B"H
Hello. Thank you for reading my post. I figured that I would write something completely fun, without any reference to all of the serious issues on some of the other forums.
Does anyone see the poetry of the Golden mean? It is an irrational number, but I will estimate it to the sixth decimal place:
1.618034
Those of you who do not quite remember, the Golden mean is the positive number that is itself squared minus one. It shows up all over nature, and connects to the Fibonacci sequence in that the ratio of each number in the Fibonacci sequence to the number right before it gets closer and closer to the Golden mean as the sequence approaches Infinity.
Artists as well as mathematicians love the Golden mean. The Greeks thought it was awesome. I fell in love with it over the summer time.
Say anything cool about it you want, or even something that is not so much a mathematical fact as something in your mind. I will start by stating that, as I have estimated it to the sixth decimal place, we begin with a "16". We then have "18". Together they add up to "34", which is found at the end.
Ok, so here's the poetry:
16 is a number that I connect to Divine Mercy. I will not go in to that too deeply, but it is a personal view of 16. "18" signifies Life in the Hebrew tradition. 34 happens to be how old I am. Go figure!
I don't see whats special about a number, they are just artificial, man-made placeholders for concepts required to describe quantity.
As for the numerology, ancient superstition, and little more.
I prefer a system based on dozens, personally.
Calculations are so much easier. Had we six digits on each hand instead of five, would maths have advanced quicker, I wonder?
I prefer a system based on dozens, personally.
Calculations are so much easier. Had we six digits on each hand instead of five, would maths have advanced quicker, I wonder?
B"H
Interesting response. I think that the "16" mention, which I personally identify with "Divine Mercy", is interesting in light of the concept of other base systems. You know, the computer programmers and engineers sometimes use base 16, do they not? For further discussion of my views on numbers, please read this link:
http://www.aspiesforfreedom.com/showthre...?tid=11687
" Number Symbolism Versus Numerology"
Number symbolism is something that can lead to enlightenment if done correctly. Occult numerology, by contrast, leads to spiritual degeneration. Under Torah Law it is a forbidden practice. Often the term "numerology" is used by righteous people who study numerical symbolism to describe what they do, but it is not an accurate term.
In my case, I like the poetic symbolism of 16 and 18, a number symbolizing life, both adding up to my age. 18 would be a number you would like, since it is based on sixes. Now, this is less of anything to do with me being especially blessed, and more of a comfort for me during a hard period in my life. It is symbolism that matters to me *personally*.
So, I guess I'll restate the purpose of my thread. Who sees anything cool in the Golden mean?
Here's one thing:
http://milan.milanovic.org/math/english/...flower.jpg
Look at the pattern in a sunflower. Can you see the Fibonacci Sequence?
http://www.popmath.org.uk/rpamaths/rpamp...lower.html
Thanks again, Tigger-the-wing. I enjoy your posts.
For a little while, I wondered why the 16-9 wide screen televisions didn't look right to me. I now know it is because they don't use the proportions of the golden mean which are 8-13. The 4-3 screens were closer to the golden mean so looked better to me. I think widescreen is pretty much of a gimmick anyway.
For a little while, I wondered why the 16-9 wide screen televisions didn't look right to me. I now know it is because they don't use the proportions of the golden mean which are 8-13. The 4-3 screens were closer to the golden mean so looked better to me. I think widescreen is pretty much of a gimmick anyway.
ATM: Thank you for responding, Pakrat. It is interesting what you are saying. I have never heard this discussed before (the ratio's of the dimensions of a television). 13-8 is a Fibonacci ratio, which continually comes closer to the Golden Ratio as we go "up" the Fibonacci number thread. 13/8, 21/13, 34/21, 55/34...comes closer to our special number.
Now, 16/9 is 1 and seven ninths. That would be 1.77777777....OK, and 4/3 would be 1.33333333....It seems as though 1.7777777 would be better according to your criteria since it is numerically closer to 1.618 than 1.3333333.....
However, the nature of how TV's look would be subjective. If it looks better to you, it looks better. Here in America we have such mind-enhancing entertainment as "Big Brother", "American Idol", and the late, great, "Simple Life." 
Don't tell anybody, as it would ruin my moralistic, "true believer", piranha-in-a-tank image around here; I *DO* kind of miss the "Simple Life." If you quote me, I'll deny it! Who says that TV is not good for your mind and spirit?....
On a serious note, there is an interesting thing to leave off with. If you look at the formula for obtaining a Fibonacci number, you find this:
[(Phi^n) - (-Phi^-n)]/Sqrt5
n would be the Fibonacci number we want. How this gets a series of integers is a mystery that confounds me. And yet, it does. We can clearly see how the ratio of each Fibonacci number gets closer and closer to Phi.
How cool is that?
http://en.wikipedia.org/wiki/Fibonacci_number
http://en.wikipedia.org/wiki/Golden_ratio
http://www.mcs.surrey.ac.uk/Personal/R.K...nesque.jpg
All the best. Have a wonderful weekend.
I like it the most that the Golden Mean appears naturally in the Pentagram. And, closely related, in the inner structure of the Icosahedron.
B"H
In all seriousness, I never actually saw the "Simple Life."
So, I do not know enough to miss it or not...
Have a good weekend. All the best.
In all seriousness, I never actually saw the "Simple Life."
Why should you, for educational purposes? No need to dive into a pit full of bullshit to legitimately say that it stinks. Better invest the time in watching George Carlin's shows on Google video, I recommend.
B"H
I've never seen Big Brother or American Idol either...
In fact, both names are really scary if you think about the implications.
All the best.
Ah, good ol' (1 + sqroot(5))/2!
This was my primary interest between ages 12 and 17.
In fact it was how I got myself introduced to number theory at 16. I learned how to write proofs, and realized that I was much better at that type of math than in calculations.
For a little while, I wondered why the 16-9 wide screen televisions didn't look right to me. I now know it is because they don't use the proportions of the golden mean which are 8-13. The 4-3 screens were closer to the golden mean so looked better to me. I think widescreen is pretty much of a gimmick anyway.
ATM: Thank you for responding, Pakrat. It is interesting what you are saying. I have never heard this discussed before (the ratio's of the dimensions of a television). 13-8 is a Fibonacci ratio, which continually comes closer to the Golden Ratio as we go "up" the Fibonacci number thread. 13/8, 21/13, 34/21, 55/34...comes closer to our special number.
Now, 16/9 is 1 and seven ninths. That would be 1.77777777....OK, and 4/3 would be 1.33333333....It seems as though 1.7777777 would be better according to your criteria since it is numerically closer to 1.618 than 1.3333333.....
However, the nature of how TV's look would be subjective. If it looks better to you, it looks better. Here in America we have such mind-enhancing entertainment as "Big Brother", "American Idol", and the late, great, "Simple Life." Don't tell anybody, as it would ruin my moralistic, "true believer", piranha-in-a-tank image around here; I *DO* kind of miss the "Simple Life." If you quote me, I'll deny it! Who says that TV is not good for your mind and spirit?....
On a serious note, there is an interesting thing to leave off with. If you look at the formula for obtaining a Fibonacci number, you find this:
[(Phi^n) - (-Phi^-n)]/Sqrt5
n would be the Fibonacci number we want. How this gets a series of integers is a mystery that confounds me. And yet, it does. We can clearly see how the ratio of each Fibonacci number gets closer and closer to Phi.
How cool is that?
http://en.wikipedia.org/wiki/Fibonacci_number
http://en.wikipedia.org/wiki/Golden_ratio
http://www.mcs.surrey.ac.uk/Personal/R.K...nesque.jpg
All the best. Have a wonderful weekend.
I remember the day I found that formula! It was when I was sixteen, after attending a summer math program for people going into Algebra II. I had gotten a graphing calculator for the first time and a whiteboard and was messing with the programming functions and looking for patterns. I have no idea how I came up with it; at that time I was having a lot of weird moments of figuring multi-step problems in an instant (during this time period I would see the answers to multi-step logarithms come instantly before I could articulate any steps or work - unfortunately, I no longer can do these things).
Ah, good ol' (1 + sqroot(5))/2!
This was my primary interest between ages 12 and 17.
In fact it was how I got myself introduced to number theory at 16. I learned how to write proofs, and realized that I was much better at that type of math than in calculations.
I was introduced to number theory rather late in life. As it was, my mathematics education was strong in Calculus and those types of abstractions. However, number theory introduces a "coolness" to math that would inspire more students.
Plato and Socrates believed that "all knowing is remembering." We do not learn mathematics and philosophy according to those guys. We "remember" it! I wonder about that when I hear that you discovered all of this on your own, at a young age. "All knowing is remembering"...What do you remember, Earthmonkey?
Oh, and to clarify a point I made before, not only did I never see "The Simple Life", "Big Brother or the like; I have also never seen Dudley the Dragon, Gorilizza, or some of the other cultural phenomenon mentioned on this forum. I think that, in all probability, I would rather have seen those than "Big Brother" or American Idolatry.
All the best.
My dad showed me something in a book about the golden mean at about age 12 or 13, and I was fascinated with it. Then when I was walking in a bookstore three years later, with 11 dollars on hand, I ran across a Dover book on number theory. At first when I read it, I couldn't understand a bit of it, and just read the first 10 pages over and over again. Eventually I started to understand, and within a year I had read and understood the first four chapters. I also have acquired books on topology and abstract algebra.