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Fibonacci and Golden Ratio – Phi


Here’s some facts:

  • Fibonacci number is the sequence of numbers found in nature and naural processes
  • The ratio of two adjacent Fibonacci number becomes closer to 1.618 (phi) as we move higher in the Fibonacci series

Here’s my java program to print first 99 Fibonacci numbers:

public class Fibonaci {

public static void main(String[] args) {
double fib[] = new double[102] ;
fib[0] = 0;
fib[1] = 1;
for (int i=0; i <100 ;i++) {
fib[i+2] = fib[i] + fib[i+1];
}
System.out.println(“Fibonnaci Numbers”);
for (int i=1; i <100 ;i++) {
System.out.println(i+” = “+ fib[i] + ” Ratio=”+fib[i+1]/fib[i]);
}
}

}

And here are the first 99 Fibonacci Numbers and their ratios:

Fibonnaci Numbers
1 = 1.0 Ratio=1.0
2 = 1.0 Ratio=2.0
3 = 2.0 Ratio=1.5
4 = 3.0 Ratio=1.6666666666666667
5 = 5.0 Ratio=1.6
6 = 8.0 Ratio=1.625
7 = 13.0 Ratio=1.6153846153846154
8 = 21.0 Ratio=1.619047619047619
9 = 34.0 Ratio=1.6176470588235294
10 = 55.0 Ratio=1.6181818181818182
11 = 89.0 Ratio=1.6179775280898876
12 = 144.0 Ratio=1.6180555555555556
13 = 233.0 Ratio=1.6180257510729614
14 = 377.0 Ratio=1.6180371352785146
15 = 610.0 Ratio=1.618032786885246
16 = 987.0 Ratio=1.618034447821682
17 = 1597.0 Ratio=1.6180338134001253
18 = 2584.0 Ratio=1.618034055727554
19 = 4181.0 Ratio=1.6180339631667064
20 = 6765.0 Ratio=1.6180339985218033
21 = 10946.0 Ratio=1.618033985017358
22 = 17711.0 Ratio=1.6180339901755971
23 = 28657.0 Ratio=1.618033988205325
24 = 46368.0 Ratio=1.618033988957902
25 = 75025.0 Ratio=1.6180339886704431
26 = 121393.0 Ratio=1.6180339887802426
27 = 196418.0 Ratio=1.618033988738303
28 = 317811.0 Ratio=1.6180339887543225
29 = 514229.0 Ratio=1.6180339887482036
30 = 832040.0 Ratio=1.6180339887505408
31 = 1346269.0 Ratio=1.6180339887496482
32 = 2178309.0 Ratio=1.618033988749989
33 = 3524578.0 Ratio=1.618033988749859
34 = 5702887.0 Ratio=1.6180339887499087
35 = 9227465.0 Ratio=1.6180339887498896
36 = 1.4930352E7 Ratio=1.618033988749897
37 = 2.4157817E7 Ratio=1.618033988749894
38 = 3.9088169E7 Ratio=1.6180339887498951
39 = 6.3245986E7 Ratio=1.6180339887498947
40 = 1.02334155E8 Ratio=1.618033988749895
41 = 1.65580141E8 Ratio=1.618033988749895
42 = 2.67914296E8 Ratio=1.618033988749895
43 = 4.33494437E8 Ratio=1.618033988749895
44 = 7.01408733E8 Ratio=1.618033988749895
45 = 1.13490317E9 Ratio=1.618033988749895
46 = 1.836311903E9 Ratio=1.618033988749895
47 = 2.971215073E9 Ratio=1.618033988749895
48 = 4.807526976E9 Ratio=1.618033988749895
49 = 7.778742049E9 Ratio=1.618033988749895
50 = 1.2586269025E10 Ratio=1.618033988749895
51 = 2.0365011074E10 Ratio=1.618033988749895
52 = 3.2951280099E10 Ratio=1.618033988749895
53 = 5.3316291173E10 Ratio=1.618033988749895
54 = 8.6267571272E10 Ratio=1.618033988749895
55 = 1.39583862445E11 Ratio=1.618033988749895
56 = 2.25851433717E11 Ratio=1.618033988749895
57 = 3.65435296162E11 Ratio=1.618033988749895
58 = 5.91286729879E11 Ratio=1.618033988749895
59 = 9.56722026041E11 Ratio=1.618033988749895
60 = 1.54800875592E12 Ratio=1.618033988749895
61 = 2.504730781961E12 Ratio=1.618033988749895
62 = 4.052739537881E12 Ratio=1.618033988749895
63 = 6.557470319842E12 Ratio=1.618033988749895
64 = 1.0610209857723E13 Ratio=1.618033988749895
65 = 1.7167680177565E13 Ratio=1.618033988749895
66 = 2.7777890035288E13 Ratio=1.618033988749895
67 = 4.4945570212853E13 Ratio=1.618033988749895
68 = 7.2723460248141E13 Ratio=1.618033988749895
69 = 1.17669030460994E14 Ratio=1.618033988749895
70 = 1.90392490709135E14 Ratio=1.618033988749895
71 = 3.08061521170129E14 Ratio=1.618033988749895
72 = 4.98454011879264E14 Ratio=1.618033988749895
73 = 8.06515533049393E14 Ratio=1.618033988749895
74 = 1.304969544928657E15 Ratio=1.618033988749895
75 = 2.11148507797805E15 Ratio=1.618033988749895
76 = 3.416454622906707E15 Ratio=1.618033988749895
77 = 5.527939700884757E15 Ratio=1.618033988749895
78 = 8.944394323791464E15 Ratio=1.6180339887498947
79 = 1.447233402467622E16 Ratio=1.618033988749895
80 = 2.3416728348467684E16 Ratio=1.618033988749895
81 = 3.7889062373143904E16 Ratio=1.6180339887498947
82 = 6.1305790721611584E16 Ratio=1.618033988749895
83 = 9.9194853094755488E16 Ratio=1.618033988749895
84 = 1.60500643816367072E17 Ratio=1.618033988749895
85 = 2.5969549691112256E17 Ratio=1.618033988749895
86 = 4.2019614072748966E17 Ratio=1.618033988749895
87 = 6.7989163763861222E17 Ratio=1.618033988749895
88 = 1.10008777836610189E18 Ratio=1.6180339887498947
89 = 1.77997941600471398E18 Ratio=1.618033988749895
90 = 2.880067194370816E18 Ratio=1.618033988749895
91 = 4.6600466103755305E18 Ratio=1.618033988749895
92 = 7.5401138047463465E18 Ratio=1.618033988749895
93 = 1.2200160415121877E19 Ratio=1.618033988749895
94 = 1.9740274219868226E19 Ratio=1.6180339887498947
95 = 3.19404346349901E19 Ratio=1.618033988749895
96 = 5.168070885485833E19 Ratio=1.618033988749895
97 = 8.362114348984843E19 Ratio=1.618033988749895
98 = 1.3530185234470676E20 Ratio=1.618033988749895
99 = 2.189229958345552E20 Ratio=1.618033988749895

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