Symmetry on Paper

In class yesterday, we were tasked with making snowflakes out of sheets of paper to create the sort of rosette that we were learning about. There is another way to get to that sort of shape without the use for scissors, an art form that I and I sure everyone else is familiar with, origami.

8 Fold Rosette of origami cranes

Since the world invented paper, so has folding paper been a part of civilization. Until relatively recently in history has paper become cheap enough that more than nobles and priests were able to experience it the art. Today its a past-time shared by millions of people in all countries, and there are hundreds of different folding patterns that you can find to start you off. But I wanted to focus this post on origami that follows rosette patterns.

In fact, this is an origami pattern known as the rosette, one of the simplest ones to make. This was made from a single piece of paper, with thirty-six folds around the center. If that seems like it would be too difficult, you might want to try out the next one:

This pinwheel is far simpler on the rosette pattern with only four folds, but I would rate both this and the previous project to be similar in difficulty – rather, they aren’t that difficult to do at all. If any one is interested in trying out this project or others, I’d suggest going to www.origami-instructions.com which has these patterns and more with video tutorials.

Last but no least, let’s look at a 3-D rosette:

Don’t let the stripes colors fool you, because this ‘dragon’s egg’ origami was actually folded out of a single piece of striped colored paper. You can see the whole process below in the video link. Check it out!

My Favorite Rosette

The rosettes I found are from the icon of my favorite app, Canvas. These are classified as Dihedral 8 with a rotation of 45 degrees. Learning about rosettes is interesting because there are a lot more of them around us than I realized. Being about to determine what kind of dihedral it is or its degrees of rotation is a fun thing to know how to do, and an easy way to sound super smart .

Rosettes in Medicine

While rosettes can be found all around us, one place that they have been more recently discovered is in the Leishmania parasite. This parasite is spread by sand flies’ bite and causes skin sores or organ trouble depending on what type the infected person has.

According to the authors of this article by forming in a rosette, the parasite is demonstrating a stage of life. This means that a cure, prevention, or treatment could have a better chance at working with this knowledge.

I knew that rosettes were often found in plants, but I never expected to see them in a disease.

Rosettes all around!

As I walk back to my dorm, I look around and think to myself “Where could I possible find an object or picture that would be a good representation of what I am trying to find for math class?” I remained stumped and got back to my dorm… I look around and right in front of me is a fan. Something that is used in every day lives that’s perfect for this. There is literally art and math around us everyday and we fail to see it until we are forced to. The fan is a cyclic rosette because of the direction of the plastic waves. They are going counterclockwise which means when reflected, they would be going clockwise with a 30 fold center.

Rosettes in life

After we had finished class I thought I would pay attention to the different rosettes that may be around me on my walk back to the dorm. As I thought more and more about looking at various things, I noticed there were a lot more than I believed. The first thing I noticed was one of the man holes on the sidewalk. I noticed this one had a honeycomb pattern if you will, but it has writing in the middle. So if the writing wasn’t there it could be rotated twice, once 180 degrees and then the full 360. It also can be mirrored once if you roughly go vertically between the two holes. This would make it a dihedral 2

I also looked at car rims because the patterns are usually the same throughout the whole rim. The thing that was stopping them from being a rosette was the logo’s in the middle. That lead me to think about the various car logos that I know. Here is a small list of the few that would work. Mercedes, Audi, Mitsubishi, I believe Hyundai, and BMW. This rim would be a dihedral 3 because it has three lines of reflection using the Mercedes logo as the point of reflection.

Rosette Fun!

The more discussion we have been having about the fact, the more I have noticed how many different types of rosettes are in my daily life. From work, to school, to home, and in nature! I took a picture of a dihedral rosette I found at one of my jobs. This is a 5 fold dihedral with a 72 degree rotation. I have been able to enjoy this class so far because I am actually understanding it, this type of math can actually be fun. Rosettes are everywhere, and they are so much more than just art patterns! I’m learning if you keep a eye out you will see them everywhere you go.

M.C. Escher and Math

I think that on some level I always understood that math was in the background, behind especially technical pieces of art. M.C. Escher has always been a favorite of mine and when I was little I would try to make sketches that matched his but could never figure out how he got the proportions right (never mind that my skill never graduated beyond 3rd grade blob bodies). Dr. Plante instantly captured my attention when he put Escher’s artwork on the screen. Math has always irritated me and chafes my ego, but I when he starting connecting Escher to math, I began to see it as a language to communicate placement and detail. A mathematical map that makes distortion possible (with clever shading) and tricks the eye. Escher’s work became more logical to me and I love me some logic. Some might think that looking at his work mathematically diminishes the magic, but I think it enhances it.

Rippled Surface

Rosettes In My Room

As I was looking around for some sort of rosette I found it at the most unusual time. I came home from class and lied down on my bed. I looked up and there on my light cover was this design. A perfect example of a rosette, specifically a dihedral. This is an 18 fold with a 20 degree rotation. I found this so fascinating because I never knew that I could mathematically calculate the light in my room! I also never thought I would be using it for an assignment. I just found this interesting because it came to me at a time I wasn’t even looking for it. Here I am simply laying on my bed, and I find a rosette on my ceiling.

What I also find interesting is the Fibonacci Sequence which was mentioned a few times in class. I love the idea of math in nature and how everything can be connected by a simple set of patterns in numbers, yet its so complex at the same time. There was once this show on Netflix all about the Fibonacci sequence and how everything was connected by these numbers. I was watching it but never finished and I can not seem to remember the name of the show either. I tried looking on Netflix and I couldn’t find anything that jogged my memory, so if anyone knows the name of the show I am talking about or happens to stumble upon it feel free to comment. For now I have found this wonderful video that illustrates the Fibonacci Sequence. I am hoping we will spend sometime talking about it in class so I can learn more about it,

and by learning I am hoping others will find it just as interesting as I do.

Math or Art??

In the first couple weeks of class, I noticed real quick that there is a strong correlation between math and art and how the two are seen in our day to day lives. One thing that cannot be denied in my opinion is that most things that can be physically seen/touched can be broken down into some type of numerical sequence or perhaps a symmetrical pattern. More often then not, more can be seen than what initially meets the eye if you just pay a little closer attention to whats going on. You may also find some form of entertainment in boring situations if you can find the connections and patterns that are so easily hiding in plain sight!

The Work of Masterminds

Two weeks ago, I left my small state of Rhode Island to come up here. I was aware that I would be dorming with art students from another school for 9 months out the year, but I had no idea what this would actually come to mean. Within the two weeks that I have been here and have been a part of Dr. Plante’s class, I can say that I’m am starting to understand. There is certainly more to art than meets the eye. From the detail behind every stroke, to the patience in every line and circle, art has the ability to capture just about anyone’s eye. Living in the dorm that I live in, I am forced to see art on a daily basis, and thanks to Dr. Plante’s class, am able to make connections to the world of math when I see various pieces. I pay attention to how the pieces are formed, what techniques are used and the underlying messages the artist wishes to convey.  I am most captivated by the ability of so many here to turn simple objects from 2D images to 3D by just adding a bit of shading or some color. I compare their pieces to what we are creating in class and am fortunate enough to see the work of masterminds come to life in front of me.

Of course I am not saying that I only see art when I am in my dorm. I see it all around me. From the shadow that bounces of the Brady-Sullivan tower on a nice day to the street signs that light up the night around 11pm. There is math everywhere. I feel that by taking this course and really allowing myself to grasp the meaning behind everything we learn, that I will eventually be able to create my own art and explain how I came to create it and the math behind it.