Welcome To 3-Space

** **

For most students, other than
considering the solids of revolution examined during Calculus I, working in and
visualizing mathematics in 3-space is foreign to them. While previously
they considered only the x-y plane and lines and curves that they could draw in
this plane, in Multivariate Calculus, students are asked to examine and to
graph lines and planes that no longer must lie flat on their desktop and to
analyze equations that generate surfaces that could correspond to shapes that
they created using Play-Doh when they were children.

In an
effort to help students to become comfortable with their study of mathematics
in 3-space, I created an ongoing assignment that provides students with
opportunities to explore mathematics in 3-space as they learn Maple and explore
some physical situations. Part of the assignment requires students to
recognize and to model the mathematics that they are studying in the world
around them. In this paper, I will discuss some of the aspects of this
assignment, present some of the Maple Worksheets that the students will use,
and discuss some simple tools that can be used to help students to visualize
mathematics in 3-space.