Thank you to BetterHelp for sponsoring this video! To get 10% off your first month of therapy, go to https://betterhelp.com/standupmaths to sign up today.

If you are need of urgent mental health support please check for crisis help lines available in your country.
USA: https://www.mentalhealth.gov/get-help...
UK: https://www.nhs.uk/mental-health/advi...

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.   / 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   / techcavy  
Kalina Panteleeva https://www.instagram.com/kalinadoesc...

Thanks to Visual Topology & Geometry for "Punctured torus homeomorphism".    • Punctured torus homeomorphism  

Me cutting two joined cylinders in half way back in 2015. Good times. (At 29:29.)    • Four Dimensional Maths: Things to See...  

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/