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INTRODUCTION:

If you have a line segment, there are an infinite number of ways you can divide the segment into two parts, but there is only one way to divide it such that it has the following property:

This concept is known as the golden ratio and is defined as follows:

The above information was obtained at the following Web Site:

http://en. w ik iped ia.o r g/ w ik i/ Go lde n_ rat io

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Additional information on the subject may be found at the following sites:

http://ww w. ma t hs is fun.co m/ numbers / go lde n- ra t io. ht m l http://www.youtube.com/watch?v=5zosU6XTgSY (Khan Academy)

The Fibonacci sequence of integers was introduced to the Western world by Leonardo Fibonacci in his Liber Abaci. If you begin with the integers 0 and 1, each successive integer in the series is obtained by adding the previous two, to obtain the following:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...

What is the relationship between the Fibonacci numbers and the golden ratio? The ratio of the last two Fibonacci integers calculated converges to the golden ratio.

Additional information may be found at the following:

http://ww w.ted. co m/ ta lk s/a rt hur_b e nja m in_t he_ ma gic_o f_ fibo nacc i_ number s. ht m l http:// mat hwor ld.wo l fra m.co m/F ibo nac c iN umber. ht ml
http://www. yo utub e.co m/wa tc h? v=kkGeOWYOFoA
http://www. yo utub e.co m/wa tc h? v=Az fHb ETDbN8

Fibonacci in music?

http://ww w. yo ut ub e.co m/wa tc h? v=wS7C ZIJ V xFY

PROBLEM TO SOLVE:

Given a specified “distance” from the golden ratio, determine how many Fibonacci numbers must be generated in order to get this close. Note that there are no units involved; the “distance” is the absolute value of the difference between two numbers of data type Double. To do this you will need to implement a loop.

First complete the FibGenerator program.

After completing the FibGenerator program, make a Lab4 folder in your CS account; copy the completed FibGenerator program into your Lab4 folder.

Recall that the project should have been named GoldenRatio. The source code file name should have been named GoldenRatio.vb. Make sure that the form has been named GoldenRatioForm.

Now make the changes needed to convert the FibGenerator program to the program to solve the Lab4 problem.

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Here are a few hints to help you get started:

  1. For this project you need to declare only one constant:
    Const GOLDEN_RATIO As Double = 1.6180339887

  2. To generate an unspecified number of Fibonacci integers, you need to declare only three variables. Just remember to store each new number in a String variable before calculating the next number; this should have been implemented in the FibGenerator program.

  3. The difference between the current ratio of the last two fibs and the golden ratio must be unsigned. To do this use the absolute value function as follows:

    diff = Math.Abs(GOLDEN_RATIO - ratio)

  4. After exiting the loop, display the fib numbers generated to the user in a multiline TextBox; set both the ReadOnly and Multiline properties to True.

  5. To determine how many Fibonacci numbers were generated you can set up a loop counter.

  6. The concept of a Boolean flag is useful to help you understand how the loop is operating. You can add the flag to the Watch Window.

  7. Note that, if needed, you can implement decision making within the body of the loop. This is known as “nesting” selection statements within a repetition statement. 

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