Submitted by amsdys t3_127uy9z in explainlikeimfive
jadnich t1_jegnx79 wrote
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.
grrangry t1_jegqqoz wrote
>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
| Fibonacci | Ratio |
|---|---|
| 0 | n/a |
| 1 | div by zero |
| 1 | 1 |
| 2 | 2 |
| 3 | 1.5 |
| 5 | 1.6666666666667 |
| 8 | 1.6 |
| 13 | 1.625 |
| 21 | 1.6153846153846 |
| 34 | 1.6190476190476 |
| 55 | 1.6176470588235 |
| 89 | 1.6181818181818 |
| 144 | 1.6179775280899 |
| 233 | 1.6180555555556 |
| 377 | 1.618025751073 |
| 610 | 1.6180371352785 |
| 987 | 1.6180327868853 |
| 1597 | 1.6180344478217 |
| 2584 | 1.6180338134001 |
| 4181 | 1.6180340557276 |
| 6765 | 1.6180339631667 |
| 10946 | 1.6180339985218 |
| 17711 | 1.6180339850174 |
| 28657 | 1.6180339901756 |
| 46368 | 1.6180339882053 |
| 75025 | 1.6180339889579 |
| 121393 | 1.6180339886704 |
| 196418 | 1.6180339887802 |
| 317811 | 1.6180339887383 |
| 514229 | 1.6180339887543 |
| 832040 | 1.6180339887482 |
| 1346269 | 1.6180339887505 |
| 2178309 | 1.6180339887497 |
| 3524578 | 1.61803398875 |
| 5702887 | 1.6180339887499 |
| 9227465 | 1.6180339887499 |
| 14930352 | 1.6180339887499 |
| 24157817 | 1.6180339887499 |
| 39088169 | 1.6180339887499 |
| 63245986 | 1.6180339887499 |
| 102334155 | 1.6180339887499 |
| 165580141 | 1.6180339887499 |
| 267914296 | 1.6180339887499 |
| 433494437 | 1.6180339887499 |
| 701408733 | 1.6180339887499 |
| 1134903170 | 1.6180339887499 |
| 1836311903 | 1.6180339887499 |
| 2971215073 | 1.6180339887499 |
| 4807526976 | 1.6180339887499 |
| 7778742049 | 1.6180339887499 |
jadnich t1_jegstip wrote
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.
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