Normal sections can be used to characterize the curvature of a surface at a point.

• A. True
• B. False
• C. They can be used to characterize curvature, though not in all directions
• D. They only exist on cylindrical surfaces

Answer: (C)

A normal section is formed by slicing the surface with a plane that contains the surface normal at the point. The curvature of that intersection curve at the point equals the normal curvature of the surface in the tangent direction of that curve. By rotating the slicing plane around the normal, you obtain normal sections in all possible directions in the tangent plane, so you can read off the normal curvature for any direction. However, a single normal section only gives curvature in one direction; to know curvature in all directions you need the full family of normal sections. The principal curvatures arise as the maximum and minimum normal curvatures among those directions.