Surface theory

Surface theory is a part of mathematics that studies the properties of surfaces—two-dimensional shapes that can exist in three-dimensional space, like a sphere or a torus (doughnut shape). It focuses on understanding how these surfaces are shaped, how they can be deformed, and their intrinsic properties that don't change when they are bent or stretched, but not torn. This theory helps in areas like geometry, physics, and computer graphics by providing tools to analyze and classify surfaces based on their curvature and topology, deepening our understanding of the shape and structure of complex forms.