Math 487 W98 Lab 2

This lab is an introduction to orthogonal circles and the associated ideas of the radical axis and inversion.

You may not make it all the way through each experiment, but the latter experiments are included since they include some construction problems from Assignment 4.

Experiment 1.

Use prepared sketches in the "m487-445 week 2" folder in the Math 487 Class Folders for this quick experiment.

• Open Sketch -- 9.1.1 Angle Between Circles. Notice that you can drag the circles, arcs, etc. Now double-click the Show Magnified Button to see the two arcs dilated. Now drag the segments FG or HI to change the ratio of dilation. The point of this sketch is that when an arc is magnified, it looks like a segment or even a ray, so that from close up (in the limit) the concept of an angle between arcs is approximately the same as an angle between rays.
• Open Sketch -- 9.1.2 Rotate Circle w Arc Arws. Observe the relationship between the angle between tangents and the angle between diameters.

Experiment 2.

Do GTC 9.1, Investigation 3, pp. 150-152 (skip the Explore More).

Experiment 3.

Read the definitions of pencils on page 153. Then do GTC 9.2, Investigation 2, pp. 154-156 (skip the Explore More).

Experiment 4.

Do GTC 9.3, Investigation 1, pp. 158-161 (skip the Explore More).

Experiment 5.

For this experiment, use Inversion Scripts in the "m487-445 week 2" folder in the class folder.

Do GTC 9.4, Investigations 1 & 2*, pp. 165-168 (skip the Explore More).

(*)Note: In the first printing, the subhead for Investigation 2 was left out, so if you have no investigation 2 in your copy of GTC, still do pp. 165-168.