NumPy – Fibonacci Series using Binet Formula
Last Updated :
03 Jun, 2020
All of us are familiar with Fibonacci Series. Each number in the sequence is the sum of the two numbers that precede it. So, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34…… In this tutorial, we will implement the same using NumPy with the aid of
Binet formula.
Binet Formula
‘
n’ is the parameter which relates the first
‘n’ numbers of Fibonacci Series. In the first example we are going to findout first 10 numbers of Fibonacci Series (n = 10), after that we takes the parameter ‘n’ from user and produce the corresponding result.
NOTE : We are ignoring the first element(0) of Fibonacci Series
Example 1: To find first 10 Fibonacci numbers .
import numpy as np
a = np.arange( 1 , 11 )
lengthA = len (a)
sqrtFive = np.sqrt( 5 )
alpha = ( 1 + sqrtFive) / 2
beta = ( 1 - sqrtFive) / 2
Fn = np.rint(((alpha * * a) - (beta * * a)) / (sqrtFive))
print ( "The first {} numbers of Fibonacci series are {} . " . format (lengthA, Fn))
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Output :
The first 10 numbers of Fibonacci series are [ 1. 1. 2. 3. 5. 8. 13. 21. 34. 55.] .
Example 2 : To find first ‘n’ Fibonacci numbers ..
import numpy as np
fNumber = int ( input ( "Enter the value of n + 1'th number : " ))
a = np.arange( 1 , fNumber)
length_a = len (a)
sqrt_five = np.sqrt( 5 )
alpha = ( 1 + sqrt_five) / 2
beta = ( 1 - sqrt_five) / 2
Fn = np.rint(((alpha * * a) - (beta * * a)) / (sqrt_five))
print ( "The first {} numbers of Fibonacci series are {} . " . format (length_a, Fn))
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Output :
# Here user input was 10
Enter the value of n+1'th number :10
The first 9 numbers of Fibonacci series are [ 1. 1. 2. 3. 5. 8. 13. 21. 34.] .
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