ASSIGNMENTS
MTH 338 — Winter 2021

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

Term paper deadlines:
2/12/21: Choose a topic
2/19/21: Project proposal due
2/26/21: Draft of introduction due
  3/5/21: Rough draft due
3/15/21: 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–§3.4.
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 3/15/21
Complete your essay.
Email a copy of your final paper to me by noon.
Late submissions will only be accepted if the delay is cleared with me in advance.
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 3/5/21
Write a rough draft of your entire essay.
A suggested minimum length for your draft 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 will also be a lab activity in class on Wednesday.
You do not need to turn anything in, but you should make sure that you verify Desargues' Theorem in at least one case.
Due 2/26/21
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 an electronic copy to class.
Due 2/19/21
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 before class on Friday and bring an electronic copy to class on Monday, 2/22/21.
There will also be a lab activity in class on Friday, 2/19/21.
If you have a (nearly) spherical object you can write on, bring it to class. Tennis balls? Oranges?
After this activity, each group should email a single image to me showing their construction, along with a list of group members and a copy of their calculation. (No explanation in words is necessary.)
(Your image can be a photo, a screenshot, a PNG image exported from GeoGebra, or a GGB file from GeoGebra.)
If you miss Friday's class you are strongly encouraged to try the activity on your own, using GeoGebra and/or some sort of ball you can write on. (There is no need to send me anything unless you would like feedback.)
Writing Assignment #3: Due 2/12/21
Choose a topic for your essay. (It's not binding yet.)
A list of potential topics has been posted here.
Write a few sentences describing your topic.
Email a copy to me and bring a copy to class.
Lab 2: Due 2/8/21
Use GeoGebra to verify SAS congruence in the Klein Disk model of single elliptic geometry.
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°.
The information on the announcements page regarding SAS applies in any geometry in which SAS congruence holds.
Draw a circle in the Klein Disk
Your SAS writeup should include both a figure and an explanation of the process used.
Your Klein circle writeup does not require any explanation, so long as it is clear where the circle is in your figure.
Turn in this assignment via Gradescope before class.
Lab 1: Due 2/1/21
Use GeoGebra to verify SAS congruence in the Poincaré Disk:
The information on the announcements page regarding SAS applies in any geometry in which SAS congruence holds.
Your writeup should include both a figure and an explanation (not merely a description) of the process used.
Turn in this assignment via Gradescope before 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 1/25/21
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 via Gradescope before class.
Lab 0: "Due" 1/25/21
Use GeoGebra to perform the following tasks (in Euclidean geometry):
Do not turn anything in.
You will use this software in future activities, so this activity is good practice.
Further details will be posted on the announcements page.
HW 2: Due 1/20/21
TG §3: 7, 15
TG §4: 13ad
Explain your answers. Use complete sentences. Turn in this assignment via Gradescope before the beginning of class.
Writing Assignment #2: Due 1/15/21
Define non-Euclidean geometry.
Email a copy to me and bring an electronic copy to class.
A single sentence may be sufficient. Your audience consists of your fellow classmates.
HW 1: Due 1/11/21
TG §2: 2, 4, 5
Explain your answers. Use complete sentences. Turn in this assignment via Gradescope before 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.
Writing Assignment #1: Due 1/6/21
Write one paragraph (roughly half a page) describing your interest in mathematics.
Email a copy to me and bring a 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.