Assignment #8

Due Thursday, 30 November, 2000 Read http://cut-the-knot.com/triangle/pythpar/NonEuclid.html and http://cut-the-knot.com/triangle/pythpar/Fifth.html Skim http://cut-the-knot.com/triangle/pythpar/Drama.html

Assignment #7

Due Tuesday, October 17, 2000 Read Section 4.2. Send me an email addressing the following questions with the subject line: your name here: 341, RA7 How do Menelaus' Theorem and Ceva's Theorem similar and how are they different? How is Ceva's Theorem related to the fact that the medians of a triangle are concurrent?

Assignment #6

Due Tuesday, September 26, 2000 Read Section 2.6. Send me an email addressing the following questions with the subject line: your name here: 341, RA6 Explain what we mean by "direct" and "opposite" motions. Why is the product of two opposite motions a direct motion? Suppose that a planar motion fixes the points (0, 0), (1, 0) and (0, 1). What can you say about this motion?

Assignment #5

Due Tuesday, September 19, 2000 Read Section 2.2 - 2.4. Send me an email addressing the following questions with the subject line: your name here: 341, RA5 Give an example of a transformation of the Euclidean plane which is not an isometry. Explain why it is important to include glide reflections in the list of isometries of the Euclidean plane.

Assignment #4

Due Thursday, September 14, 2000 Read Section 2.1 Send me an email addressing the following questions with the subject line: your name here: 341, RA4 What is the difference between a function and a mapping? What is the difference between a transformation and a mapping?

Assignment #3

Due Tuesday, September 12, 2000 Read Section 1.5 Send me an email addressing the following questions with the subject line: your name here: 341, RA3 Looking at the preliminary picture of Fano's geometry, Figure 1.8b at the bottom of page 22, why can there not be a line through points 5, 6 and 7. In broad terms, how does one show there are no more than seven lines in Fano's geometry?

Assignment #2

Due Thursday, September 7, 2000 Read Section 1.4 Send me an email addressing the following questions with the subject line: your name here: 341, RA2 Explain, in general terms, what one needs to do to prove that each line of the four-line geometry has exactly three points. What is the plane dual of the statement: every line has three points on it.

Assignment #1

Due Thursday, August 30, 2000 Read Sections 1.1, the first part of 1.2 and all of 1.3 Send me an email addressing the following questions with the subject line: your name here: 341, RA1 Why are the terms point and line considered to be undefined in geometry? Can there be parallel lines in the three-point geometry of section 1.3? Why or why not?