I have always
preferred being outside than being inside. There was always a pull for me to go
camping, or backpacking, or rock climbing. I’ve gone on many adventures all
over the U.S, and one thing remains the same across the board. Nature is
beautiful. Leaves and flowers are so simple in their construction, yet so
pleasing to look at. Spider webs, while not pleasant to get on you, are lovely
to look at all covered in dew in the early morning. Starfish and anemone stand
out in tide pools. Butterflies are vibrant and you can’t help but watch them if
they choose to flutter by you. But why is this? Why is nature so aesthetically
pleasing more often than not?
The answer to this
question is symmetry. Symmetry is defined as, “the correspondence in size, form, and
arrangement of parts on opposite sides of a plane, line, or point; regularity
of form or arrangement in terms of like, reciprocal, or corresponding parts.”
This is the technical definition, but it can also be defined as, “beauty
based on or characterized by such excellence of proportion.” The Greeks
based their ideas on symmetry on regular polyhedrons. Each regular polyhedral
was also associated with a natural element. Fire was the tetrahedron. Air was
an octahedron. Earth was a cube. Water was an icosahedron. The universe itself
was a penta-dodecahedron. The Greeks tried to explain biological symmetry in
terms of geometry. They had little success determining the underlying cause,
but they opened the door for further exploration of the root cause for
symmetry.
In nature, there are many types of symmetry. Each
has a specific axis for reflection. In organisms, the type of symmetry it
exhibits is an adaptation that the organism has evolved to in order to survive.
The first type of symmetry is called linear, or bilateral symmetry.
This means that you
can make an axis of symmetry straight down the center. One could also think of
it as a reflection along the line that you draw. Humans display this type of
symmetry, although most people are not perfectly symmetrical.
Another type of
symmetry is radial symmetry. Radial symmetry is what Starfish have. This type of symmetry means that the parts of
an organism are all arranged around one main axis. Flowers most often exhibit
this type of symmetry, but when other organism manage to come together in this
configuration it is stunning. There is research being done currently trying to
link the Fibonacci sequence to radial symmetry. I found this very interesting
due to the fact that we have discussed the Fibonacci sequence so often in
class.
The third type of symmetry often found in nature is called Strip Pattern symmetry. This is most often found with striping patterns on snakes, and the spacing of animal tracks and tree branches. There are seven main patterns within this category. They are Translation symmetry, Horizontal mirror symmetry, Vertical mirror symmetry, Rotational symmetry, or Glide reflection symmetry. In the case of tree branches, scientists can use Strip Pattern in order to tell when a tree was having a hard year for growth. If the space between two supporting weight branches varies significantly, scientist can tell something was wrong. They can use a similar strategy for animal tracks. Any deviations from the symmetrical pattern can indicate an injury or disease in the animal that is affecting its strides.
The last type of symmetry commonly found
in nature, and my personal favorite, is Wallpaper symmetry. This type of
symmetry is the most complex and is based on tessellation. The most common
example of this type of symmetry is honeycomb. The hexagons are all identical.
There is also a very interesting place in Ireland where the stones form
hexagonal prism. It is called the Giant’s Causeway. These patterns are caused
by the repetition of a certain pattern or shape, that isn’t symmetrical on its
own, over and over until it completes a cycle. One way to achieve this type of
symmetry artificially is to create a vibration diagram using a Goold elliptic
pendulum.
While most of my post has talked about
symmetry in the realm of biology, many time organic compounds are symmetrical
as well. For instance, a water molecule is symmetrical. When frozen, water
remains symmetrical. Many people are aware of this phenomenon. Snowflakes
exhibit radial symmetry. Although snowflakes may all be unique, I think that it
is interesting to note that all snowflakes are radially symmetrical.
It is fascinating how so many things are
symmetrical. Is there a cause for this? According to researchers at the
University of San Paulo in Brazil, the answer is yes. Using ALICE (a large ion
collision experiment), they found that ions exhibit a fundamental symmetry due
to their charges.
Symmetry has been a topic of interest for
very long time. As some of the drawings that Monica posted by Leonardo DaVinci,
it has been a subject who’s meaning has been debated and questioned time and
time again. Personally, I am glad for symmetry. It makes nature beautiful, and
provides a bit of mystery for each of us.
Iachello,
Francesco. "Beauty in Nature: Symmetry." AIP Conference
Proceedings 1488.1 (2012): 401-12. Print.
Jaeger, F. M. b. 1877. (1917). Lectures on the principle
of symmetry and its applications in all natural sciences. Amsterdam:
Publishing company "Elsevier,”.
Macnab, Maggie. (2012) Design by nature :using universal
forms and principles in design Berkeley, CA : New Riders
Abney, Angel, Andy Tyminski, and Pawel Nazarewicz.
"Symmetry in Nature." UGA Student. University of Georgia
Press, n.d. Web.
A very interesting topic of choice. I like how symmetry is something that is so simple yet so elegant, as displayed by some of the pictures provided by Jo. I once saw a documentary that explained that humans look at beauty through symmetry. The movie describes that the more symmetrical a person's face, the more attractive it will be to another person. They had conducted experiments and tests to prove this theory. I think in this post, Jo would approve the tests and theory of this documentary I saw. As she stated, nature is beautiful and symmetry in these pictures captures our eye. Take for example the butterfly, most people would say how cool or beautiful it looks. This may be because of its symmetry, it may not, but the topic for discussion is there. I agree with Jo, symmetry creates a very interesting and beautiful world along with an air of mystery.
ReplyDeleteSymmetry in nature is absolutely stunning as seen in the pictures Jo used in this post. I have learned about strip pattern, radial, and linear symmetry prior to reading this post, but I have never heard of wallpaper symmetry. It seems the most complex, but interesting type. I also had never heard of Giant's Causeway before, so I look up some picture and it is absolutely stunning and intriguing to look at! I am currently taking organic chemistry so I know quite a bit about symmetry in molecules, and fair warning, it’s unique, but rather annoying to be tested over. Symmetry definitely makes the world a more beautiful place, I’m very pleased that we are able to enjoy it.
ReplyDeleteI thought that this was a very interesting idea. It relates to our final project on the mathematics behind snowflakes. I found it interesting that there is even symmetry behind animal tracks to be able to tell how fast they were going or if they were injured or sick. The whole idea of nature being symmetrical is fascinating considering it just occurs its not necessarily planned. Not only is it cool to look at but its necessary for certain animals to live, such as butterflies. If their wings are not symmetrical, they won’t be able to fly. Having those proportions is not only beautiful, but necessary for life to continue.
ReplyDeleteI thought that this was a very interesting idea. It relates to our final project on the mathematics behind snowflakes. I found it interesting that there is even symmetry behind animal tracks to be able to tell how fast they were going or if they were injured or sick. The whole idea of nature being symmetrical is fascinating considering it just occurs its not necessarily planned. Not only is it cool to look at but its necessary for certain animals to live, such as butterflies. If their wings are not symmetrical, they won’t be able to fly. Having those proportions is not only beautiful, but necessary for life to continue.
ReplyDeleteSymmetry in nature is really cool to me. Seeing something that mathematically shows up in real life is nice to see in a class like this. Not only is symmetry in nature cool, but it is stunning. I especially liked the section on snowflakes. It is so interesting that something that is geometrically perfect falls from the sky and is formed from water vapor. In the past I have always seen symmetry as what Jo calls linear, or bilateral symmetry, but in reality there is more than just one type of symmetry. All in all I thoroughly enjoyed this particular blog post.
ReplyDeleteThis post was very intriguing because nature has so many beautiful things, each of which have their own beautiful qualities. Symmetry is one of the many qualities in nature, that is actually very interesting to me. I do also find it very interesting that things are made symmetrical in many different ways. It is a challenging concept to think about why and how these things end up becoming symmetrical in my opinion. This is also a relation to everyday life, it is always most interesting to learn about mathematical things that actually relate to our everyday lives. Overall this post was fascinating and I loved seeing all of the pictures!
ReplyDeleteSymmetry is such a beautiful part of nature, so much so that people can be obsessed with it. Some people will go to great lengths to have almost perfect symmetry in their daily lives, from things like the pillows on their beds being aligned in a linearly symmetrical pattern like a butterfly’s wings. Personally linear and radial symmetry are my favorite types of symmetry. Linear is the easiest type for me to imitate in daily life, I have some OCD’s that make it hard for me to focus on a task if certain things aren’t lined up in the proper symmetrical fashion. Something I never knew was how you are able to tell if an animal is hurt or sick based on the patter of their foot prints in the snow.
ReplyDeleteI find it really interesting how drawn to symmetry humans are, but it's also intuitive at the same time. Symmetry is, in many ways, simple and of course pleasing to the eye, but I feel the very simplicity of it is what makes it so attractive. Humans gravitate towards aesthetically pleasing scenes and especially things we can understand and grasp easily, symmetry being one of those things. It's so crazy to me how symmetry and geometry play such a huge role in nature, which includes not only things like plants and animals, but humans too. It is a fact that people are more attracted, whether they realize it or not, to others who have more symmetrical features.
ReplyDeleteI feel like I relate to you in the sense that nature has always been really interesting to me. My dad has always enjoyed taking my family camping and I've always loved the nature aspect of it. I've always noticed symmetry in nature but never really thought of it in this sense. One thing I liked was how you noted the different types of symmetry found in nature. I've always noticed the horizontal and vertical symmetry since they are obvious. However, some of the other types are not so much. My favorite example that you used in this was the Ireland one since I am Irish and I've always wanted to travel there.
ReplyDeleteWhen you think about the formation of nature from when born or born etc. it's amazing how majority of nature follows this underlying rule of symmetry. In my opinion, when imaging a world without symmetry, the world wouldn't be nearly as beautiful. I agree with you that wallpaper symmetry is the most intriguing. Honeycombs are amazing feats of nature and really pleasant to the eye. Though, when I think of symmetry, I tend to see it as a more biological stand point rather than mathematical. Symmetry is very important to all like surrounding us. I love when math and the real world collide and find common similarities.
ReplyDeleteI feel like we don't take nature seriously in the natural beauty that it gives to us. This was very intriguing to read just because you don't realize how many things are symmetrical in their own ways. when reading this it just made me look around and see how symmetric nature was that I took for granted. so many animals and plants are symmetrical in some way and it just made me think about it. Like there aren't many things that aren't symmetrical and I didn't even realize it. I would have to agree with Jo that my favorite type of symmetry was also the wallpaper symmetry. it is fascinating to see how one shape can be repeated and continue to be completely identical. I also like how she mentioned the snow flake and how they are identical when cut down the middle. I didn't however know the reason for why this happened and she did a good job explaining why and it made since.
ReplyDeleteI have never really thought about the symmetry in nature. It wasn’t until this year in biology that I learned that there were different types of symmetry of animals. The strangest thing I found in this article is the way the Greeks categorized symmetry using polyhedral. Each of the different elements having a different shape is pretty astonishing. Jo did a really nice job of combining what we already learned in biology and new symmetry types. The stripe pattern symmetry was my favorite because it looks the coolest without being as complex as the wallpaper symmetry.
ReplyDelete