Spirograph in Polar Coordinates

This example demonstrates the creation of a spirograph in polar coordinates, illustrating how the rolling motion of two circles generates intricate patterns. The core mathematical concepts involved include the definition of polar coordinates, the application of parametric equations, the periodic behavior of trigonometric functions, and curve sketching techniques. The construction leverages GeoGebra commands such as CurveCartesian, utilizing parameters like R (radius), r (inner circle radius), s (distance of fixed point), and a (rotation angle) to control the shape. It is suitable for high school students studying analytical geometry, parametric equations, and trigonometric functions, as well as for mathematical interest groups.