Fibonacci numbers

[youngblooded]

Can anyone tell me what they are? Sort of a rough description?

[1OFMANY]

take 2 numbers and add them together ( 1+1 =2 ) then take the second one you added and the answer and add THOSE together ( 1+2=3) repeat: ( 2+3=5) ...( 3+5=8)

thats the fib. sequesnce what do you need to know about it?

[youngblooded]

I just heard of it so I was wondering what it was.

[searcheagle]

take 2 numbers and add them together ( 1+1 =2 ) then take the second one you added and the answer and add THOSE together ( 1+2=3) repeat: ( 2+3=5) ...( 3+5=8)

thats the fib. sequesnce what do you need to know about it?

You have to take the numbers in order. You add the first number and add it to the second number. The numbers found in this sequence in nature a lot. Here is the first 12 numbers:
1,1,2,3,5,8,13,21,34,55,89,144...

[BlackHawk]

The sequence is famous because the ratio of any number to the one preceding it gets closer and closer to Phi (1.618) the farther in the sequence you go.
Also, you can make squares and set there edges up against one another, going around in an ever increasing spiral. Then, when you trace a curve through that spiral, it is identical to that present in a Nautilus's shell.
The sequence and ratio also appear often in the human body and other places in nature.
Very fascinating . . .

[Blaze2000]

It is fascinating. That ratio shows up all over the place in nature(galaxy formation, hurricaines, the ratio of the lengths of the parts of your body). Some people even apply it to the stock market, believing that it describes human behavior to some degree(elliott wave).

[Antares]

Wow! This is fascinating. I did this in IQ tests and didn't wonder what they are.

[malefide]

It is fascinating. That ratio shows up all over the place in nature(galaxy formation, hurricaines, the ratio of the lengths of the parts of your body). Some people even apply it to the stock market, believing that it describes human behavior to some degree(elliott wave).

That is wild.

[nemo]

Oh man, you guys could get a huge lecture on this topic (ask HeterodoxRobot).

As BlackHawk observed, it's the "natural proportion" between successive Fibonacci Numbers, which happen to be found in a sort of archetypal discrete dynamical system.

So you can almost think of it as e but for discrete growth. That's one of the reasons why it's found in nature so many places.

Also, the golden ratio is sometimes called "the most irrational number" because of it's continued fraction expansion.

Cool stuff!

[geonerd]

*sigh* I love this forum.

ok here's the formula:

f(n) = (n-2) + (n-1), n > 2, and f(0) = 1, f(1) = 1

It is a convergent sequence, meaning that as n approaches infinity, f(n)/f(n-1) approximates phi, the golden ratio (1.6180339887...)

Anyway, I saw this show on Discovery or something about how people perceive beauty. As some above said, the golden ratio can be found in parts of the body...and this study claimed that people who were deemed physically attractive had length ratios in their faces that approximated phi - for example: length to width of nose, eyes, lips, spacing of forehead to rest of the face, etc. It was very interesting.

Good times!

[True Rune]

This was interesting to learn about in a math class I took last semester. I ace'd the test too. :D I should be more observant so that I can recognize these patterns within nature.

[IFearAManOf1Book]

When I have nothing better to do, I try to reach the highest possible number. After an exam I managed to get to 9 billion and something.

[cha071c0rd3r]

*sigh* I love this forum.

ok here's the formula:

f(n) = (n-2) + (n-1), n > 2, and f(0) = 1, f(1) = 1

It is a convergent sequence, meaning that as n approaches infinity, f(n)/f(n-1) approximates phi, the golden ratio (1.6180339887...)


Just a note, technically, the Fibonacci sequence itself is divergent, but the rest is correct, the ratio does converge to phi as n -> infinity.

[Beery Swine]

Check out the Tool song Lateralus. Tons of Fibonacci.

[Monte314]

Oh man, you guys could get a huge lecture on this topic (ask HeterodoxRobot).

As BlackHawk observed, it's the "natural proportion" between successive Fibonacci Numbers, which happen to be found in a sort of archetypal discrete dynamical system.

So you can almost think of it as e but for discrete growth. That's one of the reasons why it's found in nature so many places.

Also, the golden ratio is sometimes called "the most irrational number" because of it's continued fraction expansion.

Cool stuff!
Are you sure it's not the "LEAST irrational number"? It's continued fraction expansion is totally redundant: phi =1 + 1/(1 + 1/(1 + 1/...).

Further, phi is algebraic of order 2. Wouldn't any irrational that is algebraic of order 3, 4, 5, 6, 7, 8, 9, ... be MORE irrational?

[Moriarty]

Check out the Tool song Lateralus. Tons of Fibonacci.

I just looked it up and listened to it. The musical cadence fits the pattern for the most part, but the lyrics make about as much sense as a football bat.

It's the kind of song I could enjoy while it's playing in the background and I'm engaged with something else. I like the sound of it, but I think they tried a little too hard to write a Fibonacci song. The choppy, almost incoherent vocals remind me somehow of a bad haiku: it fits the pattern, but makes little sense.

Still, neat that a band actually wrote a song based on the sequence. That in itself makes it unique I think.

[Beery Swine]

I just looked it up and listened to it. The musical cadence fits the pattern for the most part, but the lyrics make about as much sense as a football bat.

It's the kind of song I could enjoy while it's playing in the background and I'm engaged with something else. I like the sound of it, but I think they tried a little too hard to write a Fibonacci song. The choppy, almost incoherent vocals remind me somehow of a bad haiku: it fits the pattern, but makes little sense.

Still, neat that a band actually wrote a song based on the sequence. That in itself makes it unique I think.

Actually I'm not a big fan of the song, or Tool, I just saw a video a while back that pointed out all kinds of stuff in the song while it was playing and I thought it was interesting. The song's okay, but I'm more into metal, the kind where nobody, not even the vocalist knows what's being said.:laugh: Also aren't there animals with fibonacci patterns?

Also, you can make squares and set there edges up against one another, going around in an ever increasing spiral. Then, when you trace a curve through that spiral, it is identical to that present in a Nautilus's shell.
The sequence and ratio also appear often in the human body and other places in nature.
Very fascinating . . .

Wish I would have read all the replies before posting that last sentence.