Math 487: Lab 3. Wednesday, 1/20

This lab continues with some additional sections of GTC chapter 9, then moves on to images of inversions in Chapter 10.

Orthogonal Circles

  1. Work through Investigation 1 of 9.3. Answer the questions for your future use, but skip the Explore More.
  2. Do the constructions in Investigations 2 and 3 of 9.3. Which would be a more convenient method to do by hand?
  3. Carry out the constructions of the Explore More of Investigation 3. Write down an explanation based on similar triangles which shows why each construction produces the inversion. Which methods will work if the point A is inside the circle? What would be the most convenient method to use by hand?
  4. Do one or both of the constructions in Investigation 4. Explain why this also produces inversion.

Images under Inversion

  1. Do Exploration 10.1, Investigation 1. Experiment with several shapes. Skip the Explore More.
  2. Construct the image of a segment as a locus and also the image of an arc as a locus, in Investigation 2 of 10.1. Use these figures to answer the questions aat the end of 10.1.
  3. Work through all of 10.2