An epicycloid is a type of curve traced by a point on the circumference of a smaller circle that rolls around the outside of a larger fixed circle. The shape of the epicycloid depends on the ratio of the radii of the two circles. When the smaller circle rolls around the larger one, the point creates a series of loops, resulting in a unique and intricate pattern. Epicycloids are related to other mathematical curves, such as hypotrochoids and cycloids. They have applications in various fields, including mechanical engineering and computer graphics, where they can be used to design gears and create complex animations.