Today, a long overdue foray into the realm of VORTEX MATHEMATICS :) 00:00 Intro 04:16 The vortex 08:10 The maths of remainders and digital roots 13:25 Demystifying the vortex 16:30 A matter of base. The 8 fingered Tesla. 19:21 Explanation why the digital root is the remainder on division by 9 24:01 Tristan's challenge 24:44 The magic of modular multiplication maths 25:19 Intuition for multiplier - 1 petals 28:23 Thank You! Coding competition: My wish list for the modular times table diagram app: -Being able to color line segments according to length. -Indication of the "direction" of multiplication. 1x2 = 2 and so there should really be a little arrow from 1 to 2 not just a simple connection :) -different loops in different colors. ... Here is the prize, a copy of my and Marty's new book. https://bookstore.ams.org/mbk-141/ That early Mathologer video featuring the modular times tables Times Tables, Mandelbrot and the Heart of Mathematics https://www.youtube.com/watch?v=qhbuKbxJsk8 A really nice article about various ways to generate the cardioid by Dave Richeson https://divisbyzero.com/2018/04/02/i-heart-cardioids/ Nice debunking/demystifying article about vortex math by "Professor Puzzler" https://www.theproblemsite.com/vortex/ For a growing pile of implementation of modular times table diagrams see my comment pinned to the top of the comment section of this video. Simon Plouffe's website http://plouffe.fr/Simon%20Plouffe.htm Articles by him relevant to this video can be found in this directory http://plouffe.fr/Inverseofprimes/ See in particular the files The shape of b^n mod p.pdf La forme de bn mod p.pdf What I am talking about in this video is really just the tip of a bizarre mathematical iceberg that most mathematically minded people are completely unaware of. Have a look at this presentation by Marko Rodin on vortex math (beware serious nutty and at the same time truely beautifully presented numerology ahead :) A LOT more than is usually reported on in popular YouTube videos. https://sciencetosagemagazine.com/vbm-vortex-based-mathematics-with-marko-rodin/ In turn this iceberg is just another tip of an even bigger iceberg of mainly wishful thinking. Have a look: https://sciencetosagemagazine.com/category/library/ Today's music: Aftershocks by Ardie Son Enjoy! Burkard