My infatuation in fractals began freshmen year at Greeley after taking a Seminar with one of the seniors. I’m not sure exactly when simple interest turned to a kind of obsession, but during that lesson something seemed to click. It seemed as if this was the universe’s answer to everything; the mystery was solved, however complex the answer was to understand. I’m still not sure if I was misunderstanding the lesson, or if I had somehow seen it for what it really was; a pattern to describe the way the universe works.
Nevertheless, that day followed me, and I tried to understand more about fractals through the resources I already had at my disposal-- through courses I was taking. Sophomore year, through my European History and Architecture courses, I learned about many ancient architectural feats-- Stonehenge, the Pyramids of Giza, the Parthenon, many Gothic Cathedrals, and the Taj Mahal-- and that they all somehow involved the use of the golden ratio. I will come back to how this relates to fractals later in the article, but for now know that each of these buildings use different aspects of their design to form the golden ratio. I was intrigued by the fact that fractals, what seemed to be something only formed by the forces of nature, were being constructed by human hands. Although I wanted badly to find out more, I waited until that summer, when I discovered a YouTube account by the name of Vihart. Vihart’s videos are not tutorials on how to do math, however Vihart’s ramblings about the nature and the concepts of the mathematical world have a lot of educational value, especially on topics that are more complicated to understand then to compute. Her videos on fractal math and their comparability to nature, helped to show me that...
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... Fibonacci Pinecone. Retrieved February 13, 2014, from http://www.warren-wilson.edu/~physics/PhysPhotOfWeek/2011PPOW/20110225FibonacciPinecone/
Polo, S. (Writer). (2011, December 21). Doodling in Math Class: Spirals, Fibonacci, and Being a Plant [1 of 3] [Video]. Retrieved November 5, 2013, from http://www.youtube.com/watch?v=ahXIMUkSXX0
Polo, S. (Writer). (2012, January 9). Doodling in Math Class: Spirals, Fibonacci, and Being a Plant [2 of 3] [Video]. Retrieved October 2, 2013, from http://www.youtube.com/watch?v=lOIP_Z_-0Hs
Weisstein, E. (2013). Linear Recurrence Equation. Mathworld. Retrieved October 15, 2013, from http://mathworld.wolfram.com/LinearRecurrenceEquation.html
Polo, S. (Writer). (2012, January 20). Doodling in Math Class: Spirals, Fibonacci, and Being a Plant [3 of 3] [Video]. Retrieved November 5, 2013, from http://youtu.be/14-NdQwKz9w
While the studies at Governor’s School are noticeably more advanced and require more effort than at regular public schools, I see this rigor as the key to my academic success. For me, the classes I take that constantly introduce new thoughts that test my capability to “think outside the box”, are the ones that capture all my attention and interest. For example, while working with the Sierpinski Triangle at the Johns Hopkins Center for Talented Youth geometry camp, I was struck with a strong determination to figure out the secret to the pattern. According to the Oxford Dictionary, the Sierpinski Triangle is “a fractal based on a triangle with four equal triangles inscribed in it. The central triangle is removed and each of the other three treated as the original was, and so on, creating an infinite regression in a finite space.” By constructing a table with the number black and white triangles in each figure, I realized that it was easier to see the relations between the numbers. At Governor’s School, I expect to be provided with stimulating concepts in order to challenge my exceptional thinking.
Building gardens in schools can only distract the students from getting important information. Students need to learn as many subjects as they can in school. Students should not focus on what plant they are going to put on the ground because that is not going to get them a degree in college. Flanagan feels like there are much more important things to build the students intelligence so they can have a successful future. Using the strategies of pathos she uses many negative words when describing the usefulness of students gardening in school. Flanagan is persuading the reader that having school gardens will not improve students academic grades. She also explained in her essay how easy it would be for students to pass if schools had gardens: " students ' grades quickly improved at king, which makes sense given that a recipe is much easier to write that a coherent paragraph on The Crucible" (Flanagan
Faust, Drew, and Wynton Marsalis. “The Art of Learning.” USA Today. 02 Jan 2014: A.7. Sirs Issue Researcher. Web. 26 March 2014.
Lamb, Robert. "How are Fibonacci numbers expressed in nature?" HowStuffWorks. Discovery Communications, 24 June 2008. Web. 28 Jan. 2010. .
continue to write for pleasure as well as to disseminate information, will show an “innate” affinity for geometry, and, in general, will think more connectedly and unpredictably, or creatively”(Sheridan, 2001). Children begin scribbling without control. Therefore scribbling with be everywhere on the paper. For example, Billy just learned how to scribble. Billy scribbling is uncontrolled because he is not experienced at scribbling.
K. C. Cole pushes this idea by explaining how math applies to every imaginable thing in the universe, and how mathematicians are, in a sense, scientists. She also uses quotes to promote the coolness of math: "Understanding is a lot like sex," states the first line of the book. This rather blunt analogy, as well as the passage that explains how bubbles meet at 120-degree angles, supports Cole's theory that math can be applied to any subject. This approach of looking at commonplace objects and activities in a new way in order to associate them with math makes Cole's comparison of mathematicians with scientists easier to understand. It requires one to look at mathematicians not just as people who know lots of facts and formulas, but rather as curious people who use these formulas to understand the world around them.
Life progresses in front of our own eyes, sometimes without us noticing. The days go by, the nights grow dark and then it is morning. In the course of each passing day, countless opportunities arise, some of which we take on while others we ignore. Teaching and learning are two of these chances, two I feel upon which we should never pass. In order to ensure I am teaching and learning at nearly every prospect, I have always lived my life as if it is a coloring book. When I was a child, I scribbled on every page, leaving messy streaks of crayon and never staying in the lines. Time went by with elementary school, and I learned the importance of following rules and staying in the lines. As I grew older and entered high school, I decided it was time to strengthen the boundaries, solidifying each picture with clarity and neatness. But here I am, in college and at the completion of my Junior Professional Experience—junior student teaching. How can my coloring book already be complete? It is not. Now it is time for me to go beyond the restraints, to color the world outside of each picture. By teaching and learning at every possibility, I will enrich not only my coloring book, but the pages of others as well.
I was sure that I had used my pencil to create the next Mona Lisa at the end of those seventy minutes. Yet, years later when my family cleaned out my art folder I couldn’t even tell what the items I was supposed to have drawn were. The picture looked as if it had been drawn on a boat in the middle of a storm having its curved lines in place of straight lines. It was as if the pencil had a mind of its own and what I intended for it to do just wasn’t on the agenda for that day. During my time in art class I continued this cycle. The cycle of not thinking that I could draw, to having an epiphany moment, to realizing that what I actually created was worthless. When I began to climb the mountain of hardships involved with music and acting I had to push my failure in art class to the
White, Kit. 101 Things to Learn in Art School. Cambridge, Mass.: MIT Press, 2011. 28 March
From the anatomy of a human, the social life of insects, and the way the world functions are all interconnected through complex system science. By taking fractal geometry and implementing it into larger unmanageable scales can help provide further more in depth information pertaining to not just that individual but also the system as a whole.
Velasco, J. (2012, December 11) Scientific Learning. “How The Arts Can Help Students Excel” Retrieved April 18, 2014, from http://www.scilearn.com/blog/how-arts-help-students-excel.php
When I was a little girl, I loved to draw. I spent my days going on adventures with my dolls and then doodling the scenarios down on paper. Drawing was amusing and it brought me true pleasure and up to age eleven, I was determined to become an artist when I grew up. One day, while I was sprawled out on the floor doodling, I mentioned my ambition to my mother. There was a moment of silence, and I stoppe...
Fractals are a geometric pattern that are repeat over and over again to produce irregular shapes and surfaces that cannot be classical geometry. It is also, an innovative division of geometry and art. Conceivably, this is the grounds for why most people are familiar with fractals only as attractive pictures functional as backdrop on the PC screen or unique postcard design. But what are they really? Most physical structures of nature and lots of human artifacts are not normal geometric shapes of the typical geometry resulting from Euclid. Fractal geometry proposes almost limitless ways of depicting, evaluating, and predicting these natural occurrences. But is it possible to characterize the entire world using mathematical equations? This article describes how the two most well-known fractals were fashioned and explains the most significant fractal properties, which make fractals helpful for different domains of science. Fractals are self-similarity and non-integer dimension, which are two of the most significant properties. What does self-similarity imply? If you look methodically at a fern leaf, you will become aware that every small leaf has the identical shape as the whole fern leaf. You can conclude that the fern leaf is self-similar. The same is with fractals: you can magnetize then as many times as you like and after each time you will still see the same shape. The non-integer dimension is more complicated to explain. Classical geometry involves objects of integer dimensions: points, lines and curves, plane figures, solids. However, many natural occurrences are better explained using a dimension amid two whole numbers. So while a non-curving straight line has a component of one, a fractal curve will obtain a dimension between...
Fractal Geometry The world of mathematics usually tends to be thought of as abstract. Complex and imaginary numbers, real numbers, logarithms, functions, some tangible and others imperceivable. But these abstract numbers, simply symbols that conjure an image, a quantity, in our mind, and complex equations, take on a new meaning with fractals - a concrete one. Fractals go from being very simple equations on a piece of paper to colorful, extraordinary images, and most of all, offer an explanation to things. The importance of fractal geometry is that it provides an answer, a comprehension, to nature, the world, and the universe.
Walter, J. G. & Gerson, H. (2007). Teachers’ personal agency: Making sense of slope through additive structures. Educational Studies in Mathematics, 65(2) pp. 203-233