[…]

Do check out Jordan Ellenberg’s book Shape. This video was inspired by Chapter 2.
https://www.nytimes.com/2021/06/21/bo…
https://www.jordanellenberg.com/book/…

Support me on Patreon and I will post you a free torus balloon. I hope I don’t regret this. https://www.patreon.com/standupmaths

Here is Sam Hartburn’s geogebra file: https://www.geogebra.org/m/yjtjxr2n

Trouser animations thanks to:
Bentley Davis https://BentleyDavis.com
Em Raymond https://twitter.com/techcavy
Kalina Panteleeva https://www.instagram.com/kalinadoesc…

Thanks to Visual Topology & Geometry for “Punctured torus homeomorphism”. https://www.youtube.com/watch?v=tz3QW…

Me cutting two joined cylinders in half way back in 2015. Good times. (At 29:29.) https://youtu.be/1wAaI_6b9JE?t=1769

CORRECTIONS:
– When talking about the Euler Characteristic of the torus at 16:29 I say the value of zero is “only on our friend the torus” which is technically wrong. In the moment I was just talking about the sphere and the torus but loads of other shapes have an Euler Characteristic of zero. Like the cylinder.
– I’m undecided if the string method of thinking about holes at 17:04 was helpful. I could have talked about the dimension of the boundary manifold, but that felt like I was repeating the previous bit too much and wanted a different way to think about it. Not sure if this counts as a ‘correction’ per se, but I just needed to talk to someone about it. Thanks for listening.
– Let me know if you spot any other mistakes!

Filming and trouser sewing by Alex Genn-Bash
Editing by Michelle Martin
Graphics by Sam Hartburn
Doughnuts later eaten by Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
US book: https://www.penguinrandomhouse.com/bo…
UK book: https://mathsgear.co.uk/products/5b9f…
Nerdy maths toys: http://mathsgear.co.uk/