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.