Saturday, October 20, 2007
Week 8: Comment Due Sunday 10/29 5:00
We will use the seelogo program and class presentation to experience Fibonacci sequence in a higher dimension and feel intuitively. Students will give presentations on it just like they do in Theatre or Music classes and we will all benefit. I will be the first actor/director/teacher and you will follow. I am looking forward to see how you perform. You can use the 303 lab in williams if you did not download seelogo.
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4 comments:
I was fascinated by the in class presentations thus far. I'm a little bit confused by a few things, though.
If I understand it correctly, as you increase the dimensions of a fibonacci sequence and create a figure with 2n+1 sides of equal length(n being the number of dimensions) then the ratio of the numbers in the fibonnacci sequence if drawn as diagonals of the figure will approach exactly the distance from one vertice to the other, but will bounce back and forth from being to long to too short infinitely many times, becoming infinitely close.
Each diagonal is a multiple of the shortest diagonal, which appraches the golden ratio. If the largest multiple of this value present as a diagonal becomes n in 2n+1 all divided by n if i remember right, the product will be a number that becomes infinitely closer to pi.
Therefore, if we use infinity as our dimension, the length of the diagonal will equal phi, the golden ratio. When this number is plugged into our equation the result, will be pi.
I am kind of confused on what exactly you want us to post so i am just going to post my thoughts on all of this i guess. I am starting to understand more and more the whole seelogo thing through what we do in class and fooling around with it on my own. When using the fibonnaci sequence in seelogo( with the ratios) its pretty cool to see where the lines meet on the circle depending on the ratio used. For my final presentation me and a couple others are going to team up and TRY to use the fibonacci sequence in music much like the drummer you showed us used equations in the patterns of his drumming.
I love watching Dani and other members of the class experience the beauty of math as is is so artistically shown in seelogo. It is amazing for me to see how numbers bring our world together for us to understand more easily. I am getting frustrated though as I have not been able to bring what we are learning through it into my world of art. In dance, it is obvious how important numbers and sequences are in creating and sharing. But I have not been able to incorperate these facts into my acting technique. I would love to be able to connect seelogo and the fibonacci sequence, and pi and phi together and use them to further my learning in experiencing other peoples lives, but thus far it has only brought me into the mathematicians world. Not into their heads. I understand most of what we are doing, but other than the feeling of working for something, (which we all do ALL the time) I cannot connect the actual numbers with my work. I do however, bask in the feeling of not getting an answer right the first time, or seelogo code, because that forces me to find another way (or use another tactic in acting terms) to get what I want. The hunt ensues.
The See Logo program was really helpful in my understanding of the Fibonacci sequence. I respond a lot better to visual rather than verbal explanation and I understood more and more by watching over and over again the appearance of numbers and the relationship that each ratio had to the length of each diagonal. The more I watched the more apparent that relationship became.
Each pair (or larger group of numbers) forms a ratio which simplified (one divided by the other) draws a line, a guess if you will, as to what the correct length of the diagonal is. No matter how many sides the shape is given, the length of each side is one, and the diagonals are calculated accordingly. The more sides there are, the closer the shape is to being a circle, the closer the diameter (the diagonal going across the center of the shape) is to pi. The Fibonacci sequence goes on infinitely as does this entire process. The diagonal achieved from each Fibonacci ration will always be slightly inside or outside the shape, never quite reaching the "golden ratio".
I enjoyed watching the other kids in the class explain what they had learned. As I said, I'm not as comfortable vocalizing as others, but I understand how helpful it can be for people to work out new concepts out loud.
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