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Reading for Week 3

Read Sved, Chapter 2. Also GTC Chapter 10 and Ogilvy handout.

Study Questions for Quiz 3 are at the end of this page.

Lab Assignment C. Due Friday, 1/22

C1. Print one of the constructions of inversion on page 163. Choose one that you will use for straightedge and compass construction by hand.

C2. Print a couple of images of segments that answer two of the cases of Q5 at the end of 10.1.

C3. Construct a figure with a circle and a line and also the inversion of the line.

Math 445 Assignment 3.(Due Mon. 1/25)

  1. (5 points) Sved, Chapter 2, page 43, #1 (tangent kites).
    Do a careful construction and turn it in, as well as a clear explanation. Note: This and other constructions can be found in Ogilvy.
  2. (5 points) Sved, Chapter 2, page 43, #2. Do a careful construction of an example and turn it in. Write a clear explanation. This should be quite short if you use the theorems in the chapter.
  3. (10 points) Sved, Chapter 2, page 43, #4. Do a careful construction of each of the 4 examples and turn them in (you probably want to use Sketchpad).
    Note: You can do them all by just computing a lot of inverses, but you should observe that if you use the theorems about inversion images, that you can do rather simple constructions of lines, circles, etc., that will give the construction without using the inversion construction directly.
  4. (10 points) Sved, Chapter 2, page 43, #5. Do this as two parts.
  1. (10 points) Center of an inverted circle.
  1. (10 points) Sved, Chapter 2, page 44, #8 (plus a figure).
  1. (10 points) Composing inversions.
    Let m1 be a circle with center O and radius r1 and let m2 be a circle with the same center O and radius r2. Let J1 be inversion in m1 and let J2 be inversion in m2. (This means that J1 is the mapping or transformation so that for any point P, J1(P) = P', the inversion of P in m1.)


Study questions for Quiz 2