Assignment 6 (Draft Due Wed 2/12, Final Due Fri 2/14)

The Goal

The goal is to produce really thorough write-ups and explanations of the two stereographic situations in Lab 5. The assignment goes a bit beyond the Lab in that the write-up should be very complete with lots of details.

To make this less arduous the plan is this. Students will work in pairs. One student in each pair will write up the analysis of the first figure, the other student will write up the second. (Since there is an odd number of students in the class, there will have to be a group of 3.) Each student should review the other partner's work for correctness and clarity and quality.

See Below for Details and Due Dates

What to put in

Points on the sphere can be located by

• Space coordinates (x,y,z)
• Spherical coordinates (latitude and longitude)
• Stereographic image in (x,y,0) plane
• For two points, there is a 3-space (straightline) distance and a spherical distance
• Fro 3 points there is a plane angle measure and a spherical angle measure

Circles on the sphere (including great circles can be described by)

• Equation in x,y,z of the plane of the circle
• Center and radius in the plane
• Center(s) and radius (radii in spherical distance) on the sphere
• Stereographic image (by equation in the plane or center-radius)

So the goal for each figure is to put in ALL these details, clearly written so that others can make sense of it. Put in all 3 kinds of coordinates for points, all kinds of information about circles, also distances and angles.

Also, make a very nice, accurate drawing of the stereographic image of the figure on the sphere.

The figures (each student does one of these figures)

Figure One is the spherical cube, with the vertices defined as intersections of median lines of the 90-90-90 triangles of the octahedron.

Figure Two is the figure consisting of midpoint triangles of the same 90-90-90 triangles.

See Lab 5 for more detail about the figures. See various notes, answer sheets, etc., for methods of finding the coordinates

Due Dates

A DRAFT or WORK IN PROGRESS is due on Wed 2/12
The draft need not be reviewed. This will be recorded as "present" but won't be graded. The final version will be graded instead. The draft can have missing pieces, but it should look like something that has taken at least an hour or two, not a minute or two. Since you will need the draft to work with, you should turn in a copy that you can spare.

Before Friday,
you should receive a copy of your partner's paper to review. You should respond with written (or emailed) comments to the other student. If you get the paper by midday Thursday, you should give feedback by early Thursday evening. Of course even better is working together and getting the work done earlier.

Save your written comments if you make substantive suggestions for changes and improvements.

FINAL VERSION is due on Friday (with the signature of another student "reviewer" on it).

Length: This is a substantial assignment, but with the figure it should only run about 3 - 4 pages.

Grading and Quality
The grade will be based on the quality of the math and the presentation (and that of the paper you reviewed).The quality level should be such that you would not be embarrassed to include it in a portfolio of your work in an application to the College of Education. It need not be word-processed (though that would be good) but it should be written clearly and organized for readability (plenty of white space, subheads, etc).

Review Problems?
In the event that you cannot endorse the paper you are reviewing, you will need to have saved the comments you made to show that you tried to improve the paper. Let's hope this does not happen.

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