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InvisibleHelltick
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1.618 The Golden Ratio.
    #8792433 - 08/18/08 09:34 PM (9 years, 10 months ago)

Wow...this is the universal ratio, thats for sure!

Link


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Edited by Helltick (08/18/08 10:11 PM)


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OfflinePhanTomCat
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Re: 1.168 The Golden Ratio. [Re: Helltick]
    #8792561 - 08/18/08 10:09 PM (9 years, 10 months ago)

* 1.618....    :wink:


>^;;^<


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InvisibleHelltick
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Re: 1.168 The Golden Ratio. [Re: PhanTomCat]
    #8792565 - 08/18/08 10:12 PM (9 years, 10 months ago)

:blush:


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OfflinePhanTomCat
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Re: 1.168 The Golden Ratio. [Re: Helltick]
    #8792577 - 08/18/08 10:16 PM (9 years, 10 months ago)

The ratio is found in good classic art and architecture, and I think in the human body proportions as well....
Neat stuff....
A lot of the "sacred geometry" is cool stuff to check out....    :thumbup:


>^;;^<


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"The most important things in life that are often ignored, are the things that one cannot see...."

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Invisiblelavod
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Re: 1.168 The Golden Ratio. [Re: PhanTomCat]
    #8792621 - 08/18/08 10:30 PM (9 years, 10 months ago)

93
Yeah, it be special.  I just cut down a copper pipe to the conjugate golden ratio in relation to the distance from my elbow to the tip of my pinky for use as a wand.
93 93/93


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InvisibleDieCommie


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Re: 1.168 The Golden Ratio. [Re: Helltick]
    #8792626 - 08/18/08 10:31 PM (9 years, 10 months ago)

Be wary! 

Though interesting, most of the 'facts' about the golden ratio are myths!  For example the Parthenon was not constructed with the golden ratio in mind.  Also, the Nautilus shell, which does grow in a logarithmic spiral does not turn at an angle of the golden ratio.  There are ratios on the human body that are about 1.6, but they are highly contrived and varied.  If you look, you can find any ratio on the human body.  People claim that Da Vinici used the golden ratio in Vitruvian Man, but there is no evidence for that.  Also, it is claimed by some that the pyramids were built with the golden ratio, but there is absolutely no evidence for that.  Classical music, architecture... many areas myths persist in spite of no evidence. 

In fact the famous book, "The Golden Ratio: The Story of PHI, the World's Most Astonishing Number" actually spends most of the book dispelling many of these myths and also makes a good case that phi is the most overrated number there is. 

This usually angers people who have a special fondness for the number, but its just not as ubiquitous or natural as the myths make it out to be.  They dont even have a button for it on a calculator because its not important! (unlike pi or e which are quite important)


EDIT - Links below
http://blog.sciencenews.org/view/generic/id/8660/title/Math_Trek__A_Golden_Sales_Pitch
http://www.maa.org/devlin/devlin_05_07.html
http://www.freethoughtassociation.org/minutes/2004/Feb25-2004.htm
http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm


Edited by Qubit (08/18/08 10:35 PM)


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InvisibleHelltick
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Re: 1.168 The Golden Ratio. [Re: PhanTomCat]
    #8792676 - 08/18/08 10:41 PM (9 years, 10 months ago)

yeah...and as long as you follow the sequence it doesn't matter what number you start with...could be:


999,999,1998,2997,4995,7992,12987,20979,33966,54945,88911

first and last don't count.
So...

1998/999
2997/1998
4995/2997
7992/4995
12987/7992
20979/12987
33966/20979
54945/33966  =  1.618

and you can use this math to build a golden spiral if you want.

This is prolly how they came up with compound interest.


--------------------
  My Agar Tek. 
  My Greenhouse Tek. 

"It's not good when it's done, it's done when it's good"


Edited by Helltick (08/18/08 10:57 PM)


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Invisibleblewmeanie
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Re: 1.168 The Golden Ratio. [Re: Helltick]
    #8819989 - 08/24/08 02:46 PM (9 years, 10 months ago)



:hypnotoad:

Conservation of energy at its most evil.


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InvisibledeCypher
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Re: 1.168 The Golden Ratio. [Re: blewmeanie]
    #8820782 - 08/24/08 05:55 PM (9 years, 10 months ago)

I always liked the recursive method for generating the golden mean:

Take any number, say 2.
Take its reciprocal, and add 1.
Repeat.

Such infinite complexity summed up in three algorithmic lines.


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Invisiblelukeboots
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Re: 1.168 The Golden Ratio. [Re: DieCommie]
    #9067776 - 10/12/08 08:52 PM (9 years, 9 months ago)

Quote:

DieCommie said:
Be wary! 

Though interesting, most of the 'facts' about the golden ratio are myths!  For example the Parthenon was not constructed with the golden ratio in mind.  Also, the Nautilus shell, which does grow in a logarithmic spiral does not turn at an angle of the golden ratio.  There are ratios on the human body that are about 1.6, but they are highly contrived and varied.  If you look, you can find any ratio on the human body.  People claim that Da Vinici used the golden ratio in Vitruvian Man, but there is no evidence for that.  Also, it is claimed by some that the pyramids were built with the golden ratio, but there is absolutely no evidence for that.  Classical music, architecture... many areas myths persist in spite of no evidence. 

In fact the famous book, "The Golden Ratio: The Story of PHI, the World's Most Astonishing Number" actually spends most of the book dispelling many of these myths and also makes a good case that phi is the most overrated number there is. 

This usually angers people who have a special fondness for the number, but its just not as ubiquitous or natural as the myths make it out to be.  They dont even have a button for it on a calculator because its not important! (unlike pi or e which are quite important)


EDIT - Links below
http://blog.sciencenews.org/view/generic/id/8660/title/Math_Trek__A_Golden_Sales_Pitch
http://www.maa.org/devlin/devlin_05_07.html
http://www.freethoughtassociation.org/minutes/2004/Feb25-2004.htm
http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm




I hate to raise the dead here... and I rarely post in this forum.. but I've read Livio's book, and while he does debunk a lot of myths surrounding phi (thank goodness), dismissing phi as "unimportant" is stretching the point a little bit. The Fibonacci numbers are incredibly interesting, and the self-similarity of some geometrical shapes that phi plays a large part in (most notably, a perfect pentagon/pentragram) has been important to me for quite some time. Even Euclid's simple definition of the golden mean ("as the whole is to the greater segment, the greater segment is the lesser segment") can be argued to be a mathematical metaphor for personal responsibility, realizing one's place in a family, society, world, anything larger than oneself. I may be overreaching here, but that's how I see things.

Also, as a counterargument for the pyramids (and I'm no scholar on the subject) - the Egyptians could not have, at that point in history, accurately measured phi to its precise, irrational property. Trying to hold it both against the Egyptians and phi that they did not measure to 1.6180339887.... is both strange and hypercritical (though I understand the need to debunk these things before it gets out of hand).

It may not be as universally important as pi, but it has, in Mario Livio's own words, "probably.. inspired more thinkers of all disciplines like no other number in the history of mathematics."


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InvisibleDieCommie


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Re: 1.168 The Golden Ratio. [Re: lukeboots]
    #9067856 - 10/12/08 09:11 PM (9 years, 9 months ago)

I dont think anybody is holding against the Egyptians... they simply didnt use it (or at least they never wrote about it).

Maybe it has inspired alot of people, I am just not one of them.  :tongue:  I work with numbers every day and have never, ever had to use it.  And I dont know anybody who has.

I think alot of times people see phi in things like they see a face in the clouds.


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Invisiblelukeboots
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Re: 1.168 The Golden Ratio. [Re: DieCommie]
    #9069998 - 10/13/08 10:12 AM (9 years, 9 months ago)

Point taken.

When you say "like a face in a cloud", I agree. Because of some of the "mystic" geometric properties it's been characterized with, most notably the connection to the logarithmic spiral & the pentagonal pieces of some plant life (say, the arrangement of seeds in an apple), people try to look for it everywhere. Personally, I pass sunflowers on my way to work every summer, and the spiral is in the seeds. It's not the "secret of the universe", but it is neat that pineapples and sunflowers, among others, utilize the maximizing shared-space visual property of phi, and because it IS visually appealling (even if Livio has his problems with the word "beauty"), it tends to strike a chord with a lot of people. And also, of course, because people love mystic crap.


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Re: 1.168 The Golden Ratio. [Re: lukeboots]
    #9070038 - 10/13/08 10:36 AM (9 years, 9 months ago)

Quote:

jonnywax said:
It's not the "secret of the universe", but it is neat that pineapples and sunflowers, among others, utilize the maximizing shared-space visual property of phi.....




I dont know, it sounds like the secret of the universe to me.:shrug:


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Invisiblelukeboots
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Re: 1.168 The Golden Ratio. [Re: blewmeanie]
    #9073239 - 10/13/08 11:06 PM (9 years, 9 months ago)

One of millions. :smile2:


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InvisibleDieCommie


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Re: 1.168 The Golden Ratio. [Re: lukeboots]
    #9073479 - 10/13/08 11:52 PM (9 years, 9 months ago)

No, its the secret, not a secret. 

Wait a minute... we are discussing it - Its not a secret at all!


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Invisiblelukeboots
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Re: 1.168 The Golden Ratio. [Re: DieCommie]
    #9073528 - 10/14/08 12:02 AM (9 years, 9 months ago)

It's about as secret as freemasons wearing aprons.


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InvisibleDieCommie


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Re: 1.168 The Golden Ratio. [Re: lukeboots]
    #9073532 - 10/14/08 12:03 AM (9 years, 9 months ago)

Its the worlds best known secret.  Basically, its a widely believed fact.


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Invisiblelukeboots
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Re: 1.168 The Golden Ratio. [Re: DieCommie]
    #9073539 - 10/14/08 12:05 AM (9 years, 9 months ago)

Secret shmecret, it's intriguing and that's that.


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Offlineumbrellamaker
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Re: 1.168 The Golden Ratio. *DELETED* [Re: DieCommie]
    #9080694 - 10/15/08 12:43 PM (9 years, 9 months ago)

Post deleted by umbrellamaker

Reason for deletion: I may have been out of line for posting that.



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Invisiblejohnm214
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Re: 1.168 The Golden Ratio. [Re: umbrellamaker]
    #9080828 - 10/15/08 01:07 PM (9 years, 9 months ago)

I enjoyed his post and can't find anything suggesting he's putting his opinions over other folks'.


Seems he cited some examples that many of us have heard and explained their poor fit to the claimed ubiquity of phi. 


And where does he act like he knows more than the rest of us?

He certianly knows more than me about a great number of things, including this topic, and I enjoyed it.


I don't see how the choices are diecommies is wrong or everyone is a fool either.


He provided at least as much reasoning to back his statements as others have, and I don't really know how citing sources that may not be as rigourous as you like can be seen as trying to make everyone look like a fool but failing.


Where is this arrogance you speak of?


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