Is the act of double transformations commutative? That is, does the order in which you perform two actions influence the result?
- Perform a ¾ turn, followed by a ½ turn. Which letter appears at the top?
- Then,
reverse the order of the moves. That is, perform a ½ turn, followed by a
¾ turn. Now which letter appears at the top? Is it the same letter?
Now, try this.
- Perform a vertical reflection, followed by a diagonal reflection. Which letter appears at the top?
- Then,
reverse the order of the moves. That is, perform a diagonal reflection,
followed by a vertical reflection. Now which letter appears at the top?
Is it the same letter?
Investigate other double
transformations. When the order of two transformations is reversed, is
the result the same or different?