Curvature in Geometry

Curvature in geometry describes how a line or surface bends or deviates from being straight or flat. For a curve, like a circle or a parabola, curvature measures how sharply it turns; a tighter turn has higher curvature. On a surface, curvature indicates whether it curves inward or outward, such as a saddle or a dome. The concept helps us understand shapes in nature and man-made structures, connecting the idea of bending with precise mathematical measures. In essence, curvature quantifies the degree of bending at any given point, providing insight into the geometry and behavior of curves and surfaces.