ASSIGNMENTS
MTH 338 — Winter 2016

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

Term paper deadlines:
2/12/16: Choose a topic
2/19/16: Project proposal due
2/26/16: Draft of introduction due
  3/4/16: Rough draft due
3/14/16: Final version due
Reading assignments:
Week 1: Read TG §1–§3.
Week 2: Read TG §4–§5; Skim RG §1.1–§1.2; Read RG §1.3–§1.4.
Week 3: Skim RG §2.1–2.2 & §2.6.
Week 4: Review RG §2.6; skim RG §3.2–§3.6; read RG §6.2–§6.3
Week 5: Read RG §6.6; skim RG §6.7
Week 6: Read RG §6.8
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 3/14/16
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" 3/9/16
Complete Lab 4.
You do not need to turn anything in, but you should make sure that you verify Desargues' Theorem in at least one case.
Due 3/4/16
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."
Due 2/26/16
This is the second of two different assignments this week.
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.
Due 2/26/16
This is the first of two different assignments this week.
Complete Lab 3, which will be handed out in class on Wednesday.
If you miss Wednesday's class, you will not have access to a Lénárt sphere, but you are strongly encouraged to try it on your own, either using Geometer's Sketchpad or GeoGebra, or even some sort of ball you can write on.
Each group should email a photo to me showing their area construction using lunes, along with a list of group members and a copy of their area calculation.
No explanation in words is necessary.
Due 2/19/16
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.
Due 2/12/16
There are two different assignments this week:
Choose a topic for your essay.
Write a few sentences explaining your topic.
Complete Lab 2.
A brief but polished writeup should be included for the SAS excercise, for which it is acceptable to consider a special case, such as a right triangle, so long as your assumptions are clearly stated. However, no explanation is needed for the second part of the assignment, for which it is sufficient to turn in an ordered list of routings, with the total distance clearly given in each case.
You are encouraged to complete Lab 2 by Wednesday, 2/10/16, if possible.
Due 2/5/16
Complete Lab 1.
Your writeup should include both a figure and an explanation of the process used. 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 is probably sufficient.
You may choose to use GeoGebra instead of Geometer's Sketchpad for this activity.
See the announcements page for further details.
Due 1/27/16
Prove SASAS congruence for quadrilaterals:
If the vertices of two quadrilaterals are in one-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..
"Due" 1/25/16
Complete Lab 0.
There is nothing to turn in, but you will use this or similar software in future activities, so this one is good practice.
You may choose to use GeoGebra instead of Geometer's Sketchpad for this activity.
See the announcements page for further details.
Due 1/20/16
This is the second of two different assignments this week.
TG §3: 7, 15
TG §4: 13ad
Explain your answers. Use complete sentences. Turn in this assignment at the beginning of class.
Due 1/20/16
This is the first of two different assignments this week.
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.
Due 1/13/16
This is the second of two different assignments this week.
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 1/13/16
This is the first of two different assignments this week.
Write one paragraph 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.