Generally in mathematics, the Fibonacci numbers or Fibonacci sequence
are the numbers in the following integer sequence. i.e
1,1,2,3,5,8,13... or in a more mordern convension it starts from
0,1,1,2,3,5,8,13...
looking at the above sequence, you discover something(using the first sequence):
The sequence is initialized with the starting 1, --> it then adds to nothing or say Zero( which is not seen to get another 1), resulting to {1,1}, which also adds up to get the next element of the sequence (1+1=2), hence we now have a sequence{1,1,2},to get the next element of the sequence, we add (1+2), and thus for every position of the sequence, say (i), the value of the element is {the value of [(i -1)'s value + (i-2)'s value]. As in the above we have
Note: 1 is regarded as the default start value
1 1 2 3 5 8 13 21
1, (1+0=1), (1+1=2), (1+2=3), (2+3=5), (3+5=8), (5+8=13), (8+13=21),...
Now Let's See The Python Code:
# First, we call our Fibonacci function fib, and it takes parameter or argument n.
def fib(n): # writes Fibonacci series up to n
a, b = 0, 1 # a and b are initialized as 1 and 0, respectively
while b < n:
print b,
a, b = b, a+b
# The above code (a,b = b ,a+b), just, re-initializes the values of a and b, before going back to the while loop to check if b is less than n.
looking at the above sequence, you discover something(using the first sequence):
The sequence is initialized with the starting 1, --> it then adds to nothing or say Zero( which is not seen to get another 1), resulting to {1,1}, which also adds up to get the next element of the sequence (1+1=2), hence we now have a sequence{1,1,2},to get the next element of the sequence, we add (1+2), and thus for every position of the sequence, say (i), the value of the element is {the value of [(i -1)'s value + (i-2)'s value]. As in the above we have
Note: 1 is regarded as the default start value
1 1 2 3 5 8 13 21
1, (1+0=1), (1+1=2), (1+2=3), (2+3=5), (3+5=8), (5+8=13), (8+13=21),...
Now Let's See The Python Code:
# First, we call our Fibonacci function fib, and it takes parameter or argument n.
def fib(n): # writes Fibonacci series up to n
a, b = 0, 1 # a and b are initialized as 1 and 0, respectively
while b < n:
print b,
a, b = b, a+b
# The above code (a,b = b ,a+b), just, re-initializes the values of a and b, before going back to the while loop to check if b is less than n.
How to Write the Fibonacci Sequence code in Python.
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