Geometry of Curves

Geometry of curves studies the shapes and properties of curved lines and surfaces. Curves can be simple, like circles and parabolas, or complex, like spirals and sine waves. Analysts explore aspects like length, curvature, and areas enclosed by these curves. Understanding curves helps in various fields, from art and design to physics and engineering, where precise shapes and movements are essential. By examining how curves bend and twist, we gain insights into the natural world, enabling us to model everything from the path of a planet to the flow of water in a stream.