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Chudnovsky π: by hand BONUS (Patreon)

Published:
2018-03-14 07:20:33
Imported:
2018-03

Content

Every second year I try to calculate pi by hand on pi day (the in-between years I try to calculate pi via some physical experiment). This year I went for the Chudnovsky algorithm.

But there was a mistake right at the end!

You can watch the main video here where I try to work out pi:https://youtu.be/LhlqCJjbEa0

The patreon-only footage is me sitting down at home and doing the whole last step again to make sure I can get it right. And I needed some closure to make sure I did actually calculate pi by hand. Fourteen digits is a new personal best.

I have a few ideas for next pi day’s physical pi experiment. But if you have any suggestions do let me know!

Files

Chudnovsky π: by hand AGAIN

This is the video of me finally getting the Chudnovsky algorithm k=1 calculation correct. From this patreon post: https://www.patreon.com/posts/17542566 Watch the original video: https://youtu.be/LhlqCJjbEa0 The extra k=1 set-up working out: https://youtu.be/I7YvD7dqsy8 FILES AHOY The table for laying out the multiples of the devisor: https://www.dropbox.com/s/taqq79c4klq8oax/pi-calc-layout-table.png?dl=0 The grid for the doing the division: https://www.dropbox.com/s/4sifcrfpt1dv2km/pi-calc-layout-grid.png?dl=0 Scan of all the working out: https://www.dropbox.com/s/64vc5iz7yt41r53/chudnovsky-pi-FIXED.pdf?dl=0 https://goo.gl/forms/EkasAFe89vBIZVND2

Comments

Marcell Imre Magyari

You are crazy and I LOVE IT! I was in Berlin two weeks ago, was funny to read your book under the tv tower which you measured :D Happy pi day!

Matt Parker

It’s a great tower (and a great city). Hope you enjoyed the book!

Rob Macdonald

Going from 7 to 9 you made a mistake. You said 12-8=3, which should be 4. (Right around 40 minutes). Happy Pi Day!

Rhys Llewellyn

Awesome working out. This made my Pi Day!

Andrew Marsden

I find it oddly satisfying that both your mug and coaster are puzzles.

Lisa Ugray

Physical pi experiment suggestion: Do it from the surface area of a sphere. I'd suggest cutting a giant beach ball (<a href="https://www.amazon.co.uk/BigMouth-Gigantic-10ft-Beach-Ball/dp/B004P67D1O/ref=sr_1_3?ie=UTF8&qid=1521372554&sr=8-3&keywords=giant+beach+ball)" rel="nofollow noopener" target="_blank">https://www.amazon.co.uk/BigMouth-Gigantic-10ft-Beach-Ball/dp/B004P67D1O/ref=sr_1_3?ie=UTF8&qid=1521372554&sr=8-3&keywords=giant+beach+ball)</a> into sufficiently small pieces as to be reasonably approximated as living in 2 euclidean dimensions.

Orchidseed

Tip to make subtracting long numbers from each other easier: Add the 9-complement instead, as adding is a lot easier than subtracting. The 9-complement of a digit is the one such that, when added to the original, it comes out to 9. So 0 becomes 9, 1 becomes 8, 2 becomes 7, 3->6, 4->5, 5->4, 6->3, 7->2, 8->1, 9->0. Example: to calculate 987-258=729, convert the 258 to 741, and add it to 987. Also: add an "inverted borrow" of 1 to the first digit. You will find that 987+741+1=1729, which is the correct value plus an "inverted borrow" which overflows at the left end of the number. Strike that borrow and you get 729. This method is the same principle which is used to do binary subtraction in digital computers. They add a 1-complement and set the carry (inverted borrow) beforehand.