Fibonacci Numbers Using Python

Posted on Tue 03 November 2015 in Python Projects

Introduction

Here, we write a small Python program to obtain a Fibonacci Sequence for a given number, n. In this sequence, every consecutive number is a sum of previous two numbers. That is, the series should have 1, 2, 3, 5, 8, 13, 21, 34, 55 for n = 10. This sequence can continue as the value of n increases. In the Fibonacci Sequence, the ratio between any successive numbers is nearly constant which is equal to a value of 1.618. This ratio is often referred to as the Golden Ratio and bigger the Fibonacci number, closer is the approximation. Detailed mathematical explanation regarding Fibonacci Sequence can be found here.

# Python program to find Fibonacci sequence

"""
Usage: Fibonacci-numbers.py

Generates a Fibonacci sequence up to the given number (n) and
calculates the Golden Ratio

At prompt, enter only numbers

Options
-------

-h or help      Displays this message

"""

from sys import argv, exit

Initially, we have a display message followed by importing the sys module. We then store the value of the first argument that is passed as we would require this for printing the help message.

def fibonacci(n):
    (Fn_1, Fn) = 0, 1
    FibonacciSequence = [Fn_1, Fn]
    goldenRatio = []
    for i in range(n-1):
        (Fn_1, Fn) = Fn, (Fn_1 + Fn)
        FibonacciSequence.append(Fn)
        goldenRatio.append(Fn/float(Fn_1))
return FibonacciSequence, goldenRatio

We now define a function and initialise the first two values in the sequence, that is, Fn-1 and F_n and these are done with a value of 0 and 1 respectively. Note that we do this as a tuple. We further create two lists to store the Fibonacci and golden ratio numbers as we calculate them. The Fibonacci number is evaluated as Fn, (Fn_1 + Fn) for the range of n-1 values within the for loop. The Golden Ratio is simply the ratio between Fn/Fn-1. We finally append both the Fibonacci and golden ratio numbers so that we could display a sequence.

if len(argv) > 1:
    print(__doc__)
    exit(0)

The above checks for any argument given along with the main Python script to display the help messages. In the Ipython Notebook, these three lines have been commented, else Ipython tries to exit and an exception is raised.

while True:
    number = raw_input("Enter the number, n to obtain the Fibonacci Sequence: ")
    try:
        num = int(number)
        if num > 100:
            print "Enter a value less or equal to 100"
            continue
            print "The number you have entered is: %d" % num
            break
    except:
        print "Error: Enter only numbers"
        continue

Enter the number, n to obtain the Fibonacci Sequence: 100
The number you have entered is: 100

With this while loop, we basically ask the user to enter the value of n to obtain the Fibonacci Sequence and subsequently check whether the entered number is a numerical value or a string. If the value happens to be a string, the while loop makes sure the user is repeatedly asked until a numerical value is entered. Also, to note is that a hard limit is set to n = 100, else the Fibonacci number becomes excessively large.

FibonacciSequence, goldenRatio = fibonacci(num)

We now initialise the lists that would be used to store the Fibonacci and golden ratio numbers and the initial values. This is followed by calling the function. Finally, we print the sequence as follows:

print "\nFibonacci Sequence for the value, n = %d\n" % (num)
print FibonacciSequence
print "\nGolden Ratio\n"
print goldenRatio

Fibonacci Sequence for the value, n = 100

[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, 12586269025, 20365011074, 32951280099, 53316291173, 86267571272, 139583862445, 225851433717, 365435296162, 591286729879, 956722026041, 1548008755920, 2504730781961, 4052739537881, 6557470319842, 10610209857723, 17167680177565, 27777890035288, 44945570212853, 72723460248141, 117669030460994, 190392490709135, 308061521170129, 498454011879264, 806515533049393, 1304969544928657, 2111485077978050, 3416454622906707, 5527939700884757, 8944394323791464, 14472334024676221, 23416728348467685, 37889062373143906, 61305790721611591, 99194853094755497, 160500643816367088, 259695496911122585, 420196140727489673, 679891637638612258, 1100087778366101931, 1779979416004714189, 2880067194370816120, 4660046610375530309, 7540113804746346429, 12200160415121876738L, 19740274219868223167L, 31940434634990099905L, 51680708854858323072L, 83621143489848422977L, 135301852344706746049L, 218922995834555169026L, 354224848179261915075L]

Golden Ratio

[1.0, 2.0, 1.5, 1.6666666666666667, 1.6, 1.625, 1.6153846153846154, 1.619047619047619, 1.6176470588235294, 1.6181818181818182, 1.6179775280898876, 1.6180555555555556, 1.6180257510729614, 1.6180371352785146, 1.618032786885246, 1.618034447821682, 1.6180338134001253, 1.618034055727554, 1.6180339631667064, 1.6180339985218033, 1.618033985017358, 1.6180339901755971, 1.618033988205325, 1.618033988957902, 1.6180339886704431, 1.6180339887802426, 1.618033988738303, 1.6180339887543225, 1.6180339887482036, 1.6180339887505408, 1.6180339887496482, 1.618033988749989, 1.618033988749859, 1.6180339887499087, 1.6180339887498896, 1.618033988749897, 1.618033988749894, 1.6180339887498951, 1.6180339887498947, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.6180339887498947, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.6180339887498947, 1.6180339887498947, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.6180339887498947, 1.618033988749895, 1.618033988749895, 1.618033988749895, 1.6180339887498947, 1.6180339887498951, 1.618033988749895, 1.618033988749895, 1.6180339887498947, 1.618033988749895, 1.618033988749895]

python Fibonacci Numbers