Author 
Topic: Golden Ratio or Phi (Read 5679 times) 

Mugwump101
Junior Member
Gender:
Posts: 61


Golden Ratio or Phi
« on: Dec 6^{th}, 2006, 1:20am » 
Quote Modify

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?


IP Logged 
"When I examine myself and my methods of thought, I come to the conclusion that the gift of fantasy has meant more to me than my talent for absorbing positive knowledge. "~ Albert Einstein



towr
wu::riddles Moderator Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13671


Re: Golden Ratio or Phi
« Reply #1 on: Dec 6^{th}, 2006, 1:48am » 
Quote Modify

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.


IP Logged 
Wikipedia, Google, Mathworld, Integer sequence DB



rmsgrey
Uberpuzzler
Gender:
Posts: 2821


Re: Golden Ratio or Phi
« Reply #2 on: Dec 6^{th}, 2006, 7:05am » 
Quote Modify

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.


IP Logged 



ThudnBlunder
wu::riddles Moderator Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489


Re: Golden Ratio or Phi
« Reply #3 on: Dec 6^{th}, 2006, 7:37am » 
Quote Modify

Here is a good source: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/


IP Logged 
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.



Mugwump101
Junior Member
Gender:
Posts: 61


Re: Golden Ratio or Phi
« Reply #4 on: Dec 8^{th}, 2006, 3:32am » 
Quote Modify

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?


IP Logged 
"When I examine myself and my methods of thought, I come to the conclusion that the gift of fantasy has meant more to me than my talent for absorbing positive knowledge. "~ Albert Einstein



Whiskey Tango Foxtrot
Uberpuzzler
Sorry Goose, it's time to buzz a tower.
Gender:
Posts: 1667


Re: Golden Ratio or Phi
« Reply #5 on: Dec 8^{th}, 2006, 7:29am » 
Quote Modify

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.


IP Logged 
"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use."  Galileo Galilei



Aurora
Junior Member
Gender:
Posts: 81


Re: Golden Ratio or Phi
« Reply #6 on: Mar 1^{st}, 2008, 6:58am » 
Quote Modify

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/


IP Logged 
"In these days, a man who says a thing cannot be done is quite apt to be interrupted by some idiot doing it." Elbert Green Hubbard



Random Lack of Squiggily Lines
Senior Riddler
Everything before 7/1/2008 is now irrelevant.
Gender:
Posts: 460


Re: Golden Ratio or Phi
« Reply #7 on: Mar 9^{th}, 2008, 5:09pm » 
Quote Modify

turns out its 42


IP Logged 
You can only believe i what you can prove, and since you have nothing proven to cmpare to, you can believe in nothing.
I have ~50 posts to hack a "R" into a "D". Which one?



Roy42
Senior Riddler
Gender:
Posts: 418


Re: Golden Ratio or Phi
« Reply #8 on: Mar 18^{th}, 2008, 11:29pm » 
Quote Modify

I have a book by Mario Livio about the history of the Golden Ratio, it's origin etc. it's quite good


IP Logged 
Regards,
≈Roy42



Benny
Uberpuzzler
Gender:
Posts: 1024


Re: Golden Ratio or Phi
« Reply #9 on: Jun 5^{th}, 2009, 12:42pm » 
Quote Modify

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 » 
IP Logged 
If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.



0.999...
Full Member
Gender:
Posts: 156


Re: Golden Ratio or Phi
« Reply #10 on: Jun 17^{th}, 2009, 2:19pm » 
Quote Modify

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.


IP Logged 



Benny
Uberpuzzler
Gender:
Posts: 1024


Re: Golden Ratio or Phi
« Reply #11 on: Feb 2^{nd}, 2010, 1:24pm » 
Quote Modify

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 » 
IP Logged 
If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.



towr
wu::riddles Moderator Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13671


Re: Golden Ratio or Phi
« Reply #12 on: Feb 2^{nd}, 2010, 2:40pm » 
Quote Modify

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.


IP Logged 
Wikipedia, Google, Mathworld, Integer sequence DB



Benny
Uberpuzzler
Gender:
Posts: 1024


Re: Golden Ratio or Phi
« Reply #13 on: Feb 2^{nd}, 2010, 2:58pm » 
Quote Modify

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. 



IP Logged 
If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.



rmsgrey
Uberpuzzler
Gender:
Posts: 2821


Re: Golden Ratio or Phi
« Reply #14 on: Feb 2^{nd}, 2010, 5:01pm » 
Quote Modify

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.


IP Logged 



Benny
Uberpuzzler
Gender:
Posts: 1024


Re: Golden Ratio or Phi
« Reply #15 on: Feb 2^{nd}, 2010, 5:49pm » 
Quote Modify

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)?


IP Logged 
If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.



JohanC
Senior Riddler
Posts: 460


Re: Golden Ratio or Phi
« Reply #16 on: Feb 3^{rd}, 2010, 3:22am » 
Quote Modify

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?


IP Logged 



pex
Uberpuzzler
Gender:
Posts: 880


Re: Golden Ratio or Phi
« Reply #17 on: Feb 3^{rd}, 2010, 3:48am » 
Quote Modify

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.


IP Logged 



towr
wu::riddles Moderator Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13671


Re: Golden Ratio or Phi
« Reply #18 on: Feb 3^{rd}, 2010, 4:23am » 
Quote Modify

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 » 
IP Logged 
Wikipedia, Google, Mathworld, Integer sequence DB



Benny
Uberpuzzler
Gender:
Posts: 1024


Re: Golden Ratio or Phi
« Reply #19 on: Feb 3^{rd}, 2010, 1:18pm » 
Quote Modify

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 » 
IP Logged 
If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.



Benny
Uberpuzzler
Gender:
Posts: 1024


Re: Golden Ratio or Phi
« Reply #20 on: Feb 20^{th}, 2010, 2:53pm » 
Quote Modify

This site suggests that there is a relationship between Fibonacci series and Stock Market prices http://goldennumber.net/stocks.htm What do you think?


IP Logged 
If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.



Grimbal
wu::riddles Moderator Uberpuzzler
Gender:
Posts: 7448


Re: Golden Ratio or Phi
« Reply #22 on: Feb 23^{rd}, 2010, 2:14am » 
Quote Modify

Not mad, just salespeople. The madmen are those who buy from them.


IP Logged 



Benny
Uberpuzzler
Gender:
Posts: 1024


Re: Golden Ratio or Phi
« Reply #23 on: Feb 23^{rd}, 2010, 10:51am » 
Quote Modify

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.


IP Logged 
If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.



