Geometry of Curves and Surfaces

Geometry of curves and surfaces explores the shapes and forms in space, focusing on their properties and how they bend or stretch. Curves are one-dimensional paths like circles or lines, characterized by their shape and how they change direction. Surfaces are two-dimensional shapes like spheres or planes, examined for features like curvature and smoothness. This field uses mathematics to understand and describe the geometry of objects, whether natural or designed, revealing how their shape influences their behavior and interactions in space. It combines visual intuition with precise formulas to analyze the structure of the physical and abstract worlds.