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

Video Description

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-animation/ (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/MathologerStars (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: https://www.youtube.com/c/Mathologer2 New Mathologer instagram account: https://www.instagram.com/the_real_mathologer/ Hypotrochoids: https://en.wikipedia.org/wiki/Hypotrochoid 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_rotation_paradox Tusi couple: https://en.wikipedia.org/wiki/Tusi_couple Funfair Twister ride: https://www.youtube.com/watch?v=laQeA47NN0E Today's music is Altitude by Muted. Enjoy! Burkard