# 0x030 Differential Geometry

Summary of differential geometry of curves and surfaces [1]

## Curves

### Parametrized Curves

Definition 1.1 (parametrized curve) A parametrized curve in $mathbf{R}^n$ is a smooth function $\gamma: I \to \mathbf{R}^n$ where $I \in \mathbf{R}$ is an interval