The toy currently sold under the Spirograph name is not nearly as good as the old Spirograph of the 1960s. It's been dumbed-down, made less mathematical, and is harder to use.
It's worth searching online auction sites for an original Spirograph. Compare what you find to the picture at the lower left. There are two large circles with center holes, with gear teeth on both inside and out, plus two oblong bars with gear teeth on the outside, and eight solid circles with gear teeth on the outside edge. An old set may be missing map pens or the ball-point pens, but you can easily buy the map pins from a map store, and trial-and-error will turn up pens with points that are long enough to work for you.
The mathematics of the geometric patterns you can make are obviously interesting. In the simplest example, if you have two circular gears of the same size, with the same number of teeth, you can draw a cardioid, the heart-shaped figure whose Cartesian equation is(x2 + y2 - 2ax)2 = 4a2(x2 + y2).
The biggest drawback of plastic Spirograph toys is that the gears will slip when used carelessly, making it frustrating as a toy for children whose dexterity is not yet sufficiently mature. The static gear should be pinned down firmly, then, as you draw, the moving gear must be pressed toward the closest part of the static gear, so that it does not slip.
Posted: Wed - December 3, 2008 at 08:48 AM