Assignments for Week 1
Greenberg's book contains too much material for one semester. To ensure
that we have enough time to cover the basics of hyperbolic geometry and
its implications (Chapters 7 and 8), I will occasionally authorize you to
skim over ("deemphasize") certain sections in earlier chapters.
Although each chapter contains roughly 50 pages, the chapters are not
alike in their degree of technicality. For example, we'll need to spend
several weeks on the fundamental theorems and proofs in Chapter 3.
Chapter 1 is mostly history and philosophy; we can and must get through it
in a hurry (one week).
Skip the Preface, but read the Introduction and Chapter 1.
Pause after p. 25 to think about the discussion questions (below).
Then read the rest of the chapter;
deemphasize Viète, Descartes, and Pi (pp. 34-40).
Be prepared to discuss these in class on Wednesday, Sept. 6.
- Exercises 1-4, pp. 42-44. (Instructions start on p. 42!)
- Exercise 14, pp. 46-47.
Homework due Wednesday, Sept. 6 (in Week 2)
You will have a chance to ask questions on Monday, Sept. 4.
WARNING: In Greenberg's textbook, be sure to distinguish among
Exercises", "Exercises", "Major Exercises", and "Projects".
Regular homework problems will almost always be "Exercises".
ON EVERY ASSIGNMENT:
Turn in answers to the question
marked "(W)" on separate paper (and expect it to be subjected to
especially penetrating scrutiny).
- Show that Ahmes's 8/9 formula (see p. 1 of text) is equivalent to a
certain numerical approximation of Pi. Compare its accuracy with other
famous approximations, 22/7 and the square root of 10.
- Exercise 5, p. 44. Explain clearly why this theorem is different
from the very similar statement in the middle of p. 17 ("If P lies on the
circle ... Q also lies on the circle.").
- Exercise 8, p. 45. (W) Suggestion: Possibly useful
Euclidean theorems can be found on pp. 31 and 175. Check on p.
162 that you understand the definition of
"alternate interior angles".
- Exercise 12, p. 46. Suggestion: Carefully draw the figure for
a nonisoceles triangle that you understand very well, and compare with