How Many Fibonacci Numbers are Required to Accurately Estimate The Golden-Ratio? Fn+1 Fibonacci numbers are formed by adding the two preceding numbers as shown in the series. F = 1, 1, 2, 3, 5, 8, 13 .... The ratio of the Fibonacci number approaches , the Golden-Ratio, for large values of n. In a well-documented Python program, hmwk3Q2.py, implement a program that calculates the F Fibonacci number and forms the ratio which approximates . Inside a while-loop, your program will continue to calculate the next Fibonacci until a specified level of precision in the estimate is achieved, when compared to the exact value for the Golden-Ratio. The Golden-Ratio is 1+ √5 4= Fr Your program should accept and an integer M from the user. M represents the accuracy of the estimate by comparing your estimate with 10-M. That is, if M = 2, then your program should increment n until | – | ≤ 10-² or 0.01. As a comment in your program list the number of Fibonacci terms required to attain accuracy to M = 9. That is 10-⁹. Hints: Inside a while-loop continue to form another Fibonacci number until abs (Faptus - ). -p) <= 10 ** -M.Inside the while-loop F₁ increment n - the number of terms used to compute F. Please note that F₁ = 1, F₂ = 1, F3 = 2, and so forth.
How Many Fibonacci Numbers are Required to Accurately Estimate The Golden-Ratio? Fn+1 Fibonacci numbers are formed by adding the two preceding numbers as shown in the series. F = 1, 1, 2, 3, 5, 8, 13 .... The ratio of the Fibonacci number approaches , the Golden-Ratio, for large values of n. In a well-documented Python program, hmwk3Q2.py, implement a program that calculates the F Fibonacci number and forms the ratio which approximates . Inside a while-loop, your program will continue to calculate the next Fibonacci until a specified level of precision in the estimate is achieved, when compared to the exact value for the Golden-Ratio. The Golden-Ratio is 1+ √5 4= Fr Your program should accept and an integer M from the user. M represents the accuracy of the estimate by comparing your estimate with 10-M. That is, if M = 2, then your program should increment n until | – | ≤ 10-² or 0.01. As a comment in your program list the number of Fibonacci terms required to attain accuracy to M = 9. That is 10-⁹. Hints: Inside a while-loop continue to form another Fibonacci number until abs (Faptus - ). -p) <= 10 ** -M.Inside the while-loop F₁ increment n - the number of terms used to compute F. Please note that F₁ = 1, F₂ = 1, F3 = 2, and so forth.
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Transcribed Image Text:How Many Fibonacci Numbers are Required to Accurately Estimate The Golden-Ratio?
Fr
Fibonacci numbers are formed by adding the two preceding numbers as shown in the series. F=1,1,2,3,5,8,13 .... The
ratio of the Fibonacci number + approaches p, the Golden-Ratio, for large values of n. In a well-documented Python
program, hmwk3Q2.py, implement a program that calculates the F Fibonacci number and forms the ratio which
approximates p. Inside a while-loop, your program will continue to calculate the next Fibonacci until a specified level
of precision in the estimate is achieved, when compared to the exact value for the Golden-Ratio. The Golden-Ratio is
4 =
1+ √5
Your program should accept and an integer M from the user. M represents the accuracy of the estimate by comparing
your estimate with 10-M. That is, if M = 2, then your program should increment n until | - | ≤ 10-² or 0.01. As a
<
Fr
comment in your program list the number of Fibonacci terms required to attain accuracy to M = 9. That is 10-9.
Hints:
(Faptus
Inside a while-loop continue to form another Fibonacci number until abs (Entus - p) <= 10 ** -M. Inside the while-loop
F₁
increment n - the number of terms used to compute F. Please note that F₁ = 1, F₂ = 1, F₂ = 2, and so forth.
Expert Solution
Step 1 ::
- We have to work with the golden ration of fibonacci numbers.
- We have to take the input m which is the precision required from user.
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