The 3-4-7 miracle. Why is this one not super famous?

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) (this was the very first submission submitted in record time :) (Liam Applebe) (an early submission that automatically does the whole dance for any choice of parameters) (Pierre Lancien) (with geared circles) (Christopher Gallegos) (very slick interface) (Matthew Arcus) (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): The version of the animation I show in the video I stumbled across on Instagram, Twitter, etc.: The new book by Marty and me: New short videos on Mathologer 2: New Mathologer instagram account: Hypotrochoids: Spirograph: (a nice app) Coin rotation paradox Tusi couple: Funfair Twister ride: Today’s music is Altitude by Muted. Enjoy! Burkard