The
Fibonacci Series is a sequence of numbers first created by Leonardo Fibonacci (fi-bo-na-chee)
in 1202
Sequence of numbers in which 1 appears twice as the first two numbers, and every
subsequent number is the sum of two preceding numbers: 1, 1, 2, 3, 5, 8,
13....and so on. As it continues, the ratio between any number and its successor
approaches the ratio of golden section (1:1.618). the most spectacular examples
of the Fibonacci Series in nature is in the head of the sunflower. Scientists
have measured the number of spirals in the sunflower head. They found, not only
one set of short spirals going clockwise from the centre, but also another set
of longer spirals going anti clockwise.
The Fibonacci Series is as follows 0 , 1 , 1 ,
2 , 3 , 5 , 8 , …
The property of this series is that any given element in the series after the
third element is the sum of its first and second predecessor. For example,
consider 8. Its first and second predecessors are 5 and 3. Therefore, 5 + 3 = 8.
Consider 3. Its first and second predecessors are 2 and 1. 2 + 1 = 3. The
property of Fibonacci series holds.
The following is the algorithm to generate the Fibonacci series up to a given
number of elements.
Algorithm : Fibonacci_Series
Input : n, the number of elements in the series
Output : fibonacci series upto the nth element
Method
a = -1
b = 1
for(i=1 to n in steps of +1 do)
c = a + b
display 'c'
a = b
b = c
end_for
Algorithm ends
Example
Namespace DBExample
Class Program
Private Shared Sub
Main(ByVal
args As String())
Dim i As Integer,
j As Integer
i = -1
j = 1
Dim n As Integer
n = 20
Dim fib As Integer
= 1
While fib <= n
fib = i + j
i = j
j = fib
Console.WriteLine(fib)
End While
Console.Read()
End Sub
End Class
End Namespace
Summary
The above article show how to get Fibonacci Series, hope you will
learn and use this concept as you required.