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Fibonacci sequence code python7/30/2023 It also checks the two match, as they always should.Īfter checking that n is > 2 we declare variables to hold the previous two terms of the sequence, and the current term as calculated sequentially and using Binet's formula. It does this using two methods, the conventional way of adding the two previous terms and also using Binet's Formula. The print_fibonacci_to function calculates and prints the values of the Fibonacci Sequence up to and including the given term n. Print(" N") # Set previous two terms ready for nect iteration Using both addition of the previous two terms andį_n_Binet = 0 # print heading and first two hard-coded terms Prints the Fibonacci Sequence to the given term We can now move on to the second and last function in binetsformula.py. Using √5 will force Python to evaluate the formula as a real number so the whole expression is cast to an integer using the int function. The next line is Binet's Formula itself, the result of which is assigned to the variable F_n - if you examine it carefully you can see it matches the formula in the form. The formula uses √5 no less than three times so I have assigned it to a separate variable, both for efficiency and to make the code slightly more concise. """ # pre-calculate sqrt(5) as we use it 3 timesį_n = int((( (1 + sqrt5) ** n - (1 - sqrt5) ** n ) / ( 2 ** n * sqrt5 )))Īfter importing math for its sqrt and pow functions we have the function which actually implements Binet's Formula to calculate the value of the Fibonacci Sequence for the given term n. The central function implementing Binet's Formula Open binetsformula.py and type or copy/paste this code. You can also download the source code as a zip or clone/download from Github if you prefer. Create a new folder somewhere convenient and within it create the following empty files. This project will consist on two Python files, one containing functions implementing Binet's Formula and the other containing a short piece of code to demonstrate them. Which can be represented in a way more useful for implementation in a programming language as You are probably familiar with the Fibonacci sequence and it's application to the hypothetical breeding habits of rabbits, but you may wish to brush up on the subject by reading the relevant Wikipedia article, as well as the article on Binet and his formula.įibonacci number Jacques Philippe Marie Binet This short project is an implementation of that formula in Python. You can calculate the Fibonacci Sequence by starting with 0 and 1 and adding the previous two numbers, but Binet's Formula can be used to directly calculate any term of the sequence.
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