzas for $15.70. One pizza like this "Deli" giant is more like $25 in a pizza parlor. But what I could not figure out was the astounding crowds. I got the second from the last shopping cart that was left. Usually, for the great sales, I go during the extended opening hours, before 9 AM, before they sell out, and the store is just about deserted. That day the crowd wasn't even buying the sales. They were piling up every ordinary thing in their shopping carts, and had every single checkout backed up solid! Sometimes you need to pay attention to the news.
did you know that the measurement tool on google earth you can select smoots as the unit?
@@arrgghh1555 lmao
@@arrgghh1555 Furlong-Firkin-Fortnight forever!
I just read an article about the Gauss circle problem. It is a way to approximate pi by counting lattice points in a circle. I would love to see you use it on one of your future pi day videos.
Casting out nines (and elevens) is good for more than just a magic trick. :-) The missed carry would have been instantly detected.
It gives me a deeper appreciation for the tools and techniques we have available now, and appreciating the skill of mathematicians/computers in the past had because they probably did this every day.
Thanks for the video!
It turns out that I might have come in contact with a teacher on Pi Day who tested positive for Corona. Wish me luck!
oof
If you're young then you will be fine
Did you live
Something to do when you've got all this time from self-quarantining?
24:12 I love how you brought Parker Square back up
So glad to see you elbow bump; well done
When subtracting numbers by hand and it comes time to subtract 1 from a digit in the minuend because one needs to "borrow 10", I have always found it more efficient to instead add 1 to the corresponding digit in the subtrahend.
This is a far underrated technique. It seems to create less compound carries, probably because numbers ending in lots of zeros are more common on artificial problems than those with long strings of 9s.
This is amazingly useful, thank you for sharing.
I wouldn’t be surprised if some schools taught this before common core and the like unified how it is taught. Some efficient equivalences get lost because it doesn’t “make sense”
Can we appreciate how Newton's house looks like it has integrals on it
I am so excited for the next pi day
Isaac Newton is forever my favourite physicist!
He simply was the greatest up to this due to his achievements!
Matt forgetting a carry raises my self-esteem by an incredible amount.
Thanks for a chance to be part of the vid Matt! Though could you correct the spelling of Harri in the description? I’m sure he’d appreciate it. Thanks again!
Thanks for your help! Fixed.
Loved this! Merry Pie Day, every one
I have never heard of a formula like that to find pi before. I spent the first few years of my college days searching in vein for such a formula because I believed it existed, but could never find it. I talked to many college professors trying to find it, but none of them could help me. I thought I discovered something once, but then years later I realized that what I found was trivial. My big question is where the hell are you from? Because none of the professors I’ve found have ever been able to help me try and find things I was passionate about in math, and at this point a lot of that passion has died and I’ve moved on to other areas. I was actually shocked to see you present that formula so casually after I had looked for a way to represent pi for years and had given up on it existing.
I think this is what my personal hell must look like.
it's said else where but I want to add to the engagement.. Forgot about this, what a wonderful Pi day surprise :D
As an engineering student, this is the exact amount of extra math i like in my life per week.
Well done and happy pi day
I died when he said he forgot to carry a 1. Lol
Although I should be focusing on pi like everyone else, I feel I have to praise the absolutely stunning pair of hands at 7:55.
It's definitely an amazing accomplishment!!! Go π!!!
During the Three Kingdoms period, Liu Hui used Archimedes' method to estimate the value of pi to be 3.141625. He also said that 3.14 was good enough for any practical purpose.
12:20 they're sitting like 3 feet away from each other in a cramped room without masks but high-fiving would be too risky. March 2020 was a strange time
Homer Simpson: I'm here because you said "by the end we're going to get pie"
My word! It's like Time Team with numbers!
Amazing calculation by Sir Issac Newton....
Matt to Brady in a Numberphile video years ago: Please don't call it a Parker Square.
Brady titles video Parker Square, keeps using the term until it becomes a meme.
Matt in this video: I'll draw a Parker Square on a thing I'll sign and send out to my viewers.
12:24 this is not going to make sense to anyone watching many years from now
covid's going down in history
even if for this year won't be number 1
we'll still remember in years, we will understand
That's optimistic.
It'll be remembered as either a really bad thing, or a really overblown thing.
It’s safe to assume any disease that shuts down several countries for weeks will become part of the school curriculum for a few decades, even if only in passing. See also the Spanish Flu.
Someone won’t I understand, someone will.
Clearly this video will get millions of hits. I don't doubt it
You're so great!!!