Introduction to Geometries 2000-01.

Course Director: Walter Whiteley
Office: South 616 Ross
Telephone: 736-5250 Extension 33971
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

New information

We will soon be doing work with the dynamic geometry program Geometer's Sketchpad - GSP for short. We will do some inclass work in the Gauss Lab Ross S110. To use this lab you will need to use the Maya system to set up a York Arts account.

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.

NEW 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: Should you find that in any of your courses that the Senate Policy on accomodation for the disruption are being violated, or that you have questions about what is happening or will happen, feel free to contact me and I will try to get you answers or pass on ways for you to get answers. Clearly this is a major disruption for everyone - and is likely to mean extra work for everyone, faculty and students alike. I hope that we can all be generous with one another under the pressures of the next few weeks. I also hope that we can rekindle the excitment and energy which was present before the strike.

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.

Past Assignments

Second Assignment, an exploration of 'what is a straight line' and a definition for the plane and the sphere - and your questions has been marked and returned. Revisions were due October 25.

First Assignment, your geometry autobiography and initial questions about geometry : was due at the second class September 13

Course Outline

The Course Outline is on the web.

Text and References

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:

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!]

Classes and Comments.

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 projects for presentation near the end of thecourse. In early December, I will ask for a written response about the topics you are planning to work on.

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.

Here are some web sites to explore:

Interesting Geometry Web Sites

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