Normal plane (geometry)

A normal plane is a special flat surface used in geometry. It includes the normal vector of another surface at one point. This means the normal plane touches the surface at that point and stands straight up from it.

The normal plane can also describe a flat surface that is perpendicular to the tangent vector of a curved line in space. This plane contains the normal vector. Learning about normal planes helps us understand how curves and surfaces connect in three-dimensional space.

Normal section

The normal section of a surface at a point is the curve made when that surface meets a normal plane.

The shape of this normal section is called the normal curvature. For some shapes, the biggest and smallest of these shapes are called the principal curvatures. The average of the principal curvatures is the mean curvature. If this average is zero, the surface is called a minimal surface.