This week for the 40 week math challenge we were contemplating rotational symmetry. I love to look around in our world and see where we can find real examples of math in nature.
We first needed to define what is meant by ‘rotational symmetry’ before we could even begin to look for examples. Once we thought we had a grasp of what we were looking for, we needed to come up with a list of where we might find this geometrical wonder.
Finding the beauty in the rotational structure raised more questions. Do we always find rotational symmetry in this example? Why or why not? What causes the order and structure that produces rotational symmetry?
Cue Math states the definition for Rotational Symmetry as the following:
“An object when rotated in a particular direction, around a point is exactly similar to the original object is known to have rotational symmetry. When a geometrical shape is turned, and the shape is identical to the origin, it is known to exhibit rotational symmetry. is also known as radial symmetry. Geometrical shapes such as squares, rhombus, circles, etc. show rotational symmetry. We also see rotational symmetry existing in daily life such as exhaust fans, windmills, etc.”
We simplified this for our math challenge cards to state:
“When a shape looks the same when partially turned around the center point.”
This video will help with understanding what is meant by rotational symmetry:
Now we knew what we were looking for, we looked for places in nature where, when you turn the object, it looks the same. Our list started to grow, starting with flowers of course! Here is a list of places that we decided would give examples of the kind of symmetry that we were looking for.
- Star fish
- Cross section of fruit
But did these things ALWAYS have rotational symmetry. Could we find examples of, say, flowers that were not symmetrical around a center point?
Yes! I believe that a non-example can have great power in helping us understand concepts.
On our list we placed Galaxies last. It’s true that we can’t just pop outside and view a spiral galaxy but we do know what they look like by the amazing photos that we can find online. Looking at pictures of the various galaxies we determined that there are ones that have rotational symmetry and ones that are asymmetrical. Our own galaxy – The Milky Way is considered to be a spiral galaxy, one of the galaxies that does have rotational symmetry. But there are also galaxies that are not rotational, so we can’t state that ALL galaxies have rotational symmetry, just like we can’t say all flowers have rotational symmetry. Here is a video which show and explains the different shapes of the galaxies in our universe.
When it comes to answering the question of why there are galaxies which have such amazing symmetry this article by Science Alert seems to have the answer, it states
…look at all the spiral galaxies out there. They can be half a million light years across, but they still preserve their symmetry. How? In our new study, published in Scientific Reports, we present an explanation.
But I warn you that it is full of words like entropy, intro-entropy and electromagnetism. Although it is quite a read, I did love this statement
“The stars in the galaxy are simply choreographed by an entropic force to line up into a pair of such spirals to maximise entropy.”
Most of the research I did on Galaxies featured a common theme of the ancient age of the universe. Which is why it is great to find reliable scientists who believe in the creation of the world as stated in the Bible. You can find some great articles at Creation.com about the age of our universe.
One historical mathematician and astronomer who was strongly Christian and believed that his faith did not conflict with his profession was Johannes Kepler. You can find more information about him HERE. You might like to have your children do a project about his life and work with the free pages that you can download below.
If you would like to explore Rotational Symmetry more, you might like the free 40 weeks of Math Challenge Cards. Week 14 has 4 challenges, at different levels, for you and your children to enjoy!