Divine Proportion - What is it & How Does it Work?

[Quantum1332]

So, i didn't know what this was classified as, so i settled for this genre. Can someone explain to me exactly how this works. How does everything come back to 1.618.

 

[HallsofIvy]

It doesn't, any more than "everything comes back to" 1, or 2, or 3.14! $\pi$ (which can be approximated by 3.14) satisfies some very basic relationships that are found (again approximately) throughout nature because they are simple. The "divine proportion", $\frac{-1+\sqrt{5}}{2}$ which is approximately 1.618, satisfies the very simple relation $z=\frac{1-z}{z}$ which, just because it is simple occurs throughout nature.

 

[arildno]

ACTUALLY, Halls, $\frac{-1+\sqrt{5}}{2}$ is less than 1, and thus only extremely approximate to 1.618..













Runs and hides within a golden rectangle..

 

[HallsofIvy]

Oops, writing too fast again. I meant
$$\frac{1+\sqrt{5}}{2}$$
which is, more accurately but still not exact, 1.6180339887498948482045868343656.

 

[Miro]

So, i didn't know what this was classified as, so i settled for this genre. Can someone explain to me exactly how this works. How does everything come back to 1.618.

If u read "the Da Vinchi Code", u'll find in it all the proportions that are related to this magic number, I read it and I was some astonished but I don't have the book now to tell u more.
But I do advise u to read it, or see the film

 

[matt grime]

No, no, no, no.

That 'novel' is an (atrociously badly written) piece of fiction containing Dan Brown's (or it turns out his wife's) half assed research that is completely rubbish. Do not read it for the mathematical insight. Do not read it for literary merit either (it has none).

 

[DaveC426913]

Is the divine proportion not so because it is the simplest from of recursion? Recursion is a very common mechanism in nature.

 

[arildno]

Hmm, I'd say that the recurrence relation $a_{n+1}=a_{n}$ is even simpler than the recurrence relation for the Fibonacci numbers.

 

[matt grime]

Is the divine proportion not so[\quote]what do 'is' and 'so' mean in this context?

because it is the simplest from of recursion?

'simple' is a little subjective. see previous post by arildno.

 

[arildno]

As I see it, the reason why the divine proportion occurs so often is closely related to the probable fact that most mechanisms work on a local level, and thus, any seemingly macro-scale mechanism is actually just a compound effect of local mechanisms.
That the resultant global picture should, at times, mimick the local picture isn't a too exotic possibility. But that's basically what the "divine" proportion is about.

From this perspective, it is seen that there is nothing "divine" about that proportion; rather, its prevalence indicates that there isn't any grand, intelligent design going on in nature, independent from simple, natural mechanisms.

 

[MalayInd]

you can find everything related to it on :
http://www.lhup.edu/%7Edsimanek/pseudo/fibonacc.htm