Math 487 Lab 2 – Images Under Inversion and Inversive Geometry

Setup

In this lab we will use some of the files from the disk bound with GTC.  In case you do not have this with you, some copies of the files will be available in the lab.

• Copy the files in CIRCTOOL and CH10 to the disk of your computer. 
• The first thing you will need to have opened in Sketchpad is a script to invert a point.  For example, you can open "inverpt4.gss" from the folder CIRCTOOL.

Part A. Getting Experience with Inversion Images

We will carry out Investigation 1 using some ready-made files first. 

• Open the files in the folder CH10 > EXP1 > INV 1 and use them to carry out the explorations in Exp 10.1, Inv 1.  You should look at the Face files, but most of the work will be done with invshaps.gsp.
• Make rough drawings to answer the questions of page 182 and think about how you could answer these questions based on what you know about inversion from class.
• Learn how these files were made.  Do this by carrying out Investigation 2, starting with a blank sketch but using your inversion script.

Part B. Inversion of a Line

Carry out Exploration 10.2, Investigation 1.  You should learn this proof.  Check whether the figure for the proof still works if the line intersects the mirror circle.

Part C. Inversive Geometry

• Read GTC 10.5, pp. 195-6 for basic definitions of inversive geometry.
• Carry out Investigation 1 of 10.5.  Use the script indicated in the margin.
• Carry out Investigation 2 of 10.5.  Use the script indicated in the margin.

Note: Exploration 10.3 will be skipped in lab.  This contains the proof that a circle not through the center of inversion inverts to another circle as was done in class today.