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...
Plus if you are in Europe you can search Mental Health Europe: https://www.mhe-sme.org/

Check out Ben's Hopping Hoop Geogebra file:
https://www.geogebra.org/m/ddsfjbvy

Thanks to Lisa Mather for making the hopping hoops for me. And an extra shout-out to Joel Tatarek-Gintowt for modelling and 3D printing the ball bearing casement.

Here are all the papers mentioned:

A Mathematicians Miscellany (1953) by John Littlewood
https://archive.org/details/mathemati...

The Hopping Hoop (1997) by Tadashi F. Tokieda
https://doi.org/10.1080/00029890.1997...

Hopping Hoops Don't Hop (1999) by James P. Butler
https://doi.org/10.1080/00029890.1999...

The Hopping Hoop Revisited (1999) by Timothy Pritchett
https://doi.org/10.1080/00029890.1999...

The rolling motion of an eccentrically loaded wheel (2000) by W.F.D. Theron
https://doi.org/10.1119/1.1302324

The amazing variety of motions of a loaded hoop (2007) by W.F.D. Theron and M.F. Maritz
https://www.sciencedirect.com/science...

The dynamics of an eccentrically loaded hoop (2010) by Andrew Taylor and Mary Fehrs
https://aapt.scitation.org/doi/10.111...

CORRECTIONS
- Yes, I know, 08:33 worst cycloid ever. No need to tell me.
- At 12:23 I say "no friction" when I am talking about the hoop not skidding, and yes, that should be "infinite friction".
- Let me know if you spot anything else!

Huge thanks to my Patreon supports. They keep me rolling along.   / standupmaths  

Filming and editing by Alex Genn-Bash
Props by Lisa Mather and Joel Tatarek-Gintowt
Written and performed by Matt Parker
GeoGebra and extra material/research by Ben Sparks
Hoop catching by Nicole Jacobus
Dog wrangling by Lucie Green
Hoop chasing by Skylab the Dog
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/collections/b...