PHI, The Golden Proportion

Hello all. I am doing some deep research on Phi, AKA the golden proportion. I know all about it, but it is odd there are very few resources. If anyone knows some different-than-generic information please help.

Well, I know of a Dutch math book about it called 'de Gulden Snede', ISBN: 9050410588. This probably won't help you, because you're probably not Dutch.

The Mathworld page should give you a good start though. It also links to a list of books about the golden ratio: here.

I know it's around 1.1618 ?
Alot of things in nature are dictated by it, it's used in the Mona Lisa (something to do with drawing squares on her face), you can find it in several places in the human body,etc

I mean, you can kind of see why pi would have a significance in nature, with all the round-shaped objects in existence. Just a wild idea here, but, do you think there might be any religious aspect to that number. I mean as far as biblical quotes or other religious texts appearing close to that number?

Originally posted by philosci
Hello all. I am doing some deep research on Phi, AKA the golden proportion. I know all about it, but it is odd there are very few resources. If anyone knows some different-than-generic information please help.

One of my favorite subjects actually. Like yourself I've spent many years studying the subject. It's strange that you say you have only found few resources on it though, because I have found loads of information about it just on the net alone. There are also many many threads about it here at ATS as well. My advice would be to search using different methods instead of just PHI or Golden Proportion. Things like:

Golden Ratio
Golden Rectangle/Triangle etc.
Divine Ratio
1.618 or .618
Fibonacci
Golden Spiral
Irrational Numbers
Sacred Geometry

Another thing that is fun is to use those same search words using the 'Google Image Search' instead of the main search page. The result is much more pleasing to the eye and a refreshing change from just reading about it or using it in math.

If you want to know the golden ratio, I discovered it by accident. Using a calculator enter any number and hit enter. Then type (Ans + 1)^-1 - or your calculator's equivalent - and keep hitting enter until the calculator gives the same answer twice in a row.

If you do Ans^-1 + 1 for long enough it gives you the golden ratio - 1.

Just though I'd share that.

Originally posted by StickySteve
If you want to know the golden ratio, I discovered it by accident. Using a calculator enter any number and hit enter. Then type (Ans + 1)^-1 - or your calculator's equivalent - and keep hitting enter until the calculator gives the same answer twice in a row.

If you do Ans^-1 + 1 for long enough it gives you the golden ratio - 1.

Just though I'd share that.

What is the 'Ans' function?? I am not familiar with it or what it does.

How many decimal places is it accurate up to using your method of finding PHI?

The Ans returns the answer of the last calcution. Doing that calculation a lot of times in a row gives you a iterative process that approaches phi - 1. Any good calculater should have it.

That actually gives you the 1/ Phi value...
Phi itself is greater than 1 I believe, so
when you have two concurrent numbers
1/ans
to give 1.618033989..

The True value of Phi is found in this equation

Also the symbol for Phi is

You can find more info here

mathworld.wolfram.com...

I lost all my links for phi/Phi in a harddrive crash.

I can tell you that there are 2 phi's.

Phi = 1.618034
phi = 0.618034

There are a couple great links if you do a Google search.

I've done some work with Phi, but I'm still stumped as to how it works out the way it does (specifically in nature).

I know all of those things, and thanks.
I am looking for things that we can't easily find on the internet.

There is a great article concerning phi in the June issue of the magazine Discover (page 64) that discusses Phi to a great extent and its connection to the Fibonacci Sequence. I think that the article will help quench your thirst but if you still want more try the book The Golden Ratio and Fibonacci Numbers
by Richard Dunlap. The book is a great read.

Buy Here

One interesting thing from the Discover Article is that when a falcon swoops down on its prey its path is calculated by phi.



[edit on 11-6-2004 by BlackJackal]

I know quite a good page.. I'm trying to find it ...

Did anyone here by any chance see the movie Pi? They speak extensively of Phi, and though someone earlier asked if _pi_ had religious implications, which I don't think it did, because they say it is 3, Phi certainly did. The Fibonacci sequence (1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,1597...) Has many numbers inside ancienct Hebrew texts. This is something mentioned in the movie, actually. Hebrew doubles as an alphabet and a numberical system, words like 'mother' would add to words like 'father' to get words like 'child'. It is quite fascinating. The thing is though, something like 'The Tree Of Life' comes out to 144, and the old testament reads that the 'Tree Of Life' in 'The Garden of Eden', which comes to 233, yields a godly combination. They are not only saying that The Tree Of Life residing within The Garden Of Eden is a godly thing, but that 144 in 233 is godly - strangely enough, that's where we really start to get close to 'general' Phi in divisions.

Page links:

Here, here, and here. Unfortunately, the last one has been changed a lot, and is now more filled with anti-evolutionist, pro-creation rhetoric than cool stuff about phi, but there is still a lot there, if you can sort through the crap.

Really, just search phi or Divine Math or something like was already said. Tons appears!

Originally posted by browha
That actually gives you the 1/ Phi value...
Phi itself is greater than 1 I believe, so
when you have two concurrent numbers
1/ans
to give 1.618033989..

1/phi = phi - 1

One of the number's strange properties.

Measure your height , barefoot to top of head , and devide it by the height of your belly button . If you are divinely proportionate , it comes out to PHI . Works better on my girlfriend than me ... Serious , give it a try

Remarkable!

Well, not really. It's just kind of neat that it is so easy to identify phi through an observation of it's qualities.

In the following, we will take a bit of knowledge about phi, and apply it to an unsolved variable, to see what value we come up with.

The applied knowledge is that 1/phi = phi - 1. We will substitute phi with x, a variable, to be solved for.

1/x = x - 1
1 = x(x - 1)
0 = x^2 - x - 1

Quadratic Formula is: x= (-b+/- (b^2 - 4(a)(c))^0.5)/2(a)

x^2 - x - 1 >>> a = coefficient of x^2, 1. b = coefficient of x, -1. c = constant at end of standard form, also -1.

Filled in, the equation looks like:

x = (1 +/- (-1^2 - 4(1)(-1))^0.5)/2(1)
x = (1 +/- (1+4)^0.5)/2
x = (1 +/- 5^0.5)/2

Anything raised to 0.5 is the same as square rooting the number - and we've found the identity of phi, Root5 + or - 1, divided by 2, gives Phi.


Math is fun kids!

We should all get togather and work on Phi. It is such a mystery and when I went to my library, the only Phi book was in the main branch, which is in the center of Charlotte. Thanks evereyone, the devine proportion is one of, what I think, most interesting and inportant thing I have ever seen.