ASSIGNMENTS
MTH 338 — Spring 2012

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

Term paper deadlines:

5/11/12: Choose a topic

5/18/12: Project proposal due

5/25/12: Draft of introduction due

  6/1/12: Rough draft due

6/11/12: Final version due

Reading assignments:

Week 1: Skim RG §1.1–§1.2; read RG §1.3–§1.4

Week 2: Read TG §1–§3

Week 3: Read TG §4–§5

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: 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.

Many of the assignments in this course will need to be posted to the Student Blog.
General instructions for accessing the blog are available here.
Some of the links below will work best if you are already logged in to the blog.

Due 6/11/12

Complete your essay.

Turn in hard copy to me in my office by noon.

Include the corrected copy of your rough draft.

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" 6/4/12

Complete Lab 4, which will be handed out in class on Friday.

You do not need to turn anything in, but you should make sure that you verify Desargues' Theorem in at least one case.

Due 6/1/12

Write a rough draft of your entire essay.

Turn in hard copy to me. Include the corrected hard copy of your introduction.

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 5/25/12

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 most of a page.

You are strongly encouraged to post a copy of your introduction on the student blog. To increase visibility, I suggest that you start a new blog page.

Also submit hard copy to me on Friday, together with the corrected copy of your proposal.

You are strongly encouraged to comment on each other's introductions.

"Due" 5/21/12

Complete Lab 3, which was handed out in class on Friday.

If you missed 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 Spherical Easel, or even some sort of ball you can write on.

You do not need to turn anything in, but you should verify that you obtain the correct formula for the area of a spherical triangle in terms of its angles.

Due 5/18/12

Write a project proposal, consisting of a title and a short description of what you intend to do.

You can present this as an abstract, summarizing the main conclusions, or as an outline, giving a table of contents. An appropriate length for this assignment is roughly half a page.

Please use these instructions to post your proposal on the student blog.
You should also submit hard copy to me on Friday, together with your previously submitted topic choice.

Due 5/11/12

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 writeup is needed for the remaining pieces, for each of which it is sufficient to turn in a picture, with your answer(s) clearly indicated. The (optional) equilateral triangle should show the angle measures, and the complete circle intersecting the equator should be clearly labeled. For the London/Tokyo problem, it suffices to turn in a single picture showing all of the routings, with city names and distances added by hand.

Lab 2 may be turned in on 5/14/12, but you are encouraged to complete it sooner if possible.

A student-initiated Doodle poll for students interested in getting together to work on the lab can be found on the student blog.

Due 5/7/12

Complete Lab 1, which will be handed out in class Monday 4/30.

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 should be about right.

Due 4/30/12

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 Monday.

Due 4/23/12

TG §3: 7, 15

TG §4: 13ad

Explain your answers. Use complete sentences. Turn in this assignment at the beginning of class Monday.

Due 4/20/12

Define non-Euclidean geometry.

Yes, this is the same assignment as last week. This time, post a single, group definition of non-Euclidean geometry. Follow the same instructions as last week, and post to the bottom of the same page. But each of you should edit the same definition until you're all happy with it.

Due 4/16/12

TG §2: 2, 4, 5

Explain your answers. Use complete sentences. Turn in this assignment at the beginning of class Monday.

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 4/13/12

Define non-Euclidean geometry.

Instructions for submitting your paragraph are available here.

Due 4/9/12

Post at least one comment on the paragraphs written by the other students in your group.

Due 4/6/12

Write one paragraph describing your interest in mathematics.

Instructions for submitting your paragraph are available here.