Calculating π by hand the Isaac Newton way: Pi Day 2020

So it turns out that this year π = 3.141591678589793935225

Thanks to Ben Sparks, Deanna Judd, Max Hughes and Zoe Griffiths!

SCANS OF ALL WORKING OUT!
Any missing working out is for a term which a school did for us.

CORRECTIONS
- Nothing yet. Let me know if you spot anything! (Or find where we went wrong, so very wrong.)

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:

Music by Howard Carter
Filming and editing by Alex Genn-Bash
Design by Simon Wright

MATT PARKER: Stand-up Mathematician

[lifthrasr]

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!)

[ninjaphobos]

It's somehow comforting to know that a room full of full-time mathematicians had difficulty doing this.

[zerid]

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

[janus]

"A value that is close, but not quite"

I would call it a Parker-Pi

[gasdive]

When you're standing on the shoulders of giants, you need to be careful going through doorways. 2:10

[voltagedrop]

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.

[jimi]

Fun fact: if you have 22 pies and divide them among seven people, everyone gets a bit over one pi.

[RiverMersey]

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!

[OwlRTA]

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.

[coryman]

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 :)

[KorpseTE]

It was a Parker's Square of an attempt.

[englishmotherfucker]

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

[T_Mo]

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.

[RJSRdg]

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!

[Alvraera]

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).

[qvoorhorst]

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.

[Benny_Blue]

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.

[TheNgandrew]

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.

[landonnobles]

Watching this video retaught me all of my middle school math, and actually made it all make sense. What a great video.

[SamuelBoshier]

I forgot about this! What a wonderful surprise.