All assignments will emphasize writing rigorous proofs. Make sure you justify every single step and statement you make. Provide proper references from the textbook (such as Proposition X or Definition Y).
Chapter 1, pages 44-45: problems 4, 6
Chapter 2, pages 91-92: problems 1, 2, 6, 8, 9
Chapter 3, Exercises on congruence (pages 150-152): problems: 24, 26, 27, 29, 32
Write an essay about the taxicab plane described in
Major Exercise 6
(Chapter 3, page 156). Here is a list of what you may want to include in
your essay: (i) state and explain the new
geometry, (ii) provide some historical background, (iii) address most
(preferably all) points of the exercise 6, (iv) discuss practical,
real-world applications of such a geometry. And of course, you are
certainly encouraged to be creative and add to this list.
Important notes
Academic dishonesty (including plagiarisms) is very well described on the university policies webpage:
General comments
after marking the mini-projects:
Overall we were quite impressed by the level
of research and thought put into these
papers. Very frequently, the results made enjoyable and instructional reading. For the most
part, the mini-projects successfully conveyed an introductory summary and some original
results of Taxicab Geometry. The average was 7.5 out of 10. We made extensive comments to
provide as much feedback as possible. The main comment that applies to
most of you relates to proper citation. See the "Important notes" for the
final project listed on the course home page. There is an item that discusses citation. Read the information
provided by the library link and learn how to reference properly.
Chapter 4, pg. 194-200: Exercises 9, 12, 14, 28, 32 and Major Exercise 1.
Chapter 5, pg. 228-230: Exercises 2, 3, 5
Chapter 6, pg. 269-275: Exercises 1, 2(a-c), 12
In Exercise 1 (Chapter 6) I want you to discuss
individually each item in that list. I am not too keen on you adding to the list, I
would rather want to make sure you understand the importance of the statements already
listed. For instance, if appropriate, comment on whether
the respective statement is equivalent to the Euclidean parallel postulate or to a
weaker axiom/ property, such as the plane being semi-Euclidean.
In other instances you could show that the statement is intrinsic to Euclidean geometry
and it does not hold in hyperbolic geometry. Justify your answers. In
some instances you can invoke results we proved in class, in others (such as item 1) you
have to come up with your own proofs and interpretations. And, as the first line says,
this is perhaps the most important exercise in the book, so make sure you treat it
convincingly.
Chapter 6, pg. 269-275: Exercises 7, 8, 9
Chapter 7, pg. 358: Exercises P-1, P-4.
Homework #5 - Due Tuesday, March 8, in class
Homework #6 - Due Tuesday, March 22, in class
Homework #7 - Due Tuesday, April 5, in class