More than mirrors

Discussion about the many aspects of symmetry in design, and in the natural world.

More than mirrors

Unread postby Barrie Christian » 09 Aug 2012, 10:09

For most of us, what we understand by symmetry is left-right reflection. That is what stands out when we look at the world around us, whether it is a face, a leaf, or a church.
So many things seem neatly divided down the middle, one side the mirror image of the other.
It makes perfect sense and is wonderfully satisfying to look at.
But there are other types of symmetry apart from reflection symmetry, and there are more dimensions than just the two we normally use as a reference for symmetry.
The other types of symmetry include ROTATION, TRANSLATION, and GLIDE (translation+reflection), and SCALE.
Anyone who has tiled their bathroom or kitchen, using different types of tile, will have probably used two or more of these symmetrical layouts to create their pattern.
Spotting different symmetries in the real world can become an obsession - (read Marcus du Sautoy's book "Finding Moonshine").
Barrie Christian
Site Admin
 
Posts: 35
Joined: 02 Aug 2012, 14:45

Re: More than mirrors

Unread postby Barrie Christian » 13 Aug 2012, 18:06

For those interested in numbers, and symmetry is profoundly about numbers, there are only 17 different 2D patterns. In the Alhambra palace in Granada, the 17 different patterns have been identified.
[attachment=2]Tiles1.jpg[/attachment][attachment=1]Tiles2.jpg[/attachment]
Du Sautoy (Finding Moonshine) illustrates the rotational symmetries, around three points (6,3,2), which can be found in this pattern.
I am not an expert, but this drawing by M.C.Escher seems to show a similar pattern to the one in the Alhambra.
[attachment=0]Escher-Lizard.jpg[/attachment]
You do not have the required permissions to view the files attached to this post.
Barrie Christian
Site Admin
 
Posts: 35
Joined: 02 Aug 2012, 14:45


Return to Symmetry



cron