Spirographs are intricate geometric patterns created by tracing the path of a point attached to a circle that rolls inside or outside another fixed circle. These designs, often resembling floral or mandala-like curves, are mathematically described using parametric equations involving sine and cosine functions. Originally popularized as a drawing toy in the 1960s, spirographs beautifully demonstrate principles of rotational motion, symmetry, and periodicity. Each variation in radius, speed, or pl