Fibonacci Sequence

Open a new Excel Workbook.

The aim of this lesson is to investigate the Fibonacci sequence and attempt to answer a few questions about it.
You should be able to get all your work onto one side of A4 to print off as a record of your work.
Show your teacher your work before sending it to the printer.

The Fibonacci sequence is given by (0),1,1,2,3,5,8,13,...

The next term is generated by adding together the previous two terms.

Generate the sequence down the left hand column of the spreadsheet.
Enter the first two 1's and then enter a formula which you can copy down the column.

You can generate about 40 terms before the computer is unable to cope with the precision required.
You might need to widen the column.

To copy down the column you must select the cell. To do this you just left click on it. Then grab the bottom right hand corner of the cell with a left mouse click and drag down the page.

Now find the ratio of the new term to the previous one. Do this in the second column by dividing the value in the cell to the left by that in the cell above it.

Then copy down the column.

You need to increase the number of decimal places visible.
Do this by clicking on the top of the B column and selecting the format menu.
Select the cells option and then the number tab.
There is no point in going beyond 15 decimal places. Why?

Challenge Questions

Draw two graphs of your results to show how the numbers behave.

What is the final value of your ratio?

This ratio has a proper name. Use the Internet to find it. What is it called?

Which simple polygon is associated with this shape? Illustrate your answer.

Which buildings were designed using this ratio? Illustrate your answer.

Can this ratio be calculated in other ways? Devise a spreadsheet to demonstrate this.