Inspired by Mathologer’s video about Times Tables[1]. 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[2] explained on wikipedia
- https://www.qedcat.com/cardioid.cdf[3] (Mathematica file) (linked from the youtube page)
- https://lengler.dev/TimesTableWebGL/[4] (linked from the youtube page)
- https://seiselen.github.io/Multiplication-Circles/[5]
- https://blocks.roadtolarissa.com/olearym/ec27b9ac1bf0da42ed8a0d533181693b[6]
- https://www.desmos.com/calculator/ohry1pwq1y[7]
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.