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Topic: Golden Ratio or Phi (Read 5522 times) 

Mugwump101
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Golden Ratio or Phi
« on: Dec 6^{th}, 2006, 1:20am » 
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I'm looking for more information of where Phi or the Golden Ratio is found (I.e. exotic or creative places not like the vitruvian man or obvious) and how it was found. Any ideas?


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towr
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Re: Golden Ratio or Phi
« Reply #1 on: Dec 6^{th}, 2006, 1:48am » 
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You can find it in a lot of ancient greek architecture. Various places in math (like geometry, e.g. pentagrams); if you look hard enough you can find it in pretty faces. If you really look hard enough, everywhere (But that's just the aneristic principle at work, really) I'm not sure what exactly you want to know though. Of course wikipedia is a good start.


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rmsgrey
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Re: Golden Ratio or Phi
« Reply #2 on: Dec 6^{th}, 2006, 7:05am » 
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It turns up (as an angle) in plants because it's very irrational  spacing shoots the golden angle apart means they overlap as little as possible.


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ThudnBlunder
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Re: Golden Ratio or Phi
« Reply #3 on: Dec 6^{th}, 2006, 7:37am » 
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Here is a good source: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/


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Mugwump101
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Re: Golden Ratio or Phi
« Reply #4 on: Dec 8^{th}, 2006, 3:32am » 
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Actually more so, I'm creating a mail merge for an Excel Project and We're trying to send all the people a letter or basically advertisement for an Amusement Park that involves the Golden Ratio. Any ideas for Rides? I started out with a DNA rollar coaster and a beach with seashells, waves, lanterns, chairs that embody phi. Do any more brilliant ideas?


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Whiskey Tango Foxtrot
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Re: Golden Ratio or Phi
« Reply #5 on: Dec 8^{th}, 2006, 7:29am » 
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Pretty much anything can implement the golden ratio if you choose it to do so. Take a ferris wheel as an example. The dimensions of the cars on a ferris wheel could be determined by the Golden Ratio. The length and width of the spokes (or whatever they're called) could also do the same. Even the queue lines to get on the rides could be constructed using the Golden Ratio. There are an infinite number of applications here.


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Aurora
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Re: Golden Ratio or Phi
« Reply #6 on: Mar 1^{st}, 2008, 6:58am » 
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I found this website the other day whilst researching Phi for art coursework. There are quite a few examples of where it can be found. http://goldennumber.net/


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Random Lack of Squiggily Lines
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Re: Golden Ratio or Phi
« Reply #7 on: Mar 9^{th}, 2008, 5:09pm » 
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turns out its 42


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Roy42
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Re: Golden Ratio or Phi
« Reply #8 on: Mar 18^{th}, 2008, 11:29pm » 
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I have a book by Mario Livio about the history of the Golden Ratio, it's origin etc. it's quite good


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Benny
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Re: Golden Ratio or Phi
« Reply #9 on: Jun 5^{th}, 2009, 12:42pm » 
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on Dec 6^{th}, 2006, 7:37am, THUDandBLUNDER wrote: Yes, I like this source. Then I went to another page of the same website: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi.html See under "Similar Numbers" about other numbers that have the Phi property that when you square them their decimal parts remain the same. series of number here is 5, (9), 13, 17, 21, (25), 29, ... which are the numbers that are 1 more than the multiples of 4. I searched for this series on the "The OnLine Encyclopedia of Integer Sequences" but couldn't find it. Did I miss it?

« Last Edit: Jun 5^{th}, 2009, 12:43pm by Benny » 
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0.999...
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Re: Golden Ratio or Phi
« Reply #10 on: Jun 17^{th}, 2009, 2:19pm » 
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on Mar 18^{th}, 2008, 11:29pm, Roy wrote:I have a book by Mario Livio about the history of the Golden Ratio, it's origin etc. it's quite good 
 I have it and agree.


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Benny
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Re: Golden Ratio or Phi
« Reply #11 on: Feb 2^{nd}, 2010, 1:24pm » 
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Suppose a Fibonacci sequence starts with (a,b), that is to say: (a, b, a+b, a+2b, 2a+3b, 3a+5b, ..., F_{n2} a + F_{n1} b, ...) with f_{0} = a, f_{1} = b, f_{2} = a+b, f_{3} = a+2b, f_{4} = 2a+3b, f_{5} = 3a+5b, .................................... f_{i} = F_{i2} a + F_{i1} b and the value of f_{i} given, say, 10^{4} = 2^{4} * 5^{4} What are the values of f_{0} and f_{1} ?

« Last Edit: Feb 2^{nd}, 2010, 1:25pm by Benny » 
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towr
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Re: Golden Ratio or Phi
« Reply #12 on: Feb 2^{nd}, 2010, 2:40pm » 
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on Feb 2^{nd}, 2010, 1:24pm, BenVitale wrote:and the value of f_{i} given, say, 10^{4} = 2^{4} * 5^{4} What are the values of f_{0} and f_{1} ? 
 There is no way to tell if you're only given one f_{i} For example, if f_{2}=x, then for any a f_{0}=a, f_{1}xa works. And obviously you can work backwards for later i in a similar way.


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Benny
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Re: Golden Ratio or Phi
« Reply #13 on: Feb 2^{nd}, 2010, 2:58pm » 
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on Feb 2^{nd}, 2010, 2:40pm, towr wrote: There is no way to tell if you're only given one f_{i} 
 Could we use the Index shift rule to determine the first two terms of this sequence? I thought I could, but I got stuck ... so I posted this problem, here, requesting help. Quote: For example, if f_{2}=x, then for any a f_{0}=a, f_{1}xa works. And obviously you can work backwards for later i in a similar way. 



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rmsgrey
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Re: Golden Ratio or Phi
« Reply #14 on: Feb 2^{nd}, 2010, 5:01pm » 
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on Feb 2^{nd}, 2010, 2:58pm, BenVitale wrote: Could we use the Index shift rule to determine the first two terms of this sequence? I thought I could, but I got stuck ... so I posted this problem, here, requesting help. 
 What towr was trying to convey is that for any given f_{i}, you can choose any value you want for f_{i1} and that will give you a different (but still valid) sequence. Another way of looking at it is that you have one equation in two unknowns: f_{i} = F_{i2}a + F_{i1}b where everything but a and b is known. Adding in an expression for any other term of the sequence adds another equation and another unknown (that term of the sequence) so doesn't help make the system of equations any more solvable.


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Benny
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Re: Golden Ratio or Phi
« Reply #15 on: Feb 2^{nd}, 2010, 5:49pm » 
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Oh, I see. I'm trying to be creative with the Fibonacci series. And, I was trying to figure out a formula to test a number with a Fibo that starts with (a,b) We know that in the Fibo series that starts with (1,1), that is: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ... N is a Fibonacci number if and only if 5N^{2} + 4 or 5N^{2} – 4 is a square number What would be the formula to test numbers to see if they belong in Fibo (a,b)?


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JohanC
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Re: Golden Ratio or Phi
« Reply #16 on: Feb 3^{rd}, 2010, 3:22am » 
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on Feb 2^{nd}, 2010, 1:24pm, BenVitale wrote:Suppose a Fibonacci sequence starts with (a,b), that is to say: (a, b, a+b, a+2b, 2a+3b, 3a+5b, ..., F_{n2} a + F_{n1} b, ...) with f_{0} = a, f_{1} = b, f_{2} = a+b, f_{3} = a+2b, f_{4} = 2a+3b, f_{5} = 3a+5b, .................................... f_{i} = F_{i2} a + F_{i1} b and the value of f_{i} given, say, 10^{4} = 2^{4} * 5^{4} What are the values of f_{0} and f_{1} ? 
 A more tricky variant on this question would be: what is the largest i for which the series exists entirely of positive numbers?


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pex
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Re: Golden Ratio or Phi
« Reply #17 on: Feb 3^{rd}, 2010, 3:48am » 
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on Feb 3^{rd}, 2010, 3:22am, JohanC wrote:A more tricky variant on this question would be: what is the largest i for which the series exists entirely of positive numbers? 
 For f_{i} = 10000, I find i = 13 for (a, b) = (80, 20) by a simple exhaustive search. I don't think it's a coincidence that for these (a, b), f_{i1} is approximately 10000 / Phi.


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towr
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Re: Golden Ratio or Phi
« Reply #18 on: Feb 3^{rd}, 2010, 4:23am » 
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on Feb 2^{nd}, 2010, 5:49pm, BenVitale wrote:What would be the formula to test numbers to see if they belong in Fibo (a,b)? 
 f_{n} ~= (a+b)/sqrt(5) ^{n2}, so if a,b are given it's simple enough.

« Last Edit: Feb 3^{rd}, 2010, 4:34am by towr » 
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Benny
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Re: Golden Ratio or Phi
« Reply #19 on: Feb 3^{rd}, 2010, 1:18pm » 
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Thanks to all of you for the contributions. post deleted Reason: Basically, I asked how was the formula (5N^{2} + 4 or 5N^{2} – 4 is a square number) constructed? I found the construction of the formula.

« Last Edit: Feb 3^{rd}, 2010, 1:37pm by Benny » 
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Benny
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Re: Golden Ratio or Phi
« Reply #20 on: Feb 20^{th}, 2010, 2:53pm » 
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This site suggests that there is a relationship between Fibonacci series and Stock Market prices http://goldennumber.net/stocks.htm What do you think?


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Grimbal
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Re: Golden Ratio or Phi
« Reply #22 on: Feb 23^{rd}, 2010, 2:14am » 
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Not mad, just salespeople. The madmen are those who buy from them.


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Benny
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Re: Golden Ratio or Phi
« Reply #23 on: Feb 23^{rd}, 2010, 10:51am » 
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Yes, I agree. It is a mad attempt. It is the behavior of a snake oil salesmen. This shows our deep need for control. We are in a deep recession, and we feel out of control. We feel fear. From an evolutionary standpoint, if we are in control of our environment, then we have a far better chance of survival. The owners of that website are selling a software. Either they believe in their product or are just dishonest. They know that the stock market is driven by fear and greed.


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