1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...

Golden Ratio

x number in Fibonacci
_________________

x + 1 number in Fibonacci

≈1.61803399 (Except for with the first few).

Example: 144/89 ≈ 1.61803399

Golden Rectangle

A golden rectangle is one whose side lengths are in the golden ratio

In example: A rectangle whose sides are in the golden ratio: 1:1.618

Example:

L = 144
W = 89

144/89 ≈ 1.618

USES OF THE GOLDEN RECTANGLE IN THE WORLD:

The golden rectangle is supposed to be the rectangle most appealing to the human eye.

In Greek architecture...

In nature... (This one actually has a fibonacci spiral):

More Mind****:

There are 1, 2, 3, 5, 8, 13, 21, and 34 petaled flowers.

http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html

1/89 (Which is a Fibonacci number) is equal to .011235....

If you square a number in the Fibonacci (Let's take 34).

34^2 = 1156

Then divide that by the Fibonacci number directly after the one you squared...

1156/55 ≈ 21

Guess what. 21 is the Fibonacci number directly before 34 (The one you squared). There's lots of them that work like that.

Oh, and Tool even wrote a song based on the Fibonacci:

Feel free to post some Fibonacci mind**** having to do with the sequence, the ratios, or the rectangle. Or the spiral...
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Last edited by TheSPillow at Sep 29, 2010,
This is relevant to my interests.
I like the historical context of the Fibonacci code, like how Da Vinci and Michelangelo used it.
I like the historical context of the Fibonacci code, like how Da Vinci and Michelangelo used it, and I. See. Clearly now. About the ratio. To me it is interesting. I enjoyed this post immensely so do another.
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^You missed 2.
^TS posted the exact same link in the OP?
Quote by Windwaker
I. See. Clearly now. About the ratio. To me it is interesting. I enjoyed this post immensely so do another.

I am impressed by this cleverness, even if you did miss a number. Kudos.
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Quote by Windwaker
I. See. Clearly now. About the ratio. To me it is interesting. I enjoyed this post immensely so do another.

I just got what you did!

Kudos to you, good sir.
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^TS posted the exact same link in the OP?

didn't even notice
i'll delete it
Quote by Chylyn
I like the historical context of the Fibonacci code, like how Da Vinci and Michelangelo used it, and I. See. Clearly now. About the ratio. To me it is interesting. I enjoyed this post immensely so do another.

Wat
Tool's 'Lateralus' is a perfect example of this;

Black then white are all I see in my infancy.
Red and yellow then came to be, reaching out to me, let's me see

As below, so above and beyond, I imagine.
Drawn beyond the lines of reason.
Push the envelope, watch it bend .
Quote by tyler_j
Tool's 'Lateralus' is a perfect example of this;

Black then white are all I see in my infancy.
Red and yellow then came to be, reaching out to me, let's me see

As below, so above and beyond, I imagine.
Drawn beyond the lines of reason.
Push the envelope, watch it bend .

Quote by TheSPillow

Oh, and Tool even wrote a song based on the Fibonacci:

>_>
Quote by tyler_j
Tool's 'Lateralus' is a perfect example of this;

Black then white are all I see in my infancy.
Red and yellow then came to be, reaching out to me, let's me see

As below, so above and beyond, I imagine.
Drawn beyond the lines of reason.
Push the envelope, watch it bend .

Beat me to it.
:3
that is a damn fine looking rectangle right thar.
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>_>

Hey, I saw Fibonnacci, scanned every other post and thought "Oh boy!"
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Quote by JDawg
Huh? Oh. Fibonacci series? Yeah, that's cool. It's been around forever, though. Another interesting thing is that it's in nature. It's true, many patterns like the swirl of seashells or pinecones follow it. I remember reading about it in a book as a kid once, and didn't believe it at first, but it's proven.
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Quote by CoreysMonster
Huh? Oh. Fibonacci series? Yeah, that's cool. It's been around forever, though. Another interesting thing is that it's in nature. It's true, many patterns like the swirl of seashells or pinecones follow it. I remember reading about it in a book as a kid once, and didn't believe it at first, but it's proven.

+1

i remembered this stuff from high school whenever i watched pi and after seeing it explained in that maddening way i found it more interesting. much like the movie suggests you can find relative mathematical patterns in anything if you look hard enough. but that doesn't make it any less awesome when you look at the world and see the underlying numerical nature of things.
Yay Tool

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Mandlebrodt set > Fibonacci

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It seems this thread's going to diverge.

Probably into two, and then three, five...

Yah, probably.
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Not only the verse of Lateralus, but in the chorus, the time signature goes 9/8, 8/8, 7/8. 987 is a number in the sequence!
apparentlly if you put the tracks off the album lateralus into a fibonacci sequence the songs blend seemlessly into each other.

Debussy's La Mer is also structured using the fibonacci sequence: http://www.youtube.com/watch?v=66hX8Ms0FwE
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