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. Cycloids can be generated by rolling circles of various sizes, leading to different forms of the curve. In mathematics, cycloids are studied in the context of calculus and geometry. They have interesting properties, such as being the solution to the problem of the brachistochrone, which seeks the fastest path between two points under the influence of gravity. Cycloids also appear in physics, particularly in the study of pendulums and wave motion.