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

2021-12-30

[public] 215K views, 16.2K likes, dislikes audio only

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