Chapter 17 - Line and Surface Integrals - 17.4 Parametrized Surfaces and Surface Integrals - Preliminary Questions - Page 957: 2

The length $||{\bf{N}}||$ is a distortion factor that measures how the area of a small rectangle ${{\cal R}_{ij}}$ in the $uv$-plane is altered under the map $G$.

Let ${{\cal R}_{ij}}$ be a small rectangle in the $uv$-plane. The length $||{\bf{N}}||$ is a distortion factor that measures how the area ${{\cal R}_{ij}}$ is altered under the map $G$.