82. REFLECTIONS IN PARALLEL MIRRORS

This fun poster by Anthony Kolber of Melbourne, Australia, shows what can be done with reflections in a pair of parallel mirrors. (Although, there are some anomalies here. Where is the camera? And the feet puzzle me!)

A reflection is an example of an isometry – a length preserving transformation. We can illustrate its effect on the letter F (for example) as follows: | . Here the vertical line indicates the mirror, and the letter F is reversed under the reflection. If this backward F image is now reflected in a parallel mirror, we obtain:  |  | . We see that the combined transformation, reflection followed by reflection in a parallel mirror is a translation – another isometry. You might like to investigate further reflections in these two mirrors: we obtain a whole line of alternating forward and backward Fs – much like the effect in the photo. These reflections and translations form a group having infinite order.


http://en.wikipedia.org/wiki/Euclidean_plane_isometry

http://paulscott.info/groups/gpf/RB1.html