Chapter 2 continues the development of spatial thinking by introducing the space curve and its properties. A space curve is a one-parameter family of points, typically described in parametric form by the position vector

$\mathbf{R}\left(p\right)\=x\left(p\right) \mathbf{i}\+y\left(p\right) \mathbf{j}\+z\left(p\right) \mathbf{k}$

where $p$ is the parameter along the curve, and R is the "arrow" from the origin to the point $\left(x\left(p\right)\,y\left(p\right)\,z\left(p\right)\right)$ on the curve. Differentiation with respect to the parameter produces a vector $\mathbf{R}\prime \left(p\right)$ that is tangent to the curve. The Frenet-Serret formalism is then an analysis of the properties of a space curve to the effect that two scalars, curvature and torsion, completely determine the curve.