If you are on this site you probably already know about "The Golden Mean", a sacred shape which reoccurs over and over in nature. If not here is a website to get you going:
www.charlesgilchrist.com/SGEO/...1.html
Sacredness is all around you. Enjoy.
Swaz

Unsu...
Re: The golden Mean: 1.618
Thu, January 27, 2005  12:08 PMYes there are "shapes" that have golden mean measurments but it is not a shape itself. It is a ratio (the Golden Ratio). 1.618 is a decmal aproximation but truly this number is "irrational" (Like Pi) meaning there is no whole number ratio to express its value which is (1+sqrt.5)/2. The diagonal of a regular pentagon (equal sides, equal angles) with edge length 1 will be the golden ratio. Dividing a line segment into two parts so that the smaller segment is to the larger as the larger is to the whole. A:B::B:(A+B)
Mathematicians use the Greek letter "Tau" and artists/architects use "Phi" (pronounced FEE). A good introduction to this number is Mario Livio's book "The Golden Ratio".
There is an interesting connection between the Fibbonacci series (1,1,2,3,5,8,13,21,34,55,89....) and the Golden Ratio. Choose one term in the sequence and divide it by the previous one. The further along
the sequence you do this, the closer you will aproximate the golden ratio going above and below and coverging towards the actual number.
But you will never get to it!
1/1=1, 2/1=2 , 3/2=1.5, 5/3=1.666...., 8/5=1.6, 13/8=1.625,
21/13= 1.61538462, 34/21=1.61904762, 55/34=1.61764706,
89/55=1.61818182
So you see that 89/55 is a good aproximation.
Dan 

Unsu...
Re: The golden Mean: 1.618
Thu, January 27, 2005  6:27 PMAnother interesting occurrence of Golden Rectangles (sides 1, tau) occur in the icosahedron (regfular 3D figure with 20 triangular facets) where its twelve vertices coincide with the vertices of three mutually perpendicular golden rectangles. 

Re: The golden Mean: 1.618
Thu, January 27, 2005  8:08 PMI based my paper titled "Sacred Geometry" on the Golden Ratio. Phi (1.618) and phi (.618). I wish I could share it with you, it provides many examples of this phenomenon and links it as being the language of God.


Unsu...
Re: The golden Mean: 1.618
Sat, January 29, 2005  5:42 PMCan you share it?
I'm new to the tribe, but fascinated in all such basic physical mathematics!
Thanks!



Unsu...
Re: The golden Mean: 1.618
Sun, March 13, 2005  1:37 AMHi all
Could an enlightened someone please explain the difference between the the Golden Ratio and Fibbonacci sequence to me?
Thanks . . . 

Re: The golden Mean: 1.618
Mon, March 14, 2005  3:01 PMThey're actually interrelated in a very interesting way:
One way of representing the Golden Ration (phi) is by a continued fraction (beware the horrible ASCII formatting),
phi = 1 + 1/(1+1/(1+1/(1+...)))
Now, if you work out the first few terms of the continued fraction you start to see a pattern emerging  phi can be expressed as an infinte series,
phi = 1 + Sum(n=0>infinity){[(1)^(n+1)]/[F_n*F_(n+1)]}
where F_n is the nth Fibonacci number. Phi can also be expressed as an infinite limit of the ratio between consecutive Fibonacci numbers,
phi = Lim(n>infinity){F_n/F_(n1)}
Pretty kewl. Phi is also the most irrational of the irrational numbers due to the fact that it's expressible as a continued fraction made entirely of 1's. Hope this helped! 

Re: The golden Mean: 1.618
Mon, March 14, 2005  6:56 PM>> Phi can also be expressed as an infinite limit of the ratio between consecutive Fibonacci numbers
Yeah, baby! I'm not a mathematician, but that's the good stuff.
www.mcs.surrey.ac.uk/Persona...fib.html


Re: The golden Mean: 1.618
Fri, December 16, 2005  3:52 PMWell, this thread went off on a tangent!
I saw a few actual answers to your question that were, factual, mathematical the the nth degree.
Here is a farmboy version.
Phi is a irrational proportion....lots of decimals
The math for it is all over this thread.
The fibbonacci sequence is an approximation fo this Divine proportion found in nature, trees growth certain fern and many other "natural" places.
The difference is trees don't do decimals.
They have the ability to grow 1 limb then 2 the 3 then 5 then 8 then 13 etc as they head for the sunshine.
The farmboy method, not always spot on but usually makes it easier to grasp.
Jason



Re: The golden Mean: 1.618
Thu, March 17, 2005  4:46 PM 

Re: The golden Mean: 1.618
Thu, March 17, 2005  4:47 PMSorry, I did not notice someone had already posted the url. 

Re: The golden Mean: 1.618
Tue, April 19, 2005  8:06 PMwadup sacred geometrilytes. check this out : : 1.618 multiplied by its inverse 816.1 equals 1320
1.618 x 816.1 = 1320
1320 is a key mayan timing frequency that their sacred calendar/time map is based on
pretty neat, huh
another way to say it is "holy shit! the creative pulse of the universe is completely fucking unified!"
even as it is expressed thru different languages in different eras it reflects the same galactic elegance !
peace,
babs 

Unsu...
Re: The golden Mean: 1.618
Tue, April 19, 2005  10:25 PMbut a ratio of 13 to 20 is not the same as the value of the number 1320.
There is a superficial('semantic') correlation, ie, there are the same numbers. But a ratio is different then an actula number.
Is there anyway that multiples of the ratio equal multiples of phi?
_A 

Re: The golden Mean: 1.618
Tue, April 19, 2005  10:53 PMwhat
is
superficial
4
u
is
supernatural
for
me
the
value
is
in
the
mystery 

Unsu...
Re: The golden Mean: 1.618
Wed, April 20, 2005  9:31 AMhey babs,
all I am saying is:
prove your connection is really there  and I don't mean that in an antagonistic way! Really, show me!
_A 

Re: The golden Mean: 1.618
Wed, April 20, 2005  12:47 PMyo man i apologize if my response seemed defensive.......but rilly the proof is in the numerological pudding
1.618 x 816.1 = 1320
i could go on about how this equation carries deeper significance for me but rilly it is just this simple
the connection is self~evident
what is it you want me to prove brother ?
peace,
babs 

Unsu...
Re: The golden Mean: 1.618
Wed, April 20, 2005  3:01 PMbabslove,
a ratio is a set of numbers so there is a relationship with meaning, its dynamic.
but a number is a value with no meaninful relationship until put into relationship with another number or something else. thats why i called it semantic  if I write the word "apple" your mind conjures that concept forward. But there is no meaningful relationship to that unless you ascribe one: "apples are good" "i prefer green apples to red apples" etc etc...
13:20
looks similar to but does not behave the same as
1320
so I see a difference that maybe connects, but what is that connectino which isn't a rationalization just to make the connection *seem* more clear than it is.
_a 

This is the maximum depth. Additional responses will not be threaded.
Re: The golden Mean: 1.618
Wed, April 20, 2005  7:48 PMadampoo,
your candor has found gratitude in my heart !
but for me, the connection i resonate with is more poetic than it is rational
..if you want i could write:
1.618 x 816.1 = 13:20
but then i would be bending the laws of the universe to get you to see something that i want you to see which is totally ridiculous, however; consider this my friend:
1320 total years passes between the date the great mayan jedi Pacal Votan died and the date planet earth has with 2012..
purdy intrestin huh ?
pz 

Unsu...
Re: The golden Mean: 1.618
Wed, April 20, 2005  9:00 PMbabslove,
1.618:816.1 = 13:20 is a rationalization, I do not buy! could not hold an elephant or the weight of truth!
Howevah!:
that final fact bears some repeating now, holds some interests...
_a 

Re: The golden Mean: 1.618
Mon, April 25, 2005  9:30 PMHi,
Actually, it's not the death of Pacal V. it's the date of the dedication of his tomb that has the 1320 year significance. Check this out.....
*****quoting*****
natural time:  13:20
13 annual moon cycles, 20 fingers and toes;
13 Tones of Creation, 20 Solar Seals
artificial time  12:60
manmade 12month calendar, mechanical 60minute hour
As The Grand Wizard of Time,
Pacal Votan's message is revealed
in a manner which cannot be denied:
Pacal Votan died in 683 AD, yet 9 years passed before his tomb was dedicated and sealed in 692 AD. His tomb was not discovered and reopened until 1952.
Between 692 and 1952,
there is exactly 1260 years.
(12:60 artificial time)
Between 692 and 2012 (the closing of the cycle)
there is exactly 1320 years.
(13:20 natural time)
********end quote*********
taken from:
www.13moon.com/pacal%20link.htm
Neato huh?
and, not that this is really relevent, but the Sufi poet Hafiz was born in 1320. 

Re: The golden Mean: 1.618
Tue, November 29, 2005  1:52 AMThe odd scientific term you're looking to tie this together is synchronicity....

Unsu...
Re: The golden Mean: 1.618
Fri, December 2, 2005  11:45 AMI think it is an interesting synchronicity that the Long Count ends in the Gregorian year of 2012 and the new Long count begins in the year 2013. 2013,1320.












Re: The golden Mean: 1.618
Wed, November 30, 2005  12:17 PMIt is good t see you all here,. Not withstanding my present puter problems, I am on a neighbors computer, let me introduce an idea that may have bearing upon your present idealogical mentations.
I would introduce the connection between 'the preferential will' and dynamic occurrance'. Not so, you say, I would beg to differ. The laws of physics apply both near and far until you get down to the level of quarks and then all bets are off.
Quarks respond to the attitude of the researcher, not an anticipated distinction in the world of proper physics but, nevertheless an observable and undeniable variation that must be accounted for by the sincere and unprejudiced researcher. Quarks exibit qualities that for lack of better terminology have been designated with such names as; charm and strangeness. Hardly scientific terms yet annoyingly present. What might we discover were we to accept the factuality of these findings? What new and fascinating feilds might we explore? mmmmm?
As ever, your boxmaker,
Samuel A. Cruz 

Re: The golden Mean: 1.618
Fri, December 2, 2005  9:54 AMsorry to divert from the subject.
"Quarks exibit qualities that for lack of better terminology have been designated with such names as; charm and strangeness. "
i've also latched onto the strangeness here. things which should be given scientific names have names of emotion. dig deep into science and matter (as far as you can go), you end up querky quark names such as charming, strange, up, down ect.... coincidence?
what will further newly discovered quantum particles be named  bliss, chillout, shock, hedonist, terror, joy ?
strange, but charming. 

Re: The golden Mean: 1.618
Sat, December 3, 2005  4:18 AMWell, hello there Jon in London. Thank you for your response to my slightly off topic quark commentary, I should have known immediately from the Emma Thompson laser like wit that you were from the UK. Still, I feel compelled to point out that we were speaking of an exhibited quality and not denominating some putative particle newly discovered or otherwise.
Such is the wonder of this 21st century that I, a poor carpenter in California, should be having a conversation with a fellow from Cambridge no less.
On the subject of emotions and travel in space do you see the connection between the platonic solids, musical scales, ratios themselves and what Theodore Sturgeon phrased in his 1953 book 'More Than Human' "HomoGestalt"? Just curious, since you seem to have an interest in such things. Or do I owe you an apology? 

Re: The golden Mean: 1.618
Sun, December 4, 2005  2:53 PMhi sammuel !
god, i been reading about platonic solids, musical scales, ratios and stuff today. about "homogestalt" i'm blank, please enlighten me!
everything is all connected  form,musical scales and in what ever form nature desides to shape itself. getting back to the subject, nature is all hooked up to the golden ratio  call it a supernatural addiction. thats nature, and that includes HUMAN nature, the pattern of our feelings, or the ebb and flow of emotions. they come and go like seasons and other natural cycles, so when you think about it, when we talk of "charm" and "strangeness", as alien as it is in the quantum world, it's emotion which ebbs and flows in a magnetic golden ratio type ocean full of PHIlosophical spirals.
you related that laws break there rules at a quantum quark level. it apears so, but what if matter just changes gear/modes and experience a quantum leap/evolution to say "emotional matter" (or physical to non physical), in which the formless matter still obide to the means of the golden mean. have i lost you? think of the reoccuring nature of life events and cosmic calenders.


