Fibonacci
Numbers in Matlab
The first two Fibonacci
numbers are 0 and 1, and each remaining
number
is the sum of the
previous two. Some sources neglect the initial
0, and
instead beginning the sequence with the first two ones.
The
Fibonnacci numbers are also known as the Fibonacci series. Two consecutive
numbers in this series are in a 'Golden
Ratio'.
In mathematics and arts, two quantities are in the golden ratio if the
ratio of the sum of the quantities to the larger quantity equals the
ratio of the larger quantity to the smaller one.
The golden ratio is an
irrational constant, approximately 1.618033988. We're designing below a
simple function to see how it appears...
The command 'num2string'
changes a number into a string, so that it can be included in another
string. The command 'num2str(golden_ratio, 10)'
shows the number 'golden_ratio'
with 9 digits after the decimal point.
The simple code is here:
%Clear
screen and memory
clear;
clc; format compact
%
Initialize the first two values
f(1) =
1;
f(2) =
1;
%
Create the first 30 Fibonacci numbers
for i = 3 :
30
% Perform the sum of terms
accordingly
f(i) = f(i1) + f(i2);
% Calculate and display the
ratio of 2 consecutive elements % of the series
golden_ratio = f(i)/f(i1);
str
= [num2str(f(i)) ' '
num2str(f(i1)) '
' ...
num2str(golden_ratio, 10)];
disp(str)
end
Each line
shows three elements: a number in the series, its predecessor and the
quotient of the first number divided by the second. The results in
Matlab are here:
2 1 2
3 2 1.5
5 3
1.666666667
8 5 1.6
13 8
1.625
21 13
1.615384615
34 21
1.619047619
55 34
1.617647059
89 55
1.618181818
144 89
1.617977528
233 144
1.618055556
377 233
1.618025751
610 377
1.618037135
987 610
1.618032787
1597 987
1.618034448
2584
1597 1.618033813
4181
2584 1.618034056
6765
4181 1.618033963
10946
6765 1.618033999
17711
10946 1.618033985
28657
17711 1.61803399
46368
28657 1.618033988
75025
46368 1.618033989
121393
75025 1.618033989
196418
121393 1.618033989
317811
196418 1.618033989
514229
317811 1.618033989
832040
514229 1.618033989
You can see that, in
fact, the quotient
of two consecutive numbers reaches the 'golden ratio' after just a few
numbers in the series.
From
'Fibonacci Numbers'
to home
From
'Fibonacci Numbers' to 'Matlab programming' Menu
