| Definition: The Fibonacci sequence is defined as follows: F_1=1 , F_2=1 , F_3=F_1+F_2 , ..., F_n=F_{n-2}+F_{n-1} , ... . |
| Regulation: The ratio of pairs of consecutive Fibonacci numbers -> Golden Section, i.e. \mathop {\lim }\limits_{n \to \infty } \frac{{{F_{n - 1}}}}{{{F_n}}} = Golden Section. Fact: The Golden Section is the length of any diagonal of a regular pentagon with side=1. |
| See, Hear & Do All the Steps Mathcast by D. Novak | |
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Fibonacci Sequence and Pentagons - InterActivity Directions for interactivity
1. In column A of the spreadsheet, create the first 10 elements of the Fibonacci sequence: A1=1 , A2=1 , A3=A1+A2 , ..., A10=A8+A9 .
2. In column B of the spreadsheet, create the first 9 elements of the Fibonacci ratios: B1=A2/A1 , B2=A3/A2 , ..., B9=A10/A9 .
Notice that the numbers in column B -> 1.62 = Golden Section
3. To create a regular pentagon, click on  , and then on (0,0) and (1,0) and in the dialog box, erase 4 and type in 5 and hit Enter.
4. To create a diagonal, click on  , and then on any two vertices of the pentagon.
Notice that the "length of diagonal f " = Golden Section.
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L.Stojanovska and D.Novak
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