Transformation Geometry -- Math 331

February 25, 2004

Discussion

Exercises due Friday, February 27

  1. Let f be rotation about the point (1, 0) through the angle pi/4, and let g be rotation about the point (0, 1) through the angle pi/6. Show that g \circ f is a rotation, and find its center and its angle of rotation.

  2. When is it the case that the composition of two rotations about different centers is a rotation?

  3. What type of isometry is the composition of a reflection with the half turn, i.e., rotation through the angle pi, about a point not on the axis of the reflection?

  4. If three lines l_{1}, l_{2}, l_{3} intersect so as to form a triangle, what type of isometry is the composition sigma_{3} \circ sigma_{2} \circ sigma_{1} of the reflections in those lines?


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