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grrangry t1_jegqqoz wrote

Reply to comment by jadnich in ELI5-What is the fibonacci sequence? by amsdys

>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
31

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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