About spirographs

A spirograph is a toothed wheel rolling around inside, or outside, a toothed ring. A pen sits in one of the holes in the wheel. As the wheel rolls, the pen loops around and around, and the loops build up into a pattern of petals and points.

How the numbers make the shape

The ring and the wheel both have teeth. Divide both numbers by the biggest number that goes into each of them. The ring's answer is how many points the pattern has. The wheel's answer is how many times the wheel goes around the ring before the pattern joins up.

For example, a ring of 105 teeth and a wheel of 45 teeth: 15 goes into both, giving 7 and 3. So you get 7 points, and the wheel goes around 3 times. Try a wheel whose teeth share no number with the ring's, like 105 and 52, and the pattern goes around 52 times before it joins: a dense, lacy flower.

The pen hole changes the shape of each loop. Near the edge of the wheel you get sharp points and little loops; near the middle you get soft, rounded waves.

A little history

Mathematicians have studied these curves for centuries. A curve traced by a point on a circle rolling inside another circle is called a hypotrochoid; rolling outside, an epitrochoid. In the 1800s, machines with gears were used to engrave these looping patterns on banknotes, because they were so hard to copy by hand.

The toy called Spirograph was invented by Denys Fisher, a British engineer, and went on sale in 1965. It has been loved ever since.

Playing without sight

Turn on Sound and a soft chime rings each time the pen swings out to the tip of a petal, so you can hear the pattern's rhythm: quick chimes for many small petals, slow ones for a few big loops. Tips near the edge ring brighter than tips near the middle. Every control has a label, and each pattern is described when it starts and when it's finished. Space starts and pauses drawing.

Made for Stellar Whiskers.