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The Relation between Fibonacci Sequence and (9, 19, and 29) Numbers

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Abstract

The Fibonacci sequence is a famous equation, because it's have amazing and great properties. In this study, we prove some of the interesting properties which include the relations between Fibonacci numbers and (9, 19, 29). We found a lot of connections and relations between them
International Journal of Computation and Applied Sciences IJOCAAS Vol. 2, Issue 1, FEBRUARY 2017
The Relation between Fibonacci Sequence and (9,
19, and 29) Numbers
Safaa N. Abdul Jabbar, Raid S. Jawad
Abstract: The Fibonacci sequence is a famous equation, because
it's have amazing and great properties. In this study, we prove some
of the interesting properties which include the relations between
Fibonacci numbers and (9, 19, 29). We found a lot of connections
and relations between them.
I INTRODUCTION
The Fibonacci sequence was given its name in May of 1876
by the outstanding French mathematician Francois Edouard
Anatole Lucas, who had originally called it “the series of
Lame,” after the French mathematician Gabriel Lame [1-3]
the applications of both Golden Section, and Fibonacci series
takes a lot of interest in modernistic science, like biology,
demography or economy, and recently used in high-energy
physics, but there exist generalizations of these numbers given
by scientist as Horadam [4-10].
The Fibonacci sequence Fn are
1, 1, 2, 3, 5, 8, 13... 144, 233, 377, . . .
Each number in Fibonacci sequence (as in previous equation)
equals to the sum of the next two Fibonacci numbers. If n is
any positive integer, so Fn is what we use to explain the nth
Fibonacci number, then
Fn = Fn −1 + Fn −2
Because of this sequence Ref. [11] starts with the values:
F0 = 0, and F1 = 1
Fig.1. a. Whirlwind water, B. Galaxy heavenly, c. Tornado, d.
Dust Whirls
On the other hand the ratio of two consecutive Fibonacci
numbers converges to the Golden Mean or Golden Section [
12-15] sin (2_/5)/ sin (_/5) = 1.618.
Figure (1) shows some of the natural phenomena of the energy
giant, which is one of successive applications Fibonacci.
The following table Fibonacci numbers, with dividing the
output of each one of them with the number (19): sequence
Table 1 Fibonacci numbers dividing the output of each one
(19)
dividing by (19) Fibonacci
number
No
0.0
0 1
0.1
1 2
0.1
1 3
0.1
2 4
0.2
3 5
0.3
5 6
0.4
8 7
0.7
13 8
1.1
21 9
1.8
34 10
2.9
55 11
4.7
89 12
7.6
144 13
12.3
233 14
19.8
377 15
32.1
610 16
51.9
987 17
84.1
1597 18
136.0
2584 19
¦
¦ ¦
785808
14930352 37
¦
¦ ¦
55
86267571272
45403984
88
The summation of the first (19) numbers in the Fibonacci
sequence is divisible by the number (19):
(0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + ... + 2584) =
6764
6764 / 19 = 356
The resulting number is (6764), which is a unique feature. It is
equal to: 19 x 4 x 89 = 76 x 89
This number (89) is the number of Fibonacci His status (11)!
It reversed the wonder that is equal to: 1/89 = 0.01123595 ...
Webmasters and password in this inverted it is the only one
Safaa N. Abdul Jabbar is now in the Ministry of Industry, Baghdad,
Iraq.
Dr. Raid S. Jawad is now in Energy and Renewable Energies Tech.
Center, University of Technology, Iraq. E. mail:dr99990@yahoo.com
International Journal of Computation and Applied Sciences IJOCAAS Vol. 2, Issue 1, FEBRUARY 2017
ISSN: 2399-4509
20
that includes in breaking the ten-year consecutive Fibonacci
itself reverse this process and our destination because we
reverse the first (19) a number in the Fibonacci sequence, so
that it becomes the first to be the last and the last is first, here's
the surprise [16-22]
Table 2 Fibonacci sequence and the inverse of it and divided
by 19, part 1
Period Fibo.
sequenc
e
Calcu
lation
Fibo.
inverse
result Divid
ed by
19
1 0 + 2584 2584 136
2 1 - 1597 -1596 -84
3 1 + 987 988 52
4 2 - 610 -608 -32
5 3 + 377 380 20
6 5 - 233 -228 -12
7 8 + 144 152 8
8 13 - 89 -76 -4
9 21 + 55 76 4
10 34 - 34 0 0
11 55 + 21 76 4
12 89 - 13 76 4
13 144 + 8 152 8
14 233 - 5 228 12
15 377 + 3 380 20
16 610 - 2 608 32
17 987 + 1 988 52
18 1597 - 1 1596 84
19 2584 + 0 2584 136
As shown from the Table 2 part 2, if we add no. (1) of the
Fibonacci sequence to the offset by in the inverse sequence,
the came out number is divisible by (19) . Also if this number
rose from the number (2) of corresponding Fibonacci
sequence also the came out number is divisible by (19). Then,
if we add to the third issue in the corresponding successive
reverse, once again came out number is divisible by (19) ...
and so on until we reach the Fibonacci number (19)! It
calculations alternately: time to add and subtract time, which
is never left behind, and achieved only with the number (19)
[23-31]. Also, if the process has all the numbers that follow
ranked number holder (19), found that the calculation between
each number in the Fibonacci sequence and the corresponding
sequence in reverse, the process is always put:
Table 3 Fibonacci sequence and the inverse of it and divided
by 19, part 2
Perio
d
Fibo.i
sequenc
e
Calc
ulati
on
Fibonac
ci
sequenc
e
result Divide
d by
19
19 2584 + 0 2584 136
20 4181 - 1 4180
220
21
6765
- 1 6764
356
22
10946
- 2 10944
576
23
17711
- 3 17708
932
24
28657
- 5 28652
1508
25
46368
-
8 46360
2440
26
75025
-
13 75012 3948
27
121393
-
21 121372
6388
28
196418
-
34 196384
10336
29
317811
-
55 317756
16724
30
514229
-
89 514140
27060
31
832040
-
144 831896
43784
32
1346269
-
233 1346036
70844
33
2178309
-
377 2177932
114628
34
3524578
-
610 3523968
185472
35
5702887
-
987 5701900
300100
36 9227465
-
1597 9225868
485572
37 14930352 -
2584 14927768 785672
38 24157817 -
4181 24153636 1271244
39 39088169 -
6765
39081404 2056916
40 63245986 - 10946
63235040 3328160
Look at how successive changed body and set aside, to be
the location of number (19) directory location, and to suggest
various images that the subject of this number (19) of which is
destined recognition aesthetically surprising!
The aim of this study is to show the relation between
Fibonacci sequence and (9, 19, and 29) numbers, and to prove
that if the plants are a families, the animals and the entire
component in our world as well as the numbers are families.
This work is a part of continuous efforts in the Energy and
Renewable Energies Technology Center to study the nature
and find the best energy motivation for our live [32-55].
International Journal of Computation and Applied Sciences IJOCAAS Vol. 2, Issue 1, FEBRUARY 2017
ISSN: 2399-4509
21
II RESULTS AND DISCUSSION
1. If the first number is divided on the Fibonacci (19) is the
owner of status (19), followed by the number that this
feature is the number of Fibonacci His status (37), which is
between him and the first (19) status exactly? Then the
next is the owner of status (55), which is also the second
(19) status.
2. The sum of the preparation for the first nine successive
preparation of any number from zero to 21 is the number
54 and this number is divisible by 9, and without rest,
54 ÷ 9 = 6
3. The sum of the preparation for the first 18 consecutive
number from zero to the number 1597 is the number 4810
and this number is divisible by 19: 4810 ÷ 19 = 220
The number 18, which refers to the first number is 18 (9 *
2) It is here shown that there is a relationship between the
number 9 and number 19.
4. The number 19 is the same in successive number is
2584divisible by 19: 2584 ÷ 19 = 136
5. The number 29 is the same in successive number is
2584divisible by 29: 317811 ÷ 29 = 10959
6. The total number of successive 29 for the first number
from zero to number 317 811 is a number 832 039 and that
number is divisible by 29,
832039 ÷ 29 = 28691
7. Total prepare for the first 36 consecutive any number from
zero to number 9,227,465 is the number 24,157,816 and
this number is divisible by 19,
24157816 ÷ 19 = 1271464
And the number 36, which refers to the first number is 36
(9 * 4) and this again shows the relationship between the
number 9 and number 19.
Since there is a relationship between the number 18, which
is twice the number 9 and number 19, now we have to
prove a relationship between the
Number 19 and the next in the series after the 18 number
that is 18 +19 = 37,
A number 14,930,352 and this number divisible by on 19
without rest: 14930352 ÷ 19 = 785808.
8. There is also a relationship between the number 37 and the
next in the series after a number 18 or 18 +37 = 55, a
number 86,267,571,272 and this number divisible by on
without the rest of the 19:
86267571272 ÷ 19 = 4540398488
9. It is known that the sum of the numbers 9 +19 +29 = 57
and this number is divisible by 19 without the rest of the
57 ÷ 19 = 3. Now if we take the corresponding numbers in
the sequence of the No. 9 and the two numbers 19 and 29,
a 21 and 2584 and 317 811 does wonder if the sum of
these numbers are accepted multiple of 19 as the
corresponding numbers
21 +2584 + 317811 = 320416 and 320416 ÷ 19 = 16864
To see consistency between successive sequence and
corresponding of how to prepare in harmony with the number
19 in tune bizarre.
10. The sum of the first 19, the result is divisible
(136-84 + 52-32 + 20-12 + 8-4 +4 +0 +4 +4 +8 +12
+20 +32 +52 +84 +136 = 836)
The number 836 is divisible by 19
836 ÷19 = 44
11. When you multiply the following numbers among them
9 * 19 * 29 = 4959
And when collecting the numbers of the last one:
4+9+5+9=27 the number is divisible by 9
27 ÷9=3
And the last divided by the number 19 produces the
following: 4959 ÷ 19 = 261
Also, if we collecting the last numbers we will get:
1 +6 +2 = 9
III CONCLUSION
In this research we found and approved that there is a lot of
relations between the numbers 9, 19, 29, and Fibonacci
sequence and if we search more may be we will find more
than this.
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Emissions," International Journal of Scientific & Engineering Research,
7(3), 80-90, 2016.
... [18,19] term the total of the 2 previous terms, starting with the values F0 = zero, and F1 = 1. On the opposite hand the quantitative relation of 2 consecutive Fibonacci [20,21,22] numbers converges to the Golden [23,24] mean, or proportionality [25,26] sin (2_/5)/ sin (1/5) = 1.618.The classical Fibonacci numbers [27,28] have been very used in as different sciences [29][30][31][32][33][34] (11) (19), also if this number rose from the number (2) of corresponding Fibonacci sequence also the came out number is divisible by (19). Then, if we add to the third issue in the corresponding successive reverse, once again came out number is divisible by (19) ... and so on until we reach the Fibonacci number (19)! ...
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