Warning: this essay is rather long. However, given the stimulating (hopefully) content, this should be forgivable. Harvard is not my first choice, and I'm applying rather last-minute. I am hoping to put emphasis on the originality of my essays. Please be critical. I'd love to hear input on the content of the essay as well. Thanks!
Numbers, Numbers, Numbers
I am not a brilliant mathematician, so please don't expect any Gauss-level equations on this paper. That being said, I do quite enjoy my numbers: numbers of books, numbers of movies, numbers of maps, numbers of half-empty nail polish jars, numbers of withered or dying plants. Numbers are important things- they are the fundamental integrals of natural organization. Without numbers, there would be no order; although this may sound rather apocalyptic, it is true.
For instance, take the Fibonacci sequence. I recently watched a video describing the natural presence of Fibonacci numbers. Of course, being more artistic than mathematic, I was not very interested in learning about where in nature the Fibonacci sequence existed. But because the video was talking about the mathematical structure of spirals (which can be used to draw a variety of things- for instance, sleeping cats), I decided to watch in anyways. It was quite intriguing; the core of the video was exploration with pine cones whose seeds were organized in a counter-clockwise-clockwise fashion, with eight going one way and thirteen going the other way. As the video explained, both these numbers were found in the Fibonacci sequence, thus proving the presence of Fibonacci in nature.
I prefer to think of Fibonacci not as mathematics, but as the natural construction of evolutionary organization. That being said, I wished to make my own fascinating discoveries pertaining to the Fibonacci series. Thus, I walked around the house with a ruler in one hand, and a notepad in the other, waiting to discover Fibonacci at my doorstep.
My first stop was in my tiny greenhouse. As I mentioned earlier, I grow a number of wilted plants- mostly flowers, including: euphorbia, trilliums, black-eyed susans, Shasta daisies, columbines, and bloodroots. Although my avid passion for gardening was not exactly reflected with skill, perhaps I could discover something interesting among the organization of the petals. I plucked a sample of each flower, and went back inside to my room. It was interesting to see what I'd discover with the flowers.
The first sample I looked at was the white calla lily, a flower I'd plucked off one of my mother's forgotten bouquets. It had one large white petal. The second sample was a euphorbia, with two petals. The third, a trillium with three petals. I was beginning to see one of two patterns: either I was looking at the Fibonacci sequence, or my petals were increasing by one as I went up. However, in keeping with the Fibonacci sequence I was investigating, I had purposely chosen fit flowers. Thus, my fourth plant, the columbine, had five petals. Eight-petals were found on a sample of the bloodroot, and thirteen were found on my black-eyed susan. My Shasta daisy had twenty-one petals. I had finally run out of flowers to count.
Was this, as my theory stated, the natural construction of evolutionary organization? Or, was I simply lucky? My natural proof couldn't stop there-- it was not yet conclusive enough.
As I leaned back in my chair, grabbing the wilted flower heads off the desk, I noticed something interesting- the Shasta daisy head had an interestingly close-packed arrangement of florets in its core. This was strangely reminding of the video I had seen- because the florets were arranged in counter-flowing spirals, it would only make sense for them to be arranged in the Fibonacci sequence. The core was too small to be investigated, so I took a photo and enlarged it on my computer screen. My teeth sat on edge with excitement as I counted and highlighted the spirals in one direction, and then the spirals in the other direction; twenty one counter-clockwise, and thirty-four clockwise. It was the Fibonacci sequence! And because I found these florets on the head of a flower that had been part of my original investigation, those flowers too were part of the Fibonacci series.
However, this still wasn't enough for me; I wanted conclusive numerical evidence that what I was finding was natural law. Therefore, I decided to do a little simple mathematics. I lined the Fibonacci numbers into two columns, A and B. The first column contained the first number in the series, and the second column contained the sum of that number plus whatever came before it. Therefore, column A contained numbers two through thirty-four, and column B contained numbers three through fifty-five. As can be seen, both columns contained Fibonacci numbers. Next, I set up another column containing the quotient of the larger number divided by the smaller number, or column B divided by column A. As I lined up my numbers and did the math on my calculator, I noticed that the answers were slowly approaching 1.618. I realized there was probably some meaning to this number, although I could not gather what. Thus, I did what any twenty-first century person would do- I googled. It turns out that this number represented the Golden Ratio, and was known as Phi (or ). This universal number was applied, thus, to the Fibonacci sequence in that the quotients of all consecutive numbers approached 1.618.
At last, I was satisfied. My rather pointless quest to prove Fibonacci non-mathematical was complete. Of course, pertaining to mathematics, I explored the realms of the Golden Ratio as well. It was interesting to see how intertwined mathematics was with nature. Flowers, pine cones, branches, and florets were all organized in some sort of natural sequence with Phi being the common ratio.
As I previously mentioned, I am not a mathematician. I do not find satisfaction in performing overly complex equations. However, I still enjoy my numbers. Mostly, these are numbers of things I collect, such as empty Starbucks cards, dusty Mason jars, and used toilet paper roles. And when the opportunity presents itself, finding numbers in nature is quite enjoyable as well.
Numbers, Numbers, Numbers
I am not a brilliant mathematician, so please don't expect any Gauss-level equations on this paper. That being said, I do quite enjoy my numbers: numbers of books, numbers of movies, numbers of maps, numbers of half-empty nail polish jars, numbers of withered or dying plants. Numbers are important things- they are the fundamental integrals of natural organization. Without numbers, there would be no order; although this may sound rather apocalyptic, it is true.
For instance, take the Fibonacci sequence. I recently watched a video describing the natural presence of Fibonacci numbers. Of course, being more artistic than mathematic, I was not very interested in learning about where in nature the Fibonacci sequence existed. But because the video was talking about the mathematical structure of spirals (which can be used to draw a variety of things- for instance, sleeping cats), I decided to watch in anyways. It was quite intriguing; the core of the video was exploration with pine cones whose seeds were organized in a counter-clockwise-clockwise fashion, with eight going one way and thirteen going the other way. As the video explained, both these numbers were found in the Fibonacci sequence, thus proving the presence of Fibonacci in nature.
I prefer to think of Fibonacci not as mathematics, but as the natural construction of evolutionary organization. That being said, I wished to make my own fascinating discoveries pertaining to the Fibonacci series. Thus, I walked around the house with a ruler in one hand, and a notepad in the other, waiting to discover Fibonacci at my doorstep.
My first stop was in my tiny greenhouse. As I mentioned earlier, I grow a number of wilted plants- mostly flowers, including: euphorbia, trilliums, black-eyed susans, Shasta daisies, columbines, and bloodroots. Although my avid passion for gardening was not exactly reflected with skill, perhaps I could discover something interesting among the organization of the petals. I plucked a sample of each flower, and went back inside to my room. It was interesting to see what I'd discover with the flowers.
The first sample I looked at was the white calla lily, a flower I'd plucked off one of my mother's forgotten bouquets. It had one large white petal. The second sample was a euphorbia, with two petals. The third, a trillium with three petals. I was beginning to see one of two patterns: either I was looking at the Fibonacci sequence, or my petals were increasing by one as I went up. However, in keeping with the Fibonacci sequence I was investigating, I had purposely chosen fit flowers. Thus, my fourth plant, the columbine, had five petals. Eight-petals were found on a sample of the bloodroot, and thirteen were found on my black-eyed susan. My Shasta daisy had twenty-one petals. I had finally run out of flowers to count.
Was this, as my theory stated, the natural construction of evolutionary organization? Or, was I simply lucky? My natural proof couldn't stop there-- it was not yet conclusive enough.
As I leaned back in my chair, grabbing the wilted flower heads off the desk, I noticed something interesting- the Shasta daisy head had an interestingly close-packed arrangement of florets in its core. This was strangely reminding of the video I had seen- because the florets were arranged in counter-flowing spirals, it would only make sense for them to be arranged in the Fibonacci sequence. The core was too small to be investigated, so I took a photo and enlarged it on my computer screen. My teeth sat on edge with excitement as I counted and highlighted the spirals in one direction, and then the spirals in the other direction; twenty one counter-clockwise, and thirty-four clockwise. It was the Fibonacci sequence! And because I found these florets on the head of a flower that had been part of my original investigation, those flowers too were part of the Fibonacci series.
However, this still wasn't enough for me; I wanted conclusive numerical evidence that what I was finding was natural law. Therefore, I decided to do a little simple mathematics. I lined the Fibonacci numbers into two columns, A and B. The first column contained the first number in the series, and the second column contained the sum of that number plus whatever came before it. Therefore, column A contained numbers two through thirty-four, and column B contained numbers three through fifty-five. As can be seen, both columns contained Fibonacci numbers. Next, I set up another column containing the quotient of the larger number divided by the smaller number, or column B divided by column A. As I lined up my numbers and did the math on my calculator, I noticed that the answers were slowly approaching 1.618. I realized there was probably some meaning to this number, although I could not gather what. Thus, I did what any twenty-first century person would do- I googled. It turns out that this number represented the Golden Ratio, and was known as Phi (or ). This universal number was applied, thus, to the Fibonacci sequence in that the quotients of all consecutive numbers approached 1.618.
At last, I was satisfied. My rather pointless quest to prove Fibonacci non-mathematical was complete. Of course, pertaining to mathematics, I explored the realms of the Golden Ratio as well. It was interesting to see how intertwined mathematics was with nature. Flowers, pine cones, branches, and florets were all organized in some sort of natural sequence with Phi being the common ratio.
As I previously mentioned, I am not a mathematician. I do not find satisfaction in performing overly complex equations. However, I still enjoy my numbers. Mostly, these are numbers of things I collect, such as empty Starbucks cards, dusty Mason jars, and used toilet paper roles. And when the opportunity presents itself, finding numbers in nature is quite enjoyable as well.
