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The goal of this discussion is to have the students begin to develop
geometric intuition about regions in space and to use the Euclidean
coordinate system to describe these regions. Students will be asked
to give prose descriptions of the region, symbolic descriptions using
set notation, and to sketch the region. A brief introduction to the
coordinate system should precede this discussion and students should
have read Section 1.1: The Euclidean Coordinate System before
doing this discussion.
The first exercise asks the students to translate from a symbolic
description of a region to a prose description and the second asks for
a translation from a prose description to a symbolic one. The third
exercise applies the language of Euclidean coordinates to give a
mathematical description of the region of space which can be reached
by a robotic arm. Constraints on the location of the base of the arm
and the range of motion at each pivot in the arm are given. The
students will most likely need to complete the write-up of this
discussion outside of class.
Next: Discussion 4: Using the
Up: Multivariable Calculus: Collaborative Learning
Previous: Discussion 2: Functions of
2000-08-31