Math 445 Lab 6

Part 1: Experiments and Visualization with Orthogonal Circles

This first part of the lab illustrates various theorems and constructions from class.

1A. Examples of Inversion Images

While it would be easy to linger over this part of the lab, it is intended to be a quick look at what we learned about inversion images. It also provides a GSP tool for producing quite general inversion images.

Download the Lab06A GSP file and work through the pages for 10-15 minutes.

1B. Orthogonal Coaxal Families of Circles

This section picks up when Lab 5 left off. It provides a tool for constructing an orthogonal circle from its center. The goal is to trace the circles in each of two coaxal families. Then at the end, you will invert both families by sending a special point to infinity.

Download the Lab06B GSP file and work through the pages for 20-25 minutes.

Part 2. DWEG: Dr. Whatif's Euclidean Geometry

This is an unfamiliar model of a plane geometry that turns out to behave like a familiar geometry. The definitions are recalled at the beginning of the DWEG lab sheet. Then there is a linked GSP file to work with on constructions in DWEG.

Link to DWEG lab sheet.