The applet below simulates Spirograph™ to draw intricate geometric designs. The design is a locus, the given condition is that it is the path of the point in the inner circle as it moves around the outer circle. There are a couple of controls:
The radius setting sets the size of the inside circle as a percentage of the outside circle. (20% to 80%.)
The pen setting sets the location of the pen along the radius of the smaller circle as a percentage. (0% corresponds to the centre of the circle and 100% sets the pen on the circumference.)
The changes made to the radius and pen do not take effect until the process is stopped and the locus is redrawn. Any colour changes take place instantly, if the locus is being drawn, or when the locus is redrawn.
Draw different sized circles.
Attempt to draw a triangle, square and pentagon.
Attempt to draw an ellipse, or oval. (You'll see these again in section 7.4U)
Try to find a relationship between the number of "petals" on the "flowers" and the parameters you set the spirograph to.