| 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. |
| Attach:Fib2.mp4 | |
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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 quotient sequence: B1=A2/A1, B2=A3/A2, ..., B9=A10/A9
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Related topics:
L.Stojanovska and D.Novak
 Up one level
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