I got sidetracked again by a puzzling little mathematical miracle. And, as usual, I could not help myself and just had to figure it out. Here is the result of my efforts.

00:00 Intro
08:45 The Coin rotation paradox
16:00 Mystery number explanation
18:38 Challenges and the new book
19:53 One-minute animation on how to figure the sum of the angles in a star
21:04 Thank you :)

The winner of Marty and my book Putting Two and Two together is Alexander Svorre Jordan. Congratulations. :) Thank you again to everybody who submitted an implementation of the dance. Here are five particularly noteworthy submissions:
(Kieran Clancy) https://kieranclancy.github.io/star-a... (this was the very first submission submitted in record time :)
(Liam Applebe) https://tiusic.com/magic_star_anim.html (an early submission that automatically does the whole dance for any choice of parameters)
(Pierre Lancien) https://lab.toxicode.fr/spirograph/ (with geared circles)
(Christopher Gallegos) https://gallegosaudio.com/MathologerS... (very slick interface)
(Matthew Arcus) https://www.shadertoy.com/view/7tKXWy (implements the fact that BOTH types of rotating polygons are parts of circles rolling around DIFFERENT large circles)

Some fun and helpful links.

The animation in geogebra (by Juan Carlos Ponce Campuzano):
https://www.geogebra.org/m/tfqmub4g

The version of the animation I show in the video I stumbled across on Instagram, Twitter, etc.: https://tinyurl.com/36dy6nm3

The new book by Marty and me:
https://bookstore.ams.org/mbk-141

New short videos on Mathologer 2:
   / mathologer2  

New Mathologer instagram account:
  / the_real_mathologer  

Hypotrochoids:
https://en.wikipedia.org/wiki/Hypotro...
https://www.geogebra.org/m/pTrc52nv

Spirograph:
https://en.wikipedia.org/wiki/Spirograph
(a nice app)
https://faishasj.github.io/spirograph/

Coin rotation paradox
https://en.wikipedia.org/wiki/Coin_ro...

Tusi couple:
https://en.wikipedia.org/wiki/Tusi_co...

Funfair Twister ride:
   • twister ride at scarborough.  

Today's music is Altitude by Muted.

Enjoy!

Burkard