Fibonacci was a mathematician who published a book. The entire purpose of the book was to show how much easier it is to do mathematics using Arabic numerals, as opposed to Roman numerals. One example he gave was a simple list of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89... et cetera. The sequence is formed by adding the two most recent numbers to get the next number.

In the Fibonacci sequence, each number is the sum of the two previous ones. It is helpful in computer science, for instance, for creating random numbers and sorting data. Natural examples include the spiral shapes of shells and galaxies.

There are multiple ways to define Fibonacci numbers:

• Set the first two to be 0 and 1, and every after as the sum of those two preceding it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... .
• The number of different ways to form a strip of fixed length by glueing strips of lengths 1 and 2 together.
• The number of binary (only 0 and 1 allowed) sequences with a fixed number of digits, and 1s must not be consecutive.
• Via Binet's formula as ( φ^n - (-1/φ)^n ) / sqrt(5).
• [many more]

> how it it's supposed to be in all nature and that's sacres geometry...

That's a myth at best, and a lie at worst. There are some very few instances where they somewhat appear, but those are one in a million things. None of the claims of golden ratios appearing within humans, plants or animals has ever withstood scrutiny, sqrt(2), 1.5 and sqrt(3) are just as probable and nonsensical.

Edit: spelling.

> Natural examples include the spiral shapes of shells and galaxies.

No, those are at best just any logarithmic spirals, the factor is not the golden ratio or otherwise Fibonacci-related.

>No, those are at best just any logarithmic spirals, the factor is not the golden ratio or otherwise Fibonacci-related.

It is true in some cases but not all. Even though there may not always be a connection between math and nature, there are still instances where the golden ratio and the Fibonacci sequence can be seen.

THAAAANK you

Numbers aren’t sacred. They’re effin numbers.

There is absolutely no physical process that favours the golden ratio for spirals. The factor for a logarithmic one simply is not too large, and not too small. Like 1.3, 1.5, 1.61, or 1.8, maybe even 2 or 3. Some humans attribute patterns where there are none.

The only exceptions I've ever seen where Fibonacci numbers really (roughly) appear are growth patterns that mimic its recursion. Sunflowers are often mentioned, never checked if even those actually work but they might.

Even though it may be true that no physical process directly favors them, saying there aren't any in the natural world is inaccurate. Although they might not have been the only factors in the creation of some naturally occurring spirals, the golden ratio and the Fibonacci sequence can be seen in some of them. A nice illustration of the pattern is how seeds are distributed in sunflowers.

I did not say there are none, only that almost all of them are random and won't be there in another of the same species of object.

> A nice illustration of the pattern is how seeds are distributed in sunflowers.

That is literally what I mentioned as the only potentially correct occurrence!

It's nice to know that we are in agreement. It is true to say that the Fibonacci sequence may not account for the unpredictability of natural processes.

Other examples exist that may resemble the sequence. The spiral pattern on a ram's horns often resembles the golden ratio. As the pinecone grows bigger and you count the spiral in each direction, the ratio gets closer to the golden ratio.

They wanted the hype explained. Why would you answer if you don't get it either?

It's inaccurate to call that "the golden ratio" when it's not. If a plant has a logarithmic spiral with a factor of 1.4-1.8 then you shouldn't call it the same as a spiral of (1+sqrt(5))/2, for a lot of reasons - first, there's too much variance; second, there's no way to really prove whether it's the golden ratio or some other number. Suppose there is a slightly different number, say, (2+sqrt(8))/3, which is similar (~1.6 and ~1.6) yet entirely different - is it not just as possible that this is the magic number of life rather than the golden ratio?

The hype is just that: a hype. It is not based on anything real. Also, it was a fad at best, it never was THE big thing everyone talks about.

Anyway, the explanation goes as with most hypes: a few people made up things, consciously or not, excitedly told others, and it spread. What else do you want one to say?

There is no overall systemic use of the sequence in nature. If things match up its a fluke.

It mimics the way cells divide, the ratio between any successive numbers gets closer and closer to Phi the higher you get, the western musical scale is based on the sequence with one octave having 13 notes and a scale having 8 notes, tons of classical musicians used that ratio as a template in the process of making music, tons of architects over many cultures have used that ratio in their buildings, Our DNA strands measure 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral, the ratio between our moons radius and the Earth's radius is phi... And so on.

You know... reasons for hype.. like they asked

Not a lot of ELI5 answers, but some good history.

The Fibonacci sequence is a set of numbers with a distinct pattern (explained in other comments). What is important is that the ratio of one number to the one following it is always the same. (The second is always 1.618 times larger than the previous). That is called the golden ratio, and it is the golden ratio that is seen everywhere in nature.

If you’ve seen the image of rectangles that form into a spiral, this is what it means:

The small rectangle has sides with that exact ratio. The long side of that rectangle is the short side of the next, and that rectangle uses the golden ratio. The long side of that one is the short side of the next…. And so on. This creates a spiral pattern, and that pattern, in that ratio, happens all the time. Flowers, tree leaves, and animal shells for example. Always 1.618 times bigger than the previous part.

The number isn’t magical. 1.618 isn’t special. There is just a natural order to things, and we created a numerical system that happens to measure that order at that number.

To put it mildly, your post is full of lies and blatantly wrong statements. Most of them not even close even if one rounds the numbers very generously.

> It mimics the way cells divide

No.

> the ratio between any successive numbers gets closer and closer to Phi

Yes but that is definitely not behind the hype. I can write down a lot of sequences that converge to whatever number you like.

> the western musical scale is based on the sequence with one octave having 13 notes and a scale having 8 notes

It is actually based on powers of 2^(1/12), namely those close to rational numbers.

> tons of architects over many cultures have used that ratio in their buildings

Tons? maybe one in a thousand, at best. Which is not because the number is great, but because they fell for the hype.

> Our DNA strands measure 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral

This is completely random, measure it with any other unit and it becomes wrong. And it is completely false, too. Their length is way higher (in the order of centimeters per chromosome!), varies between chromosomes a lot, and more. And googling says it's actually 18 Angstroms in diameter, not 21, but whatever, that is random at this point anyway.

> the ratio between our moons radius and the Earth's radius is phi

Just no. Don't invent random things. The ratio is ~3.667, what the heck did you even smoke to confuse that with phi? At least check your claims sometimes?

Edit: fixed quote.

>The second is always 1.618 times larger than the previous

Ehhh... "always" is a bit of a misnomer. "Settles down to depending on how precise you are", maybe.

The more digits of precision, the longer it takes to settle. Graph, Graph of zoomed in portion

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you see it in nature especially plants, it's often an efficient simple way to space things like thorns and petals or model the growth of branches, seeds, segements etc so it occurs.

The earth/moon thing is a little off, but not incorrect. The right triangle you'd create based on their radiuses is Phi. If you knew as much as you'd like to think, you could have corrected that. Everything else stands and your first sentence is just you projecting. Like, go look at a piano, wise guy... Missing the forest for the trees

I would argue that the only thing making anything sacred is the beliefs of the person or people who believe in that thing.

The Bible or the Quran are only “sacred” because people say so.

I’m with Pythagoras on this one.

Fair.

That is an artifact of the fact that our number system is completely made up. The natural aspect of the ratio is what is real, and the way we apply numerical concepts to it isn’t perfect. It’s just close enough that we can use mathematics to describe the rules of the universe to a precision far greater than our intuition.

> The right triangle you'd create based on their radiuses is Phi.

What does that even mean? A triangle is just a number?! Still begging the question what drug you are on.

> If you knew as much as you'd like to think, you could have corrected that.

Correct it to what? I gave you the correct ratio!

> Like, go look at a piano

Read up on musical theory and don't act the way you do if you have no idea what you are talking about...

> Everything else stands

Like... all the other things I debunked, such as you seriously claiming that human DNA is only 3.4 nanometers long (and while so, by your own claim, not even twice as long as wide!), when in reality it is centimeters per strand and ~3 meters total, per cell?

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Weaponized incompetence is a lot easier than trying to understand, huh?

Nice, you figured it out :-)

Are Fibonacci numbers different than the golden ratio? Cuz to me with no discerning eye, I find it convincing enough when they show that curve on like acorns and stuff

Lol

Fibonacci sequence is a group of numbers that start with 0 and 1, and every number after that is the sum of the two numbers before it.

Before I typed a word, yes. We're both here for reasons.

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>... a myth at best, and a lie at worst.

so thankful i'm not the only one. i saw this presented in a nova docu and i couldn't help but notice that all of the examples they used were organic in origin.

earth is the only place that we know of that has organic matter and all organisms on earth are related to each other. so, in the Fibonacci numbers we're likely looking at iteration patterns of DNA controller genes (or another related organic phenomena) which is vastly different from a "universal secret number system."

I got downvoted on r/spaceporn because I replied to someone who said “this galaxy is the Fibonacci sequence.” When I asked how, it made the folks there upset lol. They would Just post the sequence of numbers, which is obviously not an explaination.

Left the fuck outta that sub. Pics are cool, but r/astrophotography is waaaaay better, and less filled with morons

The golden ratio is obtained by dividing a Fibonacci number by its previous number.

As you do this for larger and larger Fibonacci numbers, you get closer and closer to the golden ratio (phi)

As many of the other commenters are saying it is a sequence of numbers where the next number is given by the sum of the previous two numbers starting with 0, 1 (then; 0 + 1 = 1, then 1 + 1 = 2, then 1 + 2 = 3, then 2 + 3 = 5 ...)

You see the number chain occur naturally many places in nature in the development of seeds or leaves in plants, where the number of seeds or leaves in layers occur as fibonacci sequences, e.g. one layer has 3 leaves, the next has 5, next has 8 so on.

On a funny side note, you can also use it to approximate conversion of miles and kilometers, as 2 miles is approximately 3 km, 3 miles is approximately 5 km

I mean, 299,792,458 is kind of a sacred number, as far as we can tell so far.

Except for the Law of Fives.

Hail Eris

I never knew the name of Binet’s formula until now. I thought it was one of the neat things when I derived it from the matrix power form of the sequence.

A five year would have no idea what math equations with parenthesis are

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