hypotrochoid curves · inner gear traces inside outer gear · 1960s toy, math as old as euclid.
outer ring (R)100
inner gear (r)63
pen offset (d)40
line width1.5
color cycleslow
seed color
a hypotrochoid is traced by a point at distance d from the center of a small circle (radius r) rolling inside a large circle (radius R). the ratio r/R determines how many petals. when r/R is rational (p/q), the curve closes after q revolutions.