ASSIGNMENTS
MTH 338 — Winter 2020

Assignments given by number refer to either Roads to Geometry (RG) or Taxicab Geometry (TG).

Term paper deadlines:
2/14/20: Choose a topic
2/21/20: Project proposal due
2/28/20: Draft of introduction due
  3/6/20: Rough draft due
3/16/20: Final version due
Reading assignments:
Week 1: Skim RG §1.1–§1.2; Read RG §1.3–§1.4; Read TG §1–§3.
Week 2: Read TG §4–§5.
Week 3: Skim RG §2.1–2.2 & §2.6; Read RG §3.2– §3.6 §3.4.
Week 4: Review RG §2.6; Skim RG §3.5–§3.6; Read RG §6.2–§6.3 & §6.6.
Week 5: Read RG §6.8.
Week 6: (no reading assignment this week)
Week 7: Skim RG §6.4–§6.5
Week 8: (no reading assignment)
Week 9: Read RG §7.1–7.2; skim RG §7.3–§7.5
Week 10: Skim §5.1 and §5.2 of my book on special relativity, then read Chapter 4.
Due 3/16/20
Complete your essay.
Turn in hard copy to me in my office by noon.
Late submissions will only be accepted if the delay is cleared with me in advance.
Please also email a copy to me.
Any reasonable format is OK, but I encourage you to include a PDF copy as well as your source files.
ZIP archives including separate graphics files are fine.
Due 3/6/20
Write a rough draft of your entire essay.
A suggested minimum length for this assignment is 3–5 pages (single-spaced; roughly 5 pages double-spaced).
Submit electronic copy to me (PDF strongly preferred).
You should submit a complete draft at this time. At a minimum, you should submit a complete introduction and conclusion, and an abbreviated version of the remaining sections.
It is acceptable for now to say, "I will show that taxicab circles are squares," but leave out most of the details. However, it is no longer acceptable to say merely, "I will investigate taxicab circles."
There is also a lab activity this week, for you to complete on your own.
You do not need to turn anything in, but you should make sure that you verify Desargues' Theorem in at least one case.
(Do this assignment after completing your draft; the "due" date is 3/9/20.)
Due 2/28/20
Write (a draft of) the introduction for your essay.
Tell the reader what you are going to do. An appropriate length for this assignment is one full page.
Email a copy to me as an attachment and bring a printed copy to class.
Due 2/21/20
Write a project proposal, consisting of a title and a short description of what you intend to do.
You can present your proposal as an abstract, summarizing the main conclusions, or as an outline, giving a table of contents and the list of questions you intend to address. An appropriate length for this assignment is roughly half a page.
Email a copy to me and bring a printed copy to class.
There will also be a lab activity in class on Friday, 2/21/20.
After this activity, each group should email a photo to me showing their construction, along with a list of group members and a copy of their calculation. (No explanation in words is necessary.)
If you miss Friday's class, you will not have access to a Lénárt sphere, but you are strongly encouraged to try it on your own, using GeoGebra, or even some sort of ball you can write on.
Due 2/14/20
Choose a topic for your essay.
Write a few sentences describing your topic.
Lab 2: Due 2/10/20
Use GeoGebra to verify SAS congruence in the Klein Disk:
Warning: The tool for measuring elliptic angles in the Klein Disk applet is buggy!
Angle sums in elliptic triangles should always be greater than 180°.
Draw a circle in the Klein Disk
Further information will be posted on the announcements page.
Your writeup should include both a figure and an explanation of the process used.
Turn in this assignment at the beginning of class.
Lab 1: Due 2/3/20
Use GeoGebra to verify SAS congruence in the Poincaré Disk:
Further information will be posted on the announcements page.
Your writeup should include both a figure and an explanation of the process used.
Turn in this assignment at the beginning of class.
The more you automate your construction, the better for your content score – the exact duplication of a special triangle (right, equilateral, isosceles) is probably better than an approximate duplication of a general triangle, although the merit of the latter will depend on the exact procedure used. If you adjusted things by hand, say so! Your explanation should be complete and well-written; half a page to a page should be sufficient.
HW 3: Due 1/27/20
Prove SASAS congruence for quadrilaterals:
If the vertices of two quadrilaterals are in one-to-one correspondence such that three sides and the two included angles of one quadrilateral are congruent to the corresponding parts of a second quadrilateral, then the quadrilaterals are congruent.
Which SMSG axioms did you use in your proof?
You may answer this question separately, or incorporate the answer into your proof.
In which geometries is your proof valid?
Use complete sentences. Include one or more figures. Turn in this assignment at the beginning of class..
Lab 0: "Due" 1/24/20
Use GeoGebra to perform the following tasks (in Euclidean geometry):
There is nothing to turn in, but you will use this software in future activities, so this one is good practice.
See the announcements page for further details.
HW 2: Due 1/17/20
This is the first of two different assignments due the same day.
TG §3: 7, 15
TG §4: 13ad
Explain your answers. Use complete sentences. Turn in this assignment at the beginning of class.
Due 1/17/20
This is the second of two different assignments due the same day.
Define non-Euclidean geometry.
Email a copy to me and bring a printed copy to class.
A single sentence may be sufficient. Your audience consists of your fellow classmates.
HW 1: Due 1/13/20
TG §2: 2, 4, 5
Explain your answers. Use complete sentences. Turn in this assignment at the beginning of class.
A reasonable goal of this assignment is to present the problems and their solutions in such a way that you would be likely to understand them 5 years from now without reference to any other materials.
Due 1/8/20
Write one paragraph (roughly half a page) describing your interest in mathematics.
Email a copy to me and bring a printed copy to class.
A reasonable goal of this assignment is to serve as a partial introduction of yourself to a stranger; see this note about standards. Any reasonable format is fine, including plain text; see this note about formats.