Composition of Isometries - is it commutative?
1. Is "Turn slide" the same as "Slide turn"?
In other words, is composition of translation and rotation commutative? 1a. In the applet below, provide a clear visual argument to support your answer. Use a slider to define a rotation. 1b. Is there a special case (certain specific translations or rotations), for which the composition would be commutative?
1. Is "Turn slide" the same as "Slide turn"?
2. Is "Slide flip" the same as "Flip slide"?
In other words, is composition of translation and reflection commutative? 2a. In the applet below, provide a clear visual argument to support your answer. 2b. Is there a special case (certain specific translations or reflections), for which the composition would be commutative? 2c. Use your answer in 2b to discuss the relationship between a "Slide flip" and Glide Reflection.
2. Is "Slide flip" the same as "Flip slide"?
3. Is "Turn flip" the same as "Flip turn"?
In other words, is composition of reflection and rotation commutative? 3a. In the applet below, provide a clear visual argument to support your answer. Use a slider to define a rotation. 3b. Is there a special case (certain specific reflections or rotations), for which the composition would be commutative?
3. Is "Turn flip" the same as "Flip turn"?
4. Is composition of two line reflections commutative?
4a. In the applet below, provide a clear visual argument to support your answer. 4b. Is there a special case, for which the composition would be commutative?
4. Is composition of two line reflections commutative?
5. Are there isometries, the composition of which is always commutative?
5a. In the applet below, provide a clear visual argument to support your answer. If needed, use a slider to define a rotation.