Polar curves are mathematical representations of shapes in a two-dimensional plane using polar coordinates. In this system, each point is defined by a distance from a central point (the origin) and an angle from a reference direction. This allows for the creation of various shapes, such as circles, spirals, and roses, by expressing the relationship between the distance and angle as a function. To plot a polar curve, one typically uses the equation r = f(\theta) , where r is the distance from the origin and \theta is the angle. These curves can exhibit unique properties, such as symmetry and periodicity, making them useful in fields like physics, engineering, and computer graphics.