Fields · Study 009
Spirograph Desk
A virtual Spirograph: a small gear rolls inside a large ring and a pen traces the hypotrochoid. Each finished curve fades as the next begins.
What you're looking at
The curve comes from two numbers of teeth and one pen offset. The small wheel rolls inside the ring without slipping, and the pen hole sits some distance from the wheel's centre. The drawing closes once the wheel has made a whole number of trips, which depends on the common factors of the two tooth counts.
The idea behind it
Mathematically these are hypotrochoids, relatives of the paths astronomers once built from circles on circles. The toy version went on sale in 1965, the work of engineer Denys Fisher, and taught a generation that ratios have shapes.
Try this
Click or tap to throw away the current gears and start a new curve straight away.
