Plays from YouTube after a click.
Times table on a circle
Why the Times Table Draws a Heart
The times-table cardioid, explained. 200 dots on a circle, one rule — join each dot to its multiple — and a heart appears at ×2, two cusps at ×3, three at ×4. Slide the multiplier and the shapes melt into one another; at ×201 every line vanishes, and at ×202 the heart is back, because the circle only counts to 200.
The rule
Join each point n to point n × k around a circle. One multiplication draws a cardioid and its cousins.
All about the times table on a circle →