Introduction to Geometries 2000-01.

**Course Director:** Walter Whiteley

**Office:** South 616 Ross

**Telephone:** 736-5250 Extension 33971

**E-mail:** whiteley@mathstat.yorku.ca

**WWW:** http://www.math.yorku.ca/Who/Faculty/Whiteley/menu.html

**Office hours:** TBA (currently by appointment)

**Classes:** Monday Wednesday 4:00-5:30 PM Ross South 525 (the MathStat Lab)

**Teaching Assistant/Marker:** Deborah DiCaprio

**Office:** Ross North 611

**Tutorials:** Monday 2:30-3:30, Ross S501

A nice resource on sketchpad, designed for use with the
Ontario Curriculum
is the SketchMad
web site created at Queen's University. This part of a larger
effort to provide good support for the use of Geometer's Sketchpad
in Ontario Schools. A related initiative which * may *
be open to a few students from this class is a set of
four day workshops being designed for this summer.
I am on the organizing committee and tentative plans include
a few places for students currently in Faculties of Education.

The CUPE strike is now settled. Classes and tutorials have resumed for the remedial period. We will resume on Monday January 15, with both a tutorial and a class. These will be at the regular time and place. I will also be at the tutorial room, along with the tutor, to answer any urgent questions.

Here is my plan. I am, of course, prepared to discuss any specific situations which require special accomodation, or general requests which help us move along with the course.

I will follow the schedule established by Senate and hold 'remedial' classes during their 22 day schedule. We will also have regular tutorials and probably some additional tutorials. With that momentum we will continue on into the second semester (after a short break for courses which have exams).

Here is some planning you can do!:

** Note ** that because of the length of the strike,
I have adjusted the due dates for the two assignments you were
working on in October. By Senate Policy, NO deadlines are within
the first week of remediation

Assignment 3 - Definition of an angle and a proof of the vertical angle theorem
on plane and sphere - is due the **third class ** after the strike is over.

Assignment 4 - A proof that ASA gives congruent triangles on plane and sphere
- (and clarification of which 'triangles' fit this proof) is due the **
fourth class ** after the strike is over.

With the fourth assignment (at the fourth class),
I will * also* ask for a written progress report
on your project. That will likely be followed by a meeting with me
(in groups if this is a group project. As always, I will want to
know "What is **your** question?" as well as what
resources you have found or are looking for, possible ways you would
present the material, what 'proof' you anticipate including in the write-up,
etc. Please talk with me if you are stuck, have questions, etc.
about the project.

Please contact me (e-mail or at class are the most reliable) if you have any or ideas.

I have posted a few of my reflections on the strike, should you be interested. These come, in part, from work I did in collaboration with a very interesting group of students in FES.

Other information about what is happening (and not happening) and what to expect around resecheduled classes, remedial support, etc. can be found at a variety of sources. Here are some:- the registrar's office which has basic information including FAQ for students.
- general advice for instructors from the CST which implicitly gives advice for students and future teachers.

In addition to completing these assignments, I strongly encourage you
to continue work towards your project. The final project can be
a group project. It will include both a class presentation and a written
etc. form. The written form should include at least one proof.
Whether the proof is part of the in-class presentation depends on some
pedagogical choices.

The project should **start** with a question you really
would like an answer to. This may turn out to be too big, but it
is an important experience to work through from a question to an answer,
(or perhaps to the information that the answer is not known!).

Feel free to contact me by e-mail for feedback, to request additional
resources, to explore issues.

The Course Outline is on the web.

**Texts: **We have one text for the course. We will begin working from the text by the second class, working through the first 10 chapters in the fall semester, as well as working with other materials.

David Henderson: Experiencing Geometry on Plane and Sphere (Prentice Hall), 1996;

(This is also *on reserve in Steacie Library*, as PC1802)

Other reference on reserve:

- George A. Jennings, Modern Geometry with Applications (Springer-Verlag), 1994.
- Adventures on the Lenhart Sphere (Key Curriculum Press)

You are also encouraged to develope your own `model spheres' for explorations at home. Some suggestions and examples were offered during the first few classes. Samples are now available in the Undergraduate Math Lounge Ross: North 537. By the second week, I have a supply of small and medium plastic spheres and small plastic tori, which, with a yogurt container, will make a good hands-on tool for exploring spherical geometry. The *cost *of the plastic materials is $1.00 - $5.00 for the spheres and $1.00 for the torus). Perhaps the second week, after class, we will even have a `construction supper' to cut off the extraneous hangers on the spheres (with a metal saw), and shape the containers into good `spherical rulers' (great circle drawers) with a sharp knife and some sandpaper. [If you are looking on your own, they are in the `Crafts' section of stores Zellers, White Rose, Michaels - for making hanging decorations!]

*First Week**including:**First Assignment**: Due September 13**Second Assignment*Due September 25.

*Every assignment should end with a page (or so) of your current questions, or responses to an ongoing dialog with the instructor and the tutor, provoked by previous questions.* (See the handout on evaluation standards .)

At this level (third year or higher) I hope your own curiousity and questions about the mathematical material are bubbling to the surface. I strongly encourage you to ask `What if ... ?' about any or all of the material. I assume that any good assignment will leave you with more questions and a sense of other possibilities when you `finished' than when you started! It is an important objective of the course to develop you skill at asking 'geometric' questions - and knowing what to do after you have asked the question! In the marking scheme, there will be a deduction of one grade point, if you fail to include this last page of questions/dialog/responses.

** Projects **Student should start to think about possible

The dialog at the end of your assigments is likely to lead you towards a possible project. If there is a question that you really want the answer to (or at least a better understanding of), that can usually be shaped into a nice project. Take a chance and at least ask your question. Keep in touch about this.

Interesting Geometry Web Sites

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