ABSTRACT
A significant benefit of a computer algebra system such as Maple is its ability to plot a curve in three dimensions. The capability to rotate the plot in real time is a remarkably effective aid to visualizing the curve’s shape. In this chapter, we will discuss two ways to represent space curves. One is the standard curved-line representation. The other, a tube, significantly improves the three-dimensionality of the representation. We will create three new demonstrations. One shows the relationship between a vector-valued function and a space curve. Another is an elaborate one for demonstrating the directional derivative and the gradient vector. The third demonstrates in three dimensions the ideas of velocity and acceleration, showing the changing velocity and acceleration vectors as a point moves along a curved path in space.
