Why does this balloon have -1 holes?

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If you are need of urgent mental health support please check for crisis help lines available in your country.
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Do check out Jordan Ellenberg's book Shape. This video was inspired by Chapter 2.
https://www.nytimes.com/2021/06/21/books/review/jordan-ellenberg-shape.html
https://www.jordanellenberg.com/book/shape/

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/kalinadoescg/?hl=en

Thanks to Visual Topology & Geometry for "Punctured torus homeomorphism". https://www.youtube.com/watch?v=tz3QWrfPQj4

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/books/610964/humble-pi-by-matt-parker/
UK book: https://mathsgear.co.uk/products/5b9fa76f230ffa140094dc43
Nerdy maths toys: http://mathsgear.co.uk/

Видео Why does this balloon have -1 holes? канала Stand-up Maths