Calculating π by hand: the Chudnovsky algorithm

For Pi Day 2018 I calculated π by hand using the Chudnovsky algorithm.

k = 0
42698672/13591409 = 3.141592|751...

k = 0 and k = 1
42698670.666333435968/13591408.9999997446 = 3.14159265358979|619...

Watch me do the second term working out on my second channel:

See me do the entire final calculation again (without a mistake) on Patreon:

Proof that I did actually do it properly:

This was my attempt two years ago. Look at how much hair I had!

The Chudnovsky Brothers used their algorithm to be the champion pi calculators of the early 1990s: going from half a billion to four billion digits of pi.

This video was filmed at Queen Mary University of London.

CORRECTIONS
- None yet. Let me know if you spot anything!

Thanks to my Patreon supporters who enable me to spend a day doing a lot of maths by hand. Here is a random subset:

Christopher Samples
Sean Dempsey-Gregory
Emily Dingwell
Kenny Hutchings
Rick de Bruijne

Support my channel and I can make more videos:

Music by Howard Carter
Filming and editing by Trunkman Productions
Audio mastering by Peter Doggart
Design by Simon Wright

MATT PARKER: Stand-up Mathematician

[TheApple]

The accuracy on the first term was brilliant, especially considering that you used the Parker Square root of 10005.

[SchutzmarkeGMBH]

sqrt(10005)=100.025
Parker square root

[ciahciach]

Mind blown part was the most funny thing I have ever seen

[andyan]

that converges STUNNINGLY quickly. WOW.

[marcmaticas]

I find it fascinating that, looking for a good decimal approximation of the number π, you have come up with an extremely accurate approximation of the constant e at 7:25. Although I don't know if it's a coincidence or not.

[jimtuv]

The hair, or lack of it, is awesome! I did the same thing last year and it was liberating not to worry about the impending baldness. It's a bit cold in the winter so invest in a cap.

[johnchessant]

7:25 27182818 (hmm... seems familiar...)

[rainworldenthusiast]

13:45 the face I make every time I finish a calculation and my answer isnt any of the choices

[johnchessant]

Pi Day is now both Einstein's birthday and Hawking's deathday. :(

[musikSkool]

"I am going to calculate pi by hand again..." All I could think was; "You must have a really big, and really round hand."

[Jtking]

11:08 It's an older meme but it checks out.

[heyandy]

Love it. I want to see him do this with increasingly sophisticated calculation aids. Like if we granted him a slide rule, how much faster could he go?

[deluxeassortment]

Calculating Pi is such an irrational thing to

[NipunChamikaraWeerasiri]

Next year:
Calculating pi using the perfect curvature of Matt's bald head. Looking forward to that one.

[ninjamanj]

That moment you google 42698672/13591409 and it comes up with this video.

[jeffirwin]

I'm impressed that you did all this working out by hand, and more impressed that you made it that far before making a mistake.

[tomsmith]

Hey Matt, quick observation I wanted to run by you.
Today I went back and watched your old video about approximating pi by rolling dice. I wanted to see how accurate this method could be, so I wrote up some code in python to automate it. I was messing around with the variables, like # of sides on the dice and number of dice rolled, and I was trying to optimize it to give the best answer possible. Something that I noticed was that when increasing the number of sides on the dice, accuracy didn't improve linearly. Instead, a highly-divisible number of sides like 30 was more accurate than 31-35, and 36 sides were more accurate than 37-39 sides, 40 sided dice were more accurate than dice with 41-45 sides, and so on. I thought this was really interesting, and was curious if you had any insights as to why using highly divisible dice might increase the accuracy of the program's estimate of pi?
Great vid as always, thanks for reading!!

[omikronweapon]

"This is why I pay you the (slight pause) medium bucks!"
that cracks me up XD

[UltraCboy]

There’s a reason why you’re my favorite mathematician, Parker.

[Czeckie]

Hey Matt, it would be a great video to show (to some extent) why is there e at 7:25. I reckon it's connected with how the algorithm was conceived. j-invariant and all that