Assignments for Weeks 8 and 9
Reading
Read Chapter 4.
Deemphasize the non-obtuse-angle theorem (pp. 185-186) and "Note for
advanced students" (from p. 188 through the top of p. 190).
Also, we will not have time to study the proofs in this chapter as thoroughly
as those in Chapter 3; however, the statements of the propositions
(especially in the Saccheri-Lambert sections at the end) are very important
for understanding later chapters.
Discussion questions
Each team is responsible for leading the class discussion of one of the
propositions in the main text left as exercises:
- ALPHA -- Prop. 4.2 = Ex. 4
- BETA -- Prop. 4.3 (uniqueness) = Ex. 6(a)
- GAMMA -- Prop. 4.4 = Ex. 6(b)
- ALPHA -- Prop. 4.5 = Ex. 8
- BETA -- Prop. 4.6 = Ex. 9
- GAMMA -- Prop. 4.7 = Ex. 10
- ALPHA -- Prop. 4.8 = Ex. 11
- BETA -- Prop 4.9 = Ex. 12
- GAMMA -- Prop. 4.10 = Ex. 13
Homework due Wednesday, November 5
(in Week 10)
- Exercise 19, p. 197. Also, what would happen if the plane is NOT
semi-Euclidean? (See pp. 185-186. In the theorem there,
note that the "so that ..." applies to the whole statement,
not just to the acute angle hypothesis.)
(W)
- Exercise 30, p. 199. (READ Exercise 28 first.)
- Exercise 32, p. 199.
In addition, each team should post a single written version of
its proof on the Wiki in eLearning.