Program 6
Learning Objectives
Learn to implement a while or do-while loop
Increment a counter within a loop
Use a value obtained from the user to signal the end of a loop
Program 6 Assignment
The Fibonacci numbers are a sequence of integers named after the Italian mathematician
Leonardo Fibonacci. The first number, (f0), is defined as 0. The second, (f1), is defined as 1. The
third is the sum of the first two. Each subsequent number in the sequence is the sum of the
previous two. The ratio of two consecutive Fibonacci numbers converges to the golden ratio.
You may refer to the following page in Wikipedia for an explanation of the Fibonacci sequence
and its relation to the golden ratio:
http://en.wikipedia.org/wiki/Fibonacci_number
1. Write a program with three integer variables to represent three sequential Fibonacci
numbers. The first should be initialized to 0, the second initialized to 1 and the third is
the sum of the first two.
2. Declare a counter to keep track of how many Fibonacci numbers have been calculated;
this should be initialized to 3 since the first three are calculated when they are declared.
3. The actual golden ratio is set as a constant at the top of the main method. Note that for
this program only one file is required. It is the file named Fibonacci.java; this class has
all the code including the main method.
4. Prompt the user for a double value which is the maximum allowed difference between the
ratio of the last two Fibonacci numbers calculated and the actual golden ratio.The
program should continue to calculate additional numbers in the sequence until the ratio is
as close to the golden ratio as the user has specified.
5. Write a while OR do-while loop which correctly re-assigns the current Fibonacci
numbers and calculates and displays the next number in the sequence.
o Calculate the ratio of the last two numbers
oDetermine the absolute value of the difference between this ratio and the actual
golden ratio.
oUpdate a counter to keep track of how many Fibonacci numbers have been
calculated.
oThe loop should continue to calculate additional numbers in the sequence until the
absolute value of the (ratio – GOLDEN_RATIO) is less than the difference the
user has chosen. The Math.abs( ) method, with ( ratio – GOLDEN_RATIO) as
the argument of the method, can be used to determine the absolute value.
6. After the loop has terminated, display information similar to the sample output at the
bottom of this assignment.
7. The skeleton code for Fibonacci.java is at the very end of this assignment.
Note: This assignment only requires one class file that contains the main method. You do not
need to create two files for Program 6. You need only create Fibonacci.java, which contains the
main method.
