Tangential Geometry

Tangential geometry studies the properties of curves and surfaces by examining how they bend and shape in space. It focuses on understanding the directions of tangent lines or planes at each point, which are like the best straight-line or flat approximation of the surface locally. This field helps describe curvature, how surfaces bend, and the behavior of objects moving on them. Think of it as analyzing the local geometry—how a tiny patch of a surface behaves—much like studying the local behavior of a path or shape to understand its overall form.