ASSIGNMENTS
MTH 338 — Spring 2014
Assignments given by number refer to either Roads to Geometry (RG) or Taxicab
Geometry (TG).
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Term paper deadlines:
- 5/9/14: Choose a topic
- 5/16/14: Project proposal due
- 5/23/14: Draft of introduction due
- 5/30/14: Rough draft due
- 6/9/14: Final version due
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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 9: (no reading assignment)
- 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.
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Due 6/9/14
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Complete your essay.
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Turn in hard copy to me in my office by noon.
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Include the corrected copy of your rough draft.
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Late submissions will only be accepted if the delay is
cleared with me in advance.
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Please also email a copy to me.
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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.
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Due 5/30/14
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Write a rough draft of your entire essay.
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A suggested minimum length for this assignment is 3–5 pages
(single-spaced; roughly 5 pages double-spaced).
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Submit electronic copy to me (PDF strongly preferred).
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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.
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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."
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Due 5/28/14
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Bring a printed copy of your most recent draft to class, and be prepared to
explain it to a neighbor.
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Due 5/23/14
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Write (a draft of) the introduction for your essay.
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Tell the reader what you are going to do. An appropriate length for this
assignment is one full page.
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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.
You are also encouraged to comment on each other's introductions.
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Also submit electronic copy (PDF strongly preferred) to me on Friday,
together with the corrected hard copy of your proposal.
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"Due" 5/19/14
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Complete Lab 3, which was handed out in class
on Friday.
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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.
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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.
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Due 5/16/14
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Write a project proposal, consisting of a title and a short description of
what you intend to do.
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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.
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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.
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Due 5/9/14
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There are two different assignments this week:
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Choose a topic for your essay.
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Write a few sentences explaining your topic.
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Complete Lab 2.
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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
(optional)
London/Tokyo problem, it suffices to turn in a single picture showing all of
the routings, with city names and distances added by hand.
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You are encouraged to complete Lab 2 by Wednesday, 5/7/14, if possible.
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Due 5/2/14
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Complete Lab 1, which will be handed out in
class Monday 4/30.
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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.
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Due 4/28/14
- Prove SASAS congruence for quadrilaterals:
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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?
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You may answer this question separately, or incorporate the answer into your
proof.
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In which geometries is your proof valid?
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Use complete sentences. Include one or more figures. Turn in this assignment
at the beginning of class Monday.
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Due 4/21/14
Due 4/23/14
- TG §3: 7, 15
- TG §4: 13ad
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Explain your answers. Use complete sentences. Turn in this assignment at the
beginning of class
Monday Wednesday.
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Due 4/18/14
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Define non-Euclidean geometry.
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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.
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You are encouraged to pay attention to these
criteria when editing your definition.
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Due 4/14/14
- TG §2: 2, 4, 5
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Explain your answers. Use complete sentences. Turn in this assignment at the
beginning of class Monday.
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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.
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Due 4/11/14
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Define non-Euclidean geometry.
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Instructions for submitting your paragraph are available
here.
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Due 4/7/14
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Post at least one comment on the paragraphs written by the other students in
your group.
Add a comment on at least one of the paragraphs written by the other students
in your group.
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Due 4/4/14
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Write one paragraph describing your interest in mathematics.
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Instructions for submitting your paragraph are available
here.