Already knowing that the golden ratio can be found in virtually almost anything, I still did some googling. We already know that it’s found in nature in things like flowers, shells and pine cones, but it can also be found on a larger scale.
Taking an earth science course last semester, I retained a bit of knowledge about storms such as hurricanes. The image on the left is an example of wind traveling long distances around Earth, which appears to be curving rather than moving straight across. This is know as the Coriolis Effect.
It is said that hurricanes and the golden ratio are connected because of the connection between the golden ratio and the spacing of spiral arms around a hurricane; the spiral arms never touch each other because they are all perfectly spaced apart in an orderly fashion. It is apparent that the golden ratio is at work here, and you can even see it when looking at a hurricane from bird’s eye view.
I did not have to do too much searching to come across some very interesting correlations between modern day culture and images and the Fibonacci sequence or the Golden Ratio. Without even intending to, I found memes whose images corresponded very well with this. For one example, I found this meme that I assume everyone has seen by now:
And, thanks the popularity of stranger things, I stumbled upon this gem, too:
That’s right, even the “mother of 4” Joe Keery finds himself at the center of a Fibonacci spiral. I knew that I would have no problem finding exampled like this in nature, because I have seen them in snail shells and flowers, but I did NOT expect to find them in pop culture, so, if you ask me, this is pretty awesome math at work here.
After discussing the golden ratio in relation to the Fibonacci sequence, I found it very interesting to see how often this type of math is found in nature. It also got me thinking, who found this? When was the golden ration made a thing? I found this website that is simple and short but talks about how Pythagoras discovered the golden ratio from different sounds. From the sound of hammers to the sound of strung instruments he made this amazing mathematical find and it then began to be incorporated into sculptors.
So after our discussion yesterday the golden ration, I did a little bit of research towards the idea of it appearing in memes online. The fact that I just typed the above sentence makes me sad but nevertheless I found some interesting photos. I recalled seeing the golden ratio and golden spiral memes appearing on my social media feeds a few years back and when I went to “knowyourmeme.com” I found some interesting information. A main image is one of Donald Trump in which the golden spiral is crafted and shaped around the direction of his head, ear and hair itself.
There’s also information on a tweet brought by a BBC news producer which blew up virally online. The tweet included a photo of dramatic violent scenes during a Manchester UK New Year’s Eve revelry in which police are restraining an inebriated civilian as chaos runs among the street.
The photo blew up and to this day has recieved over 25,600 retweets and 29,600 favorites.
So after our discussion on the golden ratio, sometimes called the divine proportion, I wanted to learn more about how it connected to art. I then found myself typing the concept into the Google search bar and found a collection of websites each trying to explain how the two things correlate through the use of images and graphs. One website that I found most helpful took the artwork of some of the world’s most famous painters and sculptures and showed how they used the ration within their work. One of my favorites to learn about was the painting on the top of the Sistine Chapel by Michelangelo. Apparently there is a correlation between how God, the angels and man are all positioned within the photo.
I never would have thought that there was hidden math involved in this painting or others like Da Vinci’s “The Last Supper”. I had always thought that it was simply a matter of alignment and measurement that allowed a piece of art to look even and realistic.
While also researching this, I came across a page that explained how we have the Fibonacci Sequence and the Golden Ratio in our bodies. This came to me as a surprise. How can we have those things if our body is continuously growing? Well, apparently we have sections of our body that are equal to .618 . For example, our index fingers are composed of several sections each a bit larger than the one preceding it the closer you get to the wrist. Our hands and forearms act in that same manner proving that we are made up of the golden ratio.
I was amazed to learn all of this. Since our conversation in class, I knew there would be more examples of art with the ratio attached to them. What I did not know was that basic human anatomy and the golden ratio could be connected. This was one of the coolest things to research by far!
So, I thought I would continue the concept of an infinite universe with some other mind boggling terminology… dimensions! This video describes the other dimensions and what they entail. They break it down using mathematical terms and how we would perceive different dimensions in our own reality. It’s pretty neat, I think my brain exploded a couple times watching this video. But! It’s very interesting. The video also talks about time and how that in itself is another dimension. Also, why we can not view the other worlds that are ‘around’ us. Or, as mentioned in different planes. It made me think differently about my own perception. How humans can sometimes fixate so heavily on their own world not realizing there are so many others.
For this weeks post, I was a bit lost for what to post. So I did some research online and was pretty amazed at what I found and it got me thinking that there is chaos everywhere we go and especially in nature. There are some patterns in nature. I was looking up some stuff online about the weather and meteorology use the chaos theory everyday with predicting the weather and different weather patterns. Which I think is very interesting.
I’m fairly certain that we spoke about the Butterfly Effect film in class either this past week or the week before; but I feel that it’s a pretty cool film as well as general theory. If you guys don’t recall what it is, it essentially follows the idea that, “small causes can have larger effects.” Meaning that all the small choices in life, or occurrences or as the Wikipedia article I’m quoting said, “causes” can drastically effect an ultimate outcome. The theory itself is interesting to look at from a perspective of regular life. If you get in your car and drive to class, or talk to one individual you pass by, it can change things drastically. Perhaps you get into a car accident and become paralyzed from the waist down, or maybe the person you talk to ends up becoming your soul mate who you spend the rest of your life together with.
More specifically, the Butterfly effect theory is used both in weather patterns, (especially with the formation of tornadoes,) and in quantum mechanics.
It is also subject to two mediocre films. The second of which I included a poster of. It’s an absolutely dog doodoo movie, but funny to watch with friends if you’re into film or critiquing.
Wednesday in class we saw some of the tricks of Pascal’s Triangle such as the exponents of 11, the Fibonacci Sequence, and the Sierpinski Triangle. In reading more about it on mathisfun.com I came across the Chinese version that showed up more than 300 years before Pascal’s did. This version is known as Yang Hui’s Triangle. This blog post describes more about how it came about, but I found it really interesting that it showed up so many years earlier.
In a way it reminds me of Dr. Plante’s story about the tile work in Europe that he didn’t write about and publish before someone else did. The Chinese had it figured out first, but so many people today only know about Pascal’s work.
I didn’t know what to write about for this topic, so I did a quick google search of “chaos theory” and ended up on the wiki page for it. I didn’t have to scroll down very far to see a few images of interest. The first was of something called the “lorenz attractor” and the second was a gif of a “double rod pendulum” animation.
According to wikipedia: “Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions.”
The first thing that came to mind when I saw these was of something I had as a child. A toy called a Spirograph. It was a little piece of plastic you would insert your pencil into, and then move it around on a piece of paper to create really beautiful designs. It’s similar to the double rod pendulum in the sense that if you move your pencil a certain way it could completely change the outcome of your design. Also because you move your pencil around so many times and it would seem like you were just creating a big scribble on paper but it ends up being a very intricate image produced.