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The table below shows how the ratios of the successive numbers in the
Fibonacci series quickly converge on Phi or Ø, which to the first 15 places is:
1.618033988749895 . . .
After the 40th number in the series, the ratio is accurate to 15 decimal
places.
| Sequence in the series |
Resulting Fibonacci number (the sum of the two numbers before it) |
Ratio of each number to the one before it (this estimates phi or Ø) |
Difference from Ø |
|
0 |
0 |
|
|
| 1 |
1 |
|
|
| 2 |
1 |
1.000000000000000 |
+0.618033988749895 |
| 3 |
2 |
2.000000000000000 |
-0.381966011250105 |
| 4 |
3 |
1.500000000000000 |
+0.118033988749895 |
| 5 |
5 |
1.666666666666667 |
-0.048632677916772 |
| 6 |
8 |
1.600000000000000 |
+0.018033988749895 |
| 7 |
13 |
1.625000000000000 |
-0.006966011250105 |
| 8 |
21 |
1.615384615384615 |
+0.002649373365279 |
| 9 |
34 |
1.619047619047619 |
-0.001013630297724 |
| 10 |
55 |
1.617647058823529 |
+0.000386929926365 |
| 11 |
89 |
1.618181818181818 |
-0.000147829431923 |
| 12 |
144 |
1.617977528089888 |
+0.000056460660007 |
| 13 |
233 |
1.618055555555556 |
-0.000021566805661 |
| 14 |
377 |
1.618025751072961 |
+0.000008237676933 |
| 15 |
610 |
1.618037135278515 |
-0.000003146528620 |
| 16 |
987 |
1.618032786885246 |
+0.000001201864649 |
| 17 |
1,597 |
1.618034447821682 |
-0.000000459071787 |
| 18 |
2,584 |
1.618033813400125 |
+0.000000175349770 |
| 19 |
4,181 |
1.618034055727554 |
-0.000000066977659 |
| 20 |
6,765 |
1.618033963166707 |
+0.000000025583188 |
| 21 |
10,946 |
1.618033998521803 |
-0.000000009771909 |
| 22 |
17,711 |
1.618033985017358 |
+0.000000003732537 |
| 23 |
28,657 |
1.618033990175597 |
-0.000000001425702 |
| 24 |
46,368 |
1.618033988205325 |
+0.000000000544570 |
| 25 |
75,025 |
1.618033988957902 |
-0.000000000208007 |
| 26 |
121,393 |
1.618033988670443 |
+0.000000000079452 |
| 27 |
196,418 |
1.618033988780243 |
-0.000000000030348 |
| 28 |
317,811 |
1.618033988738303 |
+0.000000000011592 |
| 29 |
514,229 |
1.618033988754323 |
-0.000000000004428 |
| 30 |
832,040 |
1.618033988748204 |
+0.000000000001691 |
| 31 |
1,346,269 |
1.618033988750541 |
-0.000000000000646 |
| 32 |
2,178,309 |
1.618033988749648 |
+0.000000000000247 |
| 33 |
3,524,578 |
1.618033988749989 |
-0.000000000000094 |
| 34 |
5,702,887 |
1.618033988749859 |
+0.000000000000036 |
| 35 |
9,227,465 |
1.618033988749909 |
-0.000000000000014 |
| 36 |
14,930,352 |
1.618033988749890 |
+0.000000000000005 |
| 37 |
24,157,817 |
1.618033988749897 |
-0.000000000000002 |
| 38 |
39,088,169 |
1.618033988749894 |
+0.000000000000001 |
| 39 |
63,245,986 |
1.618033988749895 |
-0.000000000000000 |
| 40 |
102,334,155 |
1.618033988749895 |
+0.000000000000000 |
Return to Mysteries of the Fibonacci Number
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