Transformation Study Suggestions
This page has links to some practice questions asked in the past and some questions
that might be asked on the topic of transformations of the plane.
Step 1: Read the Book Thoroughly
The textbook, Transformational Geometry by Richard Brown, is
readable and short. You should be familiar with pretty much the whole book by
now (except for the "group" stuff in 2.4-2.7).
Since this is a math book, you should read every page two or three times,
always drawing and thinking of examples and questions.
List all definitions and learn them rather carefully
- Make your own list (and check it twice)!
- Definitions are often key parts of proofs. To use one, one must know just
what the definition states. Don't say "by definition" unless you
are really using the definition and not a theorem.
- If you are writing a definition, remember that a definition is a complete
sentence.
List all theorems and learn the statements and at least the ideas of the proofs
- Make a list.
- Learn carefully what the key theorems say.
- Reflect on what the theorems mean. Connect with example, problems and constructions.
- Read the proofs for the key ideas. The proofs often contain additional ideas,
such as how to carry out constructions (e.g., Theorem 22 tells how to construct
a center of rotation).
- Learn key proofs.
Step 2: List the big ideas from lab and class
Ideas that were emphasized in class or in lab are particularly key ideas for
the course.
Step 3: Follow these links for questions and sample problems
Some of these links are from earlier years and so a few questions may not fit
the 2004 edition of Math 444, so do keep this in mind (we have done less with
symmetry so far). However, most are quite relevant to this year's course.
Notes
- Aut
2003 - Class Notes : There are extensive notes on transformations starting
with the notes of 11/26. There are notes about composing two rotations and
about triple line reflections.
- Aut
2003 - Study questions: These include a lot of sample questions about
compositions.
- Glide Reflection Facts:
Notes that spell out some details about glide reflections and how to construct
the definiing data for a glide reflection.
Old Test Questions