SUNY at Stony Brook MAT 515: Geometry for teachers
Fall 2010

Welcome to MAT 515

MAT 515 is devoted to elementary geometry. The study will focus on the features of the subject which develop logical skills and geometric imagination of students.

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Announcements are listed in reverse choronological order: most recent announcement at the top.

The final exam will be on Thursday, December 16, at 2:15 pm - 4:45 pm in the room 4-130. The exam will cover the whole content of the course, except the part covered by the second midterm (vectors and analytic geometry). It will include theoretical questions about theorems and thier proofs.

One of the questions will suggest to formulate and prove a few theorems from the course closely related to each other. Here is the list of topics that are recommended for revisiting to this end.

One question will require just formulation of definitions and statements of theorems without proof. Here is the list of topics recommended for revisiting in this connection. This list is longer, it provides also a reliable skeleton for preparation to the whole exam.

Other questions in the exam will be in the traditional shape of a problem.

On Tuesday, December 14, at 5:20 in room 4-130, we will have a review session.

We start studying of the similarity geometry. This is an integral part of Euclidean Geometry. The main notions of the similarity geometry emerge in traditional presentations of Euclidean Geometry (in particular in the textbook by Hadamard that we use) in a very indirect way. A short modern introduction can be found here.

The second midterm exam will be on Thursday November 18. It will cover vector algebra and a piece of so-called Analytic Geometry related to lines and planes. It will consist of 4 problems.

This material is included into the course, because a teacher should be aware about it and should be able to solve elementary geometric problems in coordinates or using vector algebra.

The textbook does not cover this material. For vector algebra, you may find easily everything needed on the web. For example, take a look at Everything related to cross-product can be found on wikipedia. Dot-product in wikipedia starts from a perspective which differs from what we did in the class. Much closer to this course it is presented here. A good survey of equations of a line on the plane you can find on a beautiful web-site

All these sources miss vector equations, and I could not find a web site with appropriate text. That is why I wrote a concise text about various equations presenting lines and planes.


The first midterm exam will be on Thursday October 28. It will consist of 5 problems. In the homework, which is due by Tuesday, you have to compose your own version of this exam. On the page of homework you may find a detailed description of the kinds of problems. Below the material covered by the exam is described.

The exam covers the book 1 of the textbook, the first two chapters from the book 2 of the textbook and the material about isometries presented on this web site. I recommend revisiting all these texts. Pay a special attention to definitions and formulations of theorems.