ASSIGNMENTS
MTH 338 — Spring 2023

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

Term paper deadlines:

5/12/23: Choose a topic

5/18/23: Project proposal due

5/25/23: Draft of introduction due

6/1/23: Rough draft due

6/12/23: 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.

Ground rules:

• Assignments labeled "turn in" may be submitted electronically by the stated deadline. (PDF strongly preferred.)
• Other assignments should be submitted exactly as requested.
• Electronic submission of handwritten work is allowed, but use a scanning app, not a camera, and scan to PDF if possible.
• Avoid email attachments larger than 10 MB if possible, as they may not get through.
• If large messages are unavoidable, also send a separate message indicating that such a message was sent.

Writing Assignment #7: Due 6/12/23

See the note regarding submission on the announcement page.

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.

Writing Assignment #6: Due 6/1/23

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) and bring a copy to class.

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."

Lab 4: Due 5/30/23

There will be a short lab activity in class on Tuesday, 5/30/23.

After this activity, each group should email a single image to me showing their construction, along with a list of group members. (No explanation in words is necessary.)

Writing Assignment #5: Due 5/25/23

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 – single-spaced and typeset.
A bit more is fine; much less is not.

Email a copy to me as an attachment and bring a copy to class.

Lab 3: Due 5/23/23 5/25/23

There will be a lab activity in class on Tuesday, 5/23/23 Thursday, 5/25/23.

After this activity, each group should email a single image 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.)
(Your image can be a photo, a screenshot, a PNG image exported from GeoGebra, or a GGB file from GeoGebra.)

If you miss Tuesday's Thursday'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 #4: Due 5/18/23

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 (by noon if possible) and bring a copy to class.

Writing Assignment #3: Due 5/12/23 (FRIDAY!)

Choose a topic for your essay. (It's still not binding.)

Write a few sentences describing your topic.

Email a copy to me.

Writing Assignment #3a: Due 5/9/23

Choose a topic for your essay. (It's not binding yet.)

A list of potential topics has been posted here.

Bring a copy to class; no need to send me anything.

Lab 2: Due 5/9/23

Use GeoGebra to verify SAS congruence in the Klein Disk model of single elliptic geometry.

• Construct a triangle. Measure all the sides and angles.
• Construct another triangle such that two corresponding sides as well as the included angle are congruent.
  Try to use straightedge and compass only in your construction, with measurements being done only at the end.
  Avoid special triangles (right, equilateral, reflected, etc.) if possible.
• Check whether SAS congruence holds in this case by measuring the remaining sides and angles in both triangles.

The information on the announcements page regarding SAS applies in any geometry in which SAS congruence holds.

Draw a circle in the Klein Disk

• Construct a (complete) circle in the Klein Disk which intersects the "equator" in exactly two (elliptic!) points.
  That is, find all points in the Klein Disk that are a given distance from a given point, with the further restriction that the resulting set of points must contain exactly two (elliptic) points on the boundary.

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 at the beginning of class.

Lab 1: Due 5/2/23

Use GeoGebra to verify SAS congruence in the Poincaré Disk:

• Construct a triangle. Measure all the sides and angles.
• Construct another triangle such that two corresponding sides as well as the included angle are congruent.
• Check whether SAS congruence holds in this case by measuring the remaining sides and angles in both triangles.
• (Optional) Use a similar construction to check whether SSS congruence holds.

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 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 content score 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.

Lab 0: "Due" 4/27/23

Use GeoGebra to perform the following tasks (in Euclidean geometry):

• Construct a triangle. Measure all the sides and angles.
• Construct another triangle such that two corresponding sides as well as the included angle are congruent.
  Try to avoid "constructing" objects by specifying their size. Rather, attempt to duplicate an existing object.
• Check whether SAS congruence holds in this case by measuring the remaining sides and angles in both triangles.
• (Optional) Use a similar construction to check whether SSS congruence holds.

Do not turn anything in.

You are encouraged to use this software in future activities, so this activity is good practice.

HW 3: Due 4/25/23

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.

Writing Assignment #2b: Due 4/20/23

Revise your defininition of non-Euclidean geometry. (You may start from scratch if you prefer.)

Bring a copy to class. (There is no need to send me a copy.)

HW 2: Due 4/18/23

TG §3: 7, 15

TG §4: 13ad

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

Writing Assignment #2: Due 4/12/23 (WEDNESDAY!)

Define non-Euclidean geometry.

Email a plain text copy to me the night before class and bring a copy to class.

A single sentence may be sufficient. Your audience consists of your fellow classmates.

HW 1: Due 4/11/23

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.

Writing Assignment #1: Due 4/6/23

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.