Spirograph Simulation

• The small circle rolls inside the large one when you click Play ▷ at the bottom left.
• You can see the red pen's path by clicking Trace, or Show Locus, or both.
• You can change the radii of the circles using the r and s sliders.
• You can change the position of the pen within the small circle after setting α = 0°.

How are the values of r and s related to the symmetries of the figure?