Inspired by Mathologer’s video about Times Tables. Here, N is the number of points around the circle and M is the number we’re multiplying by. Watch the video to understand what it’s doing. First change N to see the cardioid shape. Then change M to see other patterns.
Alternatively: click/touch the diagram to change the parameters.
I really like the colored results!
And of course after I implemented this I found other people had done it too!
- https://en.wikipedia.org/wiki/Cardioid#Cardioid_as_envelope_of_a_pencil_of_lines explained on wikipedia
- https://www.qedcat.com/cardioid.cdf (Mathematica file) (linked from the youtube page)
- https://lengler.dev/TimesTableWebGL/ (linked from the youtube page)
If you want to export this as a mobile “app”, you can visit this page and then “Add to Home Screen”. I’ve tested on iOS but not yet on Android.