Discussion 3: The Coordinate System in ${\bf R}^{3}$

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.