From Standup Mathematician.
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These are my approximation equations:
perimeter ≈ π[53a/3 + 717b/35 – √(269a^2 + 667ab + 371b^2)]
perimeter ≈ π(6a/5 + 3b/4)
This was my pervious video featuring ellipsoids:
You can buy the ellipse from this video on eBay. I’ve written on my two new equations and signed it. All money goes to charity (the fantastic Water Aid).
Bonus content and a deleted scene are available on my Patreon.
Huge thanks to all who sent in a recording of them singing "A total ellipse of the chart." Sorry I could not include everyone. These are the people in the video:
It all started because of a request I put out on twitter.
– So far the only times (I’ve noticed that) I say "eclipse" instead of "ellipse" are 5:01 and 05:26 which was just after talking about my wife who is a solar physicist. So I think we split the blame 50/50.
– It seems everyone but me recognised the Root Mean Square. I think I only associate that with current for some reason! Thanks all.
– Let me know if you spot any other mistakes!
Thanks to my Patreons who meant I could spend about a week trying to find approximations for the length of ellipses. "Are you still working on that?" Lucie would – rightfully – ask over the weekend. "I’m going the extra mile for my patreon people!" I would reply. Here is a random subset of those fine folks:
As always: thanks to Jane Street who support my channel. They’re amazing.
Filming and editing by Matt Parker
Additional camera work by Lucie Green
VFX by Industrial Matt and Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
US book: https://www.penguinrandomhouse.com/books/610964/humble-pi-by-matt-parker/
UK book: https://mathsgear.co.uk/collections/books/products/humble-pi-signed-paperback