Super Symmetries: The Magic of Mirror Images
When you look at yourself in a mirror, do you think about how you have a “left side” and a “right side”? You have a left eye and a right eye, a left shoulder and a right shoulder, and on and on. Most parts of your body have a nearly identical twin that is its “mirror image.” This is called mirror symmetry.
People and most animals have mirror symmetry. Some scientists believe that animals are more attracted to mates with a symmetrical appearance.
For fun, the photo of the dog below was cut down the middle and each half was flipped to make its head perfectly symmetric. Can you tell which is the original photo?
Which one is the real Siberian Husky? (See answer below.)
Many Kinds of Symmetry
If you take time to notice, you’ll see symmetry all around you. Look at a flower like the one below, and you’ll see another type of symmetry. Each petal is nearly identical to the others, and they are arranged around a center in a repeating pattern. This is called rotational symmetry. The crystals of a snowflake and the arms of a starfish or an octopus have this kind of symmetry.
If you look closely at the petals you notice that each has mirror symmetry too, so an object can have more than one type of symmetry!
An echinacea flower photographed at night with a flashlight creates a dramatic purple glow.
Repeating patterns like you see in tiles below have a translational symmetry. Like a checkerboard, there is section of the floor that repeats and looks identical if you look left, right, up, or down. If you make a list of everything you see in a day that has symmetry it will be a very long list!
These colorful tiles have translational symmetry.
Because symmetries are all around us, mathematicians and scientists use them to help us understand the world. A scientist named Philip Anderson, who won a Nobel Prize for Physics, wrote “It is only slightly overstating the case to say that physics is the study of symmetry.”
Other Kinds of Symmetries
In addition to physical symmetries, there are artistic symmetries. Artists and architects often use symmetry to convey beauty and grace. The Bahá’í temple in New Delhi, India, was designed with several kinds of symmetry to look like a delicate lotus flower.
The Bahá’í House of Worship in India is known as the Lotus Temple.
Describing symmetries we see around us, ‘Abdu’l-Bahá, the leader of the Bahá’í Faith from 1892–1921, said: “It is natural for the heart and spirit to take pleasure and enjoyment in all things that show forth symmetry, harmony, and perfection. For instance: a beautiful house, a well designed garden, a symmetrical line, a graceful motion, a well written book, pleasing garments—in fact, all things that have in themselves grace or beauty are pleasing to the heart and spirit.”
Even sounds you hear can have symmetries. ‘Abdu’l-Bahá also said: “What is music? It is a combination of harmonious sounds. What is poetry? It is a symmetrical collection of words. Therefore, they are pleasing through harmony and rhythm.”*
Symmetry has even been used to describe spiritual qualities such as love. The Bahá’í mathematician William Hatcher wrote, “The giving and receiving of love is a reciprocal or symmetric relationship. It is a positive and satisfying experience for both parties.”
Illustrating another example of symmetry—symmetry between the physical and spiritual worlds—‘Abdu’l Baha wrote: “These are spiritual truths relating to the spiritual world. In like manner, from these spiritual realities infer truths about the material world. For physical things are signs and imprints of spiritual things ...”**
Some Fun With Symmetries
You can have fun discovering more about symmetry at home or with friends (even when meeting on the phone or online)! Here are some ideas:
- Use a camera to take photos of objects that show symmetry.
- Spread paint on objects from nature, like pinecones or leaves. Roll or press them onto a blank sheet of paper. You can repeat the patterns in different directions to create more intricate designs.
- Write some poetry about your time during the pandemic or your summer activities.
- Think about symmetry in your home or bedroom to see if you can create more symmetry. Maybe try organizing a book shelf or a closet.
- Ask a parent or friend about a project that you can do together that allows for an equal partnership (cooking together, learning a new dance together, etc.). The possibilities are endless.
- Spend some time using the drawing app below and have fun with your own creativity while creating symmetrical art.
Coming Soon: A Symmetrical Drawing App!
Watch for our new Super Symmetry drawing app coming soon! It can help you make snowflake-like patterns with both rotational and mirror symmetry. But instead of just the 6 symmetrical branches of a snowflake, you can have any number of branches, from 2 to 99!
Dr. Steve Scotti, STEM Education Advisor
Dr. Steve Scotti is Brilliant Star’s STEM Education Advisor and a Distinguished Research Associate at NASA Langley Research Center in Virginia, U.S. His background is in developing lighter, stronger materials and structures for aircraft and spacecraft. Watching the first astronaut launched into space inspired his interest in space exploration, and he enjoys sharing his enthusiasm about science and space with kids.
Pat Eelman, photographer and gallery co-manager
Pat Eelman has had a lifelong love for the arts in the areas of photography and gallery and exhibit planning. She studied photography and spent many hours in the darkroom before transitioning to digital photography. Pat currently works at a Cultural Arts Center where she co-manages a gallery.
ANSWER: The middle photo is the original Siberian Husky.
* These quotations are from a Bahá’í’s remembrances and may not be ‘Abdu’l-Bahá’s exact words.
**This is an initial translation and may be updated at some point.
Images: Kid in mirror by mtreasure, dog by doanme, flower by Pat Eelman, tile by lillisphotogaphy, Lotus Temple © Bahá'í International Community
DrScotti51 Science183 STEM261 Vision7 Symbols6 Art44 Beauty1 Creativity245 Architecture16 Photography30 Discover516 STEM Station30 STEAM43 STEAMS69