Smooth curves are continuous lines that do not have sharp angles or abrupt changes in direction. They can be found in various shapes and forms, such as circles, ellipses, and parabolas. These curves are often used in mathematics and design to create aesthetically pleasing visuals and to model natural phenomena. In geometry, smooth curves are defined by mathematical functions that produce a gentle flow. They are important in fields like calculus, where concepts such as derivatives help analyze the behavior of these curves. Additionally, smooth curves are essential in computer graphics for rendering shapes and animations that appear fluid and natural.