Fibonacci
www2.edu.fi/.../pics/images/fibonacci.jpg
Leonardo from Pisa, better known as Fibonacci, was a well-known Italian mathematician. He lived from 1170 to 1250.
Fibonacci Sequences (Portfolio 6)
The basic Fibonacci Sequence is:
{1, 1, 2, 3, 5, 8, 13, …}
What is the pattern???
This sequence was found by adding together the previous 2 terms to get the next term.
Any sequence which follows this pattern is considered a Fibonacci sequence.
Example 1:
Determine if each sequence is a Fibonacci sequence. Why or why not? If it is a Fibonacci sequence find the next 3 terms.
a) 1, 2, 3, 4, 5, 6, …
No. This is not a Fibonacci sequence because it is arithmetic (ie, d=+1). 2 +3 = 5 which is not the next term.
b) 0, 3, 3, 6, 9, …
Yes. This is a Fibonacci sequence because 3+3 = 6, 3+ 6 = 9, etc.
Next 3 terms: 6+9 = 15, 9+15 = 24, 15+24 = 39
Example 2:
Create your own Fibonacci sequence with 6 terms starting with the numbers 4 and 7.
{4, 7, 11, 18, 29, 47, …}
Example 3:
The 5th Fibonacci number is 4 and the 6th is 6.
What is the next Fibonacci number?
… 4, 6, …
7th term = 10 (4 +6)
What is the previous Fibonacci number?
…4, 6, 10
4th term = 2 (6 – 4 = 2)
Fibonacci in Nature
http://farm1.static.flickr.com/140/359335040_893d6bf987.jpg http://www.elliottrader.com/webpagina%20afbeeldingen/fibonacci%20zonnebloem.gif
Flowers:
1 petal: white calla lily 2 petal: euphorbia 3 petal: Trillium 5 petal: columbine
8 petal: Bloodroot 13 petal: black-eyed susan
http://images.google.ca
Shells Chameleon Tails
http://www1.istockphoto.com/file_thumbview_approve/2673512/2/istockphoto_2673512_fibonacci_chameleon_tail.jpg
http://taos-telecommunity.org/epow/EPOW-Archive/archive_2003/EPOW-031117_files/chameleon_fibonacci.jpg
Complete Fibonacci Worksheet.