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We are experimenting with a diverse group of participants in this course: high school students, high school teachers, college students, college teachers, and others.

Topics in mathematics often have many levels of meaning, and we hope and expect that despite-no, because of-the diversity, there will be a lot for everyone (including we the staff) to get from the course. As you think about something, you come to understand it from different angles, and on successively deeper levels.

We want to encourage interactions between all the participants in the course. It can be quite interesting for people with sophisticated backgrounds and with elementary backgrounds to discuss a topic with each other, and the communication can have a high value in both directions.

Scheduled meetings

The officially scheduled morning sessions, which run from 9:00 to 12:30 with a half-hour break in the middle, form the core of the course. During these sessions, various kinds of activities will take place. There will be some more-or-less traditional presentations, but the main emphasis will be on encouraging you to discover things for yourself. Thus the class will frequently break into small groups of about 5-7 people for discussions of various topics.

Discussion groups

We want to enable everyone to be engaged in discussions while at the same time preserving the unity of the course. From time to time, we will break into discussion groups of 5-7 people.

Every member of each group is expected to take part in the discussion and to make sure that everyone is involved: that everyone is being heard, everyone is listening, that the discussion is not dominated by one or two people, that everyone understands what is going on, and that the group sticks to the subject and really digs in.

Each group will have a reporter. The reporters will rotate so that everyone will serve as reporter during the next two weeks. The main role of the reporters during group discussions is to listen, rather than speak. The reporters should make sure they understand and write down the key points and ideas from the discussion, and be prepared to summarize and explain them to the whole class.

After a suitable time, we will ask for reports to the entire class. These will not be formal reports. Rather, we will hold a summary discussion among the reporters and teachers, with occasional contributions from others.


The required texts for the course are: Weeks, The Shape of Space and Coxeter, Introduction to Geometry. There are available at the University Bookstore.

Coxeter's book will mainly be used as a reference book for the course, but it is also a book that should be useful to you in the future.

Here is a list of reading assignments from The Shape of Space by Weeks. As Weeks suggests it is important to `` slowly and give things plenty of time to digest'', as much as is possible in a condensed course of this type.

In addition, there is a long list of recommended reading. The geometry room has a small collection of additional books, which you may read there. There are several copies of some books which we highly recommend such as Flatland by Abbott and What is Mathematics by Courant and Robbins. There are single copies of other books.

Other materials

We will be doing a lot of constructions during class. Beginning this Tuesday (June 18th), you should bring with you to class each time: scissors, tape, ruler, compass, sharp pencils, plain white paper. It would be a capital idea to bring extras to rent to your classmates.


Each participant should keep a journal for the course. While assignments given at class meetings go in the journal, the journal is for much more: for independent questions, ideas, and projects. The journal is not for class notes, but for work outside of class. The style of the journal will vary from person to person. Some will find it useful to write short summaries of what went on in class. Any questions suggested by the class work should be in the journal. The questions can be either speculative questions or more technical questions. You may also want to write about the nature of the class meetings and group discussions: what works for you and what doesn't work, etc.

You are encouraged to cooperate with each other in working on anything in the course, but what you put in your journal should be you. If it is something that has emerged from work with other people, write down who you have worked with. Ideas that come from other people should be given proper attribution. If you have referred to sources other than the texts for the course, cite them.

Exposition is important. If you are presenting the solution to a problem, explain what the problem is. If you are giving an argument, explain what the point is before you launch into it. What you should aim for is something that could communicate to a friend or a colleague a coherent idea of what you have been thinking and doing in the course.

Your journal should be kept on loose leaf paper. Journals will be collected every few days and read and commented upon by the instructors. If they are on loose leaf paper, you can hand in those parts which have not yet been read, and continue to work on further entries. Pages should be numbered consecutively and except when otherwise instructed, you should hand in only those pages which have not previously been read. Write your name on each page, and, in the upper right hand corner of the first page you hand in each time, list the pages you have handed in (e.g. [7,12] on page 7 will indicate that you have handed in 6 pages numbered seven to twelve).

Mainly, the journal is for you. In addition, the journals are an important tool by which we keep in touch with you and what you are thinking about. Our experience is that it is really fun and enjoyable when someone lets us into their head. No matter what your status in this course, keep a journal.

Journals will be collected and read as follows:

Your entire journal should be handed in on Friday June 27th with your final project. We will return final journals by mail.


Geometry lends itself to constructions and models, and we will expect everyone to be engaged in model-making. There will be minor constructions that may take only half an hour and that everyone does, but we will also expect larger constructions that may take longer.

Final project

We will not have a final exam for the course, but in its place, you will undertake a major project. The major project may be a paper investigating more deeply some topic we touch on lightly in class. Alternatively, it might be based on a major model project, or it might be a computer-based project. To give you some ideas, a list of possible projects will be circulated. However, you are also encouraged to come up with your own ideas for projects. If possible, your project should have some visual component, for we will display all of the projects at the end of the course at the Geometry Fair. The project will be due on the morning of Friday June 28th. The fair will be in the afternoon.

Geometry room/area

The fifth floor houses the Geometry Room. We hope that it will actually spill out into the hallways and corridors and thus become the geometry area. Thus the fifth floor will serve as a work and play room for this course. This is where you can find mathematical toys, games, models, displays and construction materials. Copies of handouts and books and other written materials of interest to students in the course will be kept here as well. It should also serve as a place to go if you want to talk to other students in the course, or to one of the teachers. Our current plan is to have this area open from 1:30 to 4:00 PM Monday through Friday, beginning right away. There will be a tour of the area at the end of Monday's morning session.

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Peter Doyle