After our discussion in class about organized chaos and the Fibonacci sequence, I was reminded of a book I read back in elementary school. The story takes you on a journey alongside child-age math geniuses who solve higher level math equations to save their friends and solve mysteries. The book is called The Wright 3.
I remember reading the story and becoming fascinated with how these young children were able to solve such advanced problems. I remember that there were pages within the story itself that explained the type of math they were using and I understood it to a degree. I may have even used the book as a source for a report to show how math correlates to every day life and how even higher level math appears in children’s books. I do remember the shocked look on my teacher’s face when I showed her the book and told her I was reading it. At that point in time I had an understanding of the Fibonacci sequence since we were learning parts of it but nothing to the degree that we are learning now. In the story, I remember the main characters using it to learn about a house and its odd structure. In the picture below, the characters are examining Escher staircases and how they functioned within the house.
I didn’t understand how the sequence and housing structure could possibly go together but after our discussion in class about how different sets of numbers within the sequence correlate to one another, it’s starting to become more clear. Though it may seem like a children’s book to some, I found it very informative and would recommend it to anyone interested in learning more about 3-d structure and the Fibonacci sequence. Apparently it is part of series!
So when Dr. Plante was showing us the many different types of fractals this past week, my mind instantly went to a toy I loved playing with as a child. The kaleidoscope! I was and still am so intrigued by how the device manages to take an ordinary image and superimpose/distort itself to look larger or smaller than what you originally looked in upon.
For those who don’t know how one works, a kaleidoscope is a tube with two or more reflecting surfaces that are positioned on one another at an angle to form symmetrical patterns that can be seen when you look into the lense. Most kaleidoscopes allow you to twist the tube, which allows you to alter the shape’s size and sometimes even the color. Some of the pictures that you can see are very closely related to mandalas and maybe even prisms.
Here are a few examples of what I’m talking about
It honestly took me a few minutes to find kaleidoscope images with fractals inside it, but hopefully these provide an idea of what I was thinking about during our lectures. This intriguing toy of my childhood, definitely not something I ever thought I would instantly think of in a math class.
I found American Sign Language (ASL) about 6 years ago and absolutely fell in love with it. How the handshapes are formed to create words or sentences captivated my attention and made me want to learn more. I started taking classes when I was 13 and that has since led me to pursue a career in ASL interpreting here at UNHM.
Never would I have thought of combining ASL and math together. Before taking this class, I wouldn’t have paid much attention to how the two correlate. After discussing various topics thus far and then being asked to think about our final projects, my first thought was that I wanted to find a way to connect the two. Then symmetry patterns and translations popped into my head. I thought about how signs in ASL could be compared to wall-paper patterns with translations and chirality and the like. At first I was going to try to find how the speed at which some signs are signed and signed fluently relates to math. Then, I thought the symmetry portion would be a much more interesting path since we have already discussed it and I would be adding to it with hands and how they are used to form words or to express meaning. Who knows?!? Maybe I’ll find a way to discuss both!
(The sign for math in ASL is being shown here)
After leaving class yesterday trying to wrap my brain around all that we learned, I tried connecting everyday items to the topics we discussed. My first thought was an orange and how it is a spherical shape with positive curvature. Then I thought that was too easy. So I took to our page to see what some people had already posted. One that caught my attention was the post about Pringles. I thought this was really cool, yet I couldn’t figure out how the shape worked. I then did some research into hyperbolic paraboloid shapes to understand it better and see if there were any other objects out there, besides a saddle, that fit the description.
What I managed to find was a picture of the Bosjes Chapel in South Africa. My first reaction was that it looked like a sideways Pringle, mostly cause I couldn’t remember the name of the shape. Now that I know the correct term is hyperbolic paraboloid and what it means for a shape to be one, I see how this chapel is one. It has negative curvature towards the front of the building and positive curvature towards the back. I thought it was so cool to find a building of all things with this shape for its design. Architecture in general is a very interesting and complex thing and to find a real life example of this shape was something I never thought it was going to happen. I loved instantly seeing the picture and my first words being “that building is pringle shaped!” . I think that will be how I remember hyperbolic paraboloids from now on!!
After our conversation in class about Frieze patterns and finding them in wallpaper, I was determined to find something I could use for this post. To my disappointment, I found that wallpaper is not a thing that exists in the dorm that I am staying in. You would think that art students would have something decorative in the means of wall paintings or pictures in my dorm, but sadly there is none of that. Anyway, when I asked a friend for her opinion, she told me to look at the pillows in the lounge area. When I did, I found that each one had its own distinct pattern, similar to the ones we have been talking about in class. Here are two of the pillows I was most drawn to and what patterns I found in them:
Pillow 1 is an example of a F2. There is no vertical reflections and no horizontal reflections, but there is glide. If you look closely at certain lines, the thin brown one or the green, then you can see it. It depends on which line you decide to focus in on.
Pillow 2 is a an example of a F3. There is vertical symmetry towards the left side of the pillow in that design along the center. There is no horizontal symmetry since the flower looking design would not match if it were reflected over the horizontal axis. There is half turn symmetry within the design as well, making the pillow design a complete F3.
I found it weird to stare at pillows for so long, but like I said I was determined to find a pattern that worked. I stare at these pillows everyday and honestly didn’t think their patterns would work, but was happy to see that they did.
Emma’s post about her pants also made me think about a pair of pants that I have that have similar Frieze patterns to hers. I always thought they just had the same pattern repeating over and over, but thanks to our conversations in class I was able to see that it has frieze patterns of F1, F2 and F4. Its fun to find patterns in things as random as pillows and pants and see how there is more to everyday things than meets the eye.
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.
Hi my name is Alida. I have never been a huge fan of the subject of math but that perception changed for me last year. I took a course my senior year called “Discrete Math”. This was a combination of various math classes combined to teach one how to use math in the real world. There were chapters on voting methods and the concept of trees to explain how circuits work in a computer of WiFi system. Taking this class opened my eyes to see that math is involved in everything around us and that is why I am excited to be taking “Excursions in Mathematics” this semester.