Mathematical curves are continuous lines that can be described using equations in a coordinate system. They can take various shapes, such as straight lines, circles, and more complex forms like parabolas and ellipses. These curves are essential in geometry and calculus, helping to represent relationships between different variables. Curves can be classified into different types based on their properties. For example, parametric curves are defined using parameters, while polar curves use angles and distances from a central point. Understanding these curves is crucial in fields like physics, engineering, and computer graphics, where they model real-world phenomena.