Http mathworld wolfram com goldenratio html

Lab 4 CS 105 Fall 1014

Objectives:

1. Gain an understanding of how to implement a loop.

2. Learn to use a loop counter to determine how many times the loop iterates. 3. Learn to use a variable of String data type.

4. Learn to store and append information in a String variable with the concatenation operator.

5. Learn to use the newline character to format String output.

6. Learn to use a multiline TextBox, with ReadOnly set to True, to display output. 7. Learn to use the absolute value function.

8. Gain an understanding of the Golden Ratio and the Fibonacci Numbers.

DUE DATES:

11 am Section: THURSDAY OCTOBER 30 BY THE END OF LAB

2 pm Section: THURSDAY OCTOBER 31 BY THE END OF LAB

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.wikipedia.org/wiki/Golden_ratio

http://en.wikipedia.org/wiki/Golden_ratio
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Additional information on the subject may be found at the following sites:

http://www.mathsisfun.com/numbers/golden-ratio.html

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://www.ted.com/talks/arthur_benjamin_the_magic_of_fibonacci_numbers.html

http://mathworld.wolfram.com/FibonacciN umber.html

http://www.youtube.com/watch?v=kkGeOWYOFoA

http://www.youtube.com/watch?v=AzfHbETDbN8

Fibonacci in music?

http://www.youtube.com/watch?v=wS7C ZIJVxFY

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.

http://www.mathsisfun.com/numbers/golden-ratio.html
http://www.youtube.com/watch?v=5zosU6XTgSY
http://www.ted.com/talks/arthur_benjamin_the_magic_of_fibonacci_numbers.html
http://mathworld.wolfram.com/FibonacciNumber.html
http://www.youtube.com/watch?v=kkGeOWYOFoA
http://www.youtube.com/watch?v=AzfHbETDbN8
http://www.youtube.com/watch?v=wS7CZIJVxFY
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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.