Radial Symmetry

These great examples of Radial Symmetry were made by my 4th, 5th and 6th graders. Please click on each picture below to see more details of their designs.

This week we did a project on radial symmetry, which is defined as having similar parts arranged around a central axis. This is a phenomenon that occurs in nature, art and mathematics. Examples of radial symmetry are rose windows in cathedrals, sliced pizzas, kaleidoscopes, mandalas, capitol rotundas, snowflakes, bike/wagon/car wheels, daisies, starfish and jellyfish.

I had wanted to do a project on rose windows or mandalas this year, and when I did a little research on these I found out about radial symmetry. I did several practice projects to get the process figured out in my own mind. We did what I'm calling simplified radial symmetry. We only used 4 repeated parts around the axis. Many of the projects I saw had 8 or more parts, which I thought was too complicated for our class time.

In class we talked about radial symmetry and looked at examples. Then we began to draw on 4-inch squares of paper. I chose this size because could make copies of the 4 joined parts (tiles) to fit a standard copy paper. I suggested nature as a theme and provided reference books for this, and most of my students went with this theme. We did rough sketches and refined the sketches as needed. We talked about rough drafts, transparency, mirror images, and light tables.

After the initial design was made and refined, all pencil lines were copied over with thick, smooth, dark lines. (Still in pencil.) Dark pencil lines will copy pretty well, or you could have students copy over their finished sketch in pen or permanent marker.

Design tips: Designs should fan out somewhat from one corner of the tile. Designs should fill the tile area pretty well. Designs that go off the page at several edges can be quite effective. Designs should have some detail, but not too much. Strive for a bit of a coloring book look.

To make the finished radial design, you need a mirror image of your original design. I offered two ways to do this. They could place the original 4-inch design (already copied out in dark lines) upside down on a window or light table and copy the lines as exactly as possible (emphasize this to them or you will be doing a lot of copying after the fact yourself), or you can use tracing paper so they can copy the back side with no back lighting. (A white background helps with this method.) The tracing paper will smudge more easily, but it worked pretty well, too. Be sure the tables they work on are smooth, or provide magazines or other smooth surfaces to do their line tracing on.

After class, I used a copier and copied all designs as follows:

Make copies: You will need two copies of the original side (A) and two copies of the back side (B). After copying, I lightly marked the back of each of the 4 4-inch square tiles with A or B to make it easier to set up the final design. The two A tiles go kitty corner from each other and the two B copies in the other two spaces. They should mirror each other and radiate from the center. Before making the copies, you might mark the edges or corners of the paper tiles with a light pencil mark to make cutting them to size after copying easier. I used a paper cutter.

Lay out the final design: You can play with different ways to lay out the design before you make your finished copy. When I had the arrangement of the 4 tiles the way I liked them, I used a bit of tape at the center of the 4 to tape them together from behind. After checking line alignment from each edge, I put a small bit of tape at the top of each juncture from behind.

Now your radial symmetry designs can be copied. I am giving each student back his original and 4-tile composition, and making coloring books for each student with one copy of every design in the class. We will color in these for our last day of class next week.

Below are my examples (including the dragonfly above) made in preparation for this lesson. Radial design is fun to do and fun to color. A new way to look at the world around us!

If you like this idea, you may want to check out the coloring books Ruth Heller's Designs for Coloring.