Create classic spirograph patterns and discover the beautiful mathematics inside. These are not mere doodles — they are precise geometric curves called hypotrochoids and epitrochoids, governed by two simple gear ratios.
A spirograph pattern is a hypotrochoid (inner gear) or epitrochoid (outer gear). The number of petals equals the denominator of the gear ratio in lowest terms. The pattern completes when the pen returns to its starting point after LCM(R,r)/r rotations.
Adjust the outer ring size, inner gear size, and pen position with sliders. Each combination creates a unique pattern. Click Animate to draw gradually, or Instant to see the full curve at once.
The Spirograph toy was invented by British engineer Denys Fisher in 1965 and won Best Toy of the Year. The mathematics behind it (roulette curves) was studied by Descartes, Pascal, and Euler centuries earlier — they just lacked plastic gears.