Orbits of Transformations

The concept of an orbit is a key one in transformational geometry.

In this course we will use the concept of orbit several ways.

• Identify an unknown transformation by its orbit.
• Create symmetric patterns as orbits.
• Create visual understanding of the rules of composition of isometries.

Orbits have been encountered informally already two or three times in the course. As you learn the new terminology, you can leverage your previous experience by reviewing these old labs.

• Lab 2 (Part b) Multiple Mirrors and Kaleidoscopes
• Lab 7 Tools -- A Lattice Tool
• Lab 8 (Part 3: Point Reflection and Translation) -- Images by Point Reflections; generation of parallelograms and lattices

Definition and Detailed Explanation, with Examples

The definition of the orbit concept, with with a number of illuminating examples, can be found at this Orbits of Transformations Page.

This is what you should read before doing the Lab 9 and Assignment 9.