I am asking that you respond to this blog before Sunday at 5:00
A journey towards Infinity.
Discovering the connection between two magic numbers: Pi and Phi
The numbers Pi and Phi captured the imagination of humanity for thousands of years and it still does. The wikepedia http://en.wikipedia.org/wiki/Pi has some fascinating information about the history of Pi and various approximations to it.
So why is Pi so captivating so many people? Every one can answer this question in his own way. As for me, Mathematics is an art form like music and one cannot explain logically why we enjoy a certain piece of music so much. Still, just like one can approximate Pi and come closer and closer to it, one can approximate the answer and it will be interesting to read your answer to this question:
Another number that captivated the imagination of humans for centuries is the number Phi (Pi with h in the middle). This number is also called the golden mean or the golden Ratio and the Wikipedia has a full explanation for it.
See: http://en.wikipedia.org/wiki/Golden_ratio
What I want to share with you here is something most beautiful that most people in the world do not know yet and this a sacred connection between these two numbers.
In order to understand this I want you to be able to go through a series of seemingly technical steps but gradually create meaning out of them. This process could be slow and a little frustrating and the one thing that can help you keep going is the knowledge that at the end of this journey you will see and feel something most beautiful, divine and sacred. I hope you want to join me in this adventure.
Here are some technical preliminary exercises:
1. What is Pi? and What is Phi (you can read in Wikipedia but write your own understanding)
2. Why are Pi and Phi so captivating?
3. Down Load SeeLogo and paste the following program and play with it by changing the value of x from 6 to 7,8,9,10,11... and also the value of y to different numbers. We will explain the program in class but I want you understand it and to explain it in your own words. It may be very frustrating at the beginning but if this happens it is a good sign and not a bad one.
LOCAL X Y
X=8 Y=3
REPEAT X [FD 40 RT 360/X]
RT 90 FD 40*X/Y
Subscribe to:
Post Comments (Atom)
15 comments:
The concept of Pi reminds me of the movie Pi. Although the movie is disturbing at times it is still really interesting. Throughout the movie the main character looks to use Pi to predict the stock market because he believes that everything in nature can be represented by numbers and therefore paterns emerge. He looks for the equation that will ultimatly be able to predict the stock market using Pi. He searches and searches and the more he trys the crazier he gets. It seems like throughout history, revolutionary mathmaticians have been on a different level of conciousness than the rest of us. The mistery and power of Pi is so capivating that if one reads too deeply into it it can take their sanity.
I would argue against Chris's understanding of Pi and the way it affects mathematicians. Mathematicians are not generally deranged and it is possible, in fact more likely that not, to gain a true understanding of mathematical concepts such as Pi without losing one's grip on the material world. In fact, if one really, truly understands such concepts I would venture to think that they would be able to apply them to the material world and have a better grasp on it, their place in it and how it relates to other dimensions of consciousness and reality. I believe that it is a stereotype, which can sometimes be true, as with all stereotypes. "Pi is the ratio of circle's circumference to its diameter". So far Pi is believed to be a "transcendental" because no one has invented a formula that can accurately describe what it is. Since numbers are uncountable, if someone could invent a formula that could name all of the digits in Pi and find a place where it stops, it would be countable. Even if someone could come up with a formula that better describes the relationship between the digits in the number Pi this would significantly change our understanding of it. Pi is captivating precisely because we don't know all of its digits and it is commonly assumed that we never will, if this is true than we will always be able to discover more digits of Pi. Over thousands of years we have already made great advances in this field, however, from 3 correct digits of Pi to 5, 7, 14 to the current 1.24 trillion digits. Phi is the essential universal rule of order and symmetry. Phi is a formula and also a number. Phi is captivating because it is found everywhere in nature and as part of the natural world humans have a natural affinity with Phi and a natural tendency to create based on Phi whether or not they are conscious of it.
as i understand it , phi is intrigueing for the same reasons fractals are, because it allows us to imagine patterns growing endlessly smaller and bigger. Phi is a ratio wherein each part is a miniature replica of the greater whole, which is exactly what fractals are. Snowflakes have fractals but I'm not sure if they necessarily have phi in them, but certainly the two concepts overlap. I'm still not sure how pi relates to phi though. After looking at see logo, I still feel clueless about all that. they are both significant ratios, pi being the ratio of the circle to the radius, and phi being the ratio of x squared being the same as x + one. one is a circle in perfect balance, the other is a spiral, which is sort of like a disrupted circle which never meets back up with itself. pi is like converging lines and phi is like parallel ones. sort of. anyway, I would like to understand more about how the two are related because see logo didn't quite make sense to me.
perhaps other people will have made sense of it by the end of the weekend.
Personally I have always been more attracted to Phi than Pi. I think the reason for this is that if you look from a mathematical standpoint you can see Phi everywhere...music, nature, architexture, etc.
Pi on the other hand is something I have been using in math classes all throughout school. This may have desensitized me to the meaning of it, as I cant see anything amazing about it on the surface.
I am hoping that through these exercises I will be able to find the formula for connecting Pi and Phi, and hopefully the things that captivate me about Phi will connect and captivate me for Pi also.
The fact that Pi is transendental does make me curious about how no one can find a formula for it. Phi has a formula but its aesthetical aspect is just so amazing to me.
First off I just wanted to say that I really enjoyed watching Donald in Mathmagicland. It brought back a lot of great memories and reminded me that math can be enjoyable. I actually went out and played pool on Friday after finally realizing what the diamonds on the side of the table are for. I forget that Math is not just numbers but it's conceptual and can be applied to everything in life, and can even be used for recreational purposes. For the record, I kicked butt not because I used the fractions but because I measured the angles and really tried to calculate each shot.
I'm going to be honest in saying that the concept of Pi is way over my head. I usually tend to gravitate towards visual learning so I clicked on Archimedes picture of the properties of pi being put into action. It truly is infinite, and no matter what shape or number you are working with it can be related to pi, or can be connected in some way.
I think that Bailey summed up the meaning and mystery of Pi rather well, "Pi is captivating precisely because we don't know all of its digits and it is commonly assumed that we never will." I agree with his statement because most mathematicians enjoy math because there is always a logical answer but with Pi the possibilities are endless and therefore it remains an intriguing enigma.
I loved learned about Pi and Phi in class the other day with Dani. I find it a very complex subject but necessary in taking life past the step of living, and into the realm of understanding. We can live our lives and not ask questions, or question everything. It is easy to think of Pi simply as a number, but it is obviously much much more than that. Same with Phi, it is everywhere in the world around us, forever affecting and changing. I must finish this blog later tonight for I have rehearsal to go to (story of my life) but I wanted to start a blog before 5 pm. Hope the Day of Fasting was meaningful to all who participated. More to come later.
I found it very interesting to learn about phi, as I had never been exposed to the idea before this class (how did I miss it all these years?)
The idea of infinity has always fascinated me. I usually associate infinity with outer space- how far does it really go? I never really think about it in terms of pi, but that seems to be just as fascinating. How can one number go on and on and on, as the idea of space seems to do. I think that these ideas are also so interesting because although mathematics can find explanations for almost anything in nature, these are two examples that simply dont have an end, for now...
I have to say that this is the first time I've started to feel that math anxiety that I know all to well from school when concepts just travel right over my head. While I understand what Phi is, I still don't have the concept completely grasped. Therefore, it's hard to explain why pi and phi are captavating for others because I'm not captavated by either. I suppose that people are fascinated by these two numbers because you will never be able to grasp all the digits of these numbers. People are always fascinated with the unknown and that's exactly what these two numbers offer: a step into the unknown.
What I have found most interesting about pi and phi is how much they show up in nature. From the proportions of our body, to how rabbits multiply all relates back to the golden ratio. The most exciting thing however is how much there is to be discovered about the number and in the world. We have only begun to scratch the surface. Quantum theories are still yet to be proven and discovered and I feel much of these discoveries will come from the idea of phi.
Another thing I like about phi is how so much of the world has to do with the number. It really makes you question the making of the universe. It does not seem like an accident how much it shows up and really makes you think.
First of all, I want to apologize for posting late. It's been such a busy weekend, I lost track of time.
So far as I understand, Pi is the constant value that, when multiplied by the radius of a circle, yields the circumference of that circle. Phi, on the other hand, is the value of the golden ratio. Both numbers are non-repeating, yet infinite, meaning they go on in decimals to infinity without any recognizable repeating pattern.
I have been interested in Pi for awhile, but the first mention of Phi that i'd ever heard was in class the other day. My idea of exactly what it represents is still quite vague, but i'm excited to learn more about it and it's relationship to Pi.
Class on Friday was the first time i had ever heard of Phi.the difference between pi and phi is that while pi is infinite, phi actually has a formula. Watching the Donald Duck in Mathe magic land really opened this up to me and having never seen i thought some of the stuff (including the math behind billiards playing, and how music originated through the Pythagoreans)was pretty cool. What captivated many people about phi is that its formula was used everywhere and in a lot of Greek architecture and sculpting. The golden ratio if i am correct is also evident in the golden rectangle, which then led to its use in Greek Society.
I had never heard of Phi until Friday's class. I'm mesmerized to realize that the golden ratio has been used for so many years and by different cultures such as the Greeks . The Parthenon is even more amazing understanding the extent of mathematical planning that went into it's construction. Phi is used to often in art and nature that i'm surprised i have never heard about it before.
I have previously learned about Pi before, but i am still always interested in learning about it. It's a constant irrational number that is used so often. Even though it's an infinite number with mystery behind it, it is still used as a mathematical staple in solving equations.
Donald in Mathamagic land was a great way to see the golden rectangle and phi used in practical applications.
I read the comments and appreciate your efforts but frankly I do not think that many of you really put much effort into it.
Sincerely,
--Dani
Over the past however many years of my education i have been introduced to the numbers pi and phi in various math and physics classes. Quite frankly, the symbols never meant much to me out of the context of those subjects. I knew they were numbers, I knew they had infinite value but at the same time I never really thought to question their real purpose or how they play into every day life. The concept of infinity is one that continues to blow my mind. THe more I read about Pi and its inability to be counted the more curious I became. I think for the most part I am limited by what I see and that is my reality. However, there are so many functions of pi that cannot be seen by the human eye. Pi is a means of measuring the diameter of circles but by manipulating it we are able to decrease in intervals on an infinite level.
Phi was also very intriguing. I have always been interested in art, I love looking at beautiful things, but I never really questioned what made them beautiful. I never stopped to think there could be a mathematical principle governing their aesthetic qualities. Looking at the mona lisa I was amazed to see a series of perfect rectangular divisions in the painting. These divisions do affect the overall look of the piece and their dimensions make it more pleasing to the eye.
Post a Comment