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/gethelp...
UK: https://www.nhs.uk/mentalhealth/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 GennBash
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: Standup 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/