A cycloid is the curve traced by a point on the circumference of a circle as it rolls along a straight line. This mathematical shape is characterized by its distinctive arch-like structure, which consists of a series of peaks and valleys. The cycloid can be described using parametric equations, making it a significant topic in geometry and calculus. Cycloids have practical applications in various fields, including physics and engineering. For example, they are used in the design of gear teeth and roller coasters to ensure smooth motion. The study of cycloids also contributes to understanding concepts like curvature and motion.