Epitrochoids are a type of mathematical curve generated by tracing a point on a circle as it rolls around the outside of another circle. The shape of the epitrochoid depends on the radii of the two circles and the position of the tracing point. These curves can create intricate patterns and are often studied in geometry and mathematics. Epitrochoids are related to other curves, such as hypotrochoids, which are formed when a circle rolls inside another circle. Both types of curves are examples of roulette curves, which are created by the motion of a point on a rolling shape. Epitrochoids can also be visualized in art and design, showcasing their aesthetic appeal.