Selected Math Themes: Groups, Permutation Games and Music by Borceux Bastian

Author:Borceux, Bastian [Borceux, Bastian]
Language: eng
Format: epub
Published: 2020-08-25T16:00:00+00:00

And the rotation of 90 degrees in the counterclockwise direction, which moves vertex A to B, vertex B to D, D to C and C to A:

Then apply the reflection first and then the rotation gives:

​ The previous road corresponds to the reflection by half of the square:

You can see what happens if we apply any of these transformations, that is, apply one of these transformations and then another one results in some rotation or reflection. But here the wonders do not end, in fact, no matter how we apply three of these transformations (but in the same order), we can first apply a transformation, then a second and the result of these two apply a third, or first apply the second followed by the third and apply it after the first one and we will have the same result, for example, take the following transformations:

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