1. The Fibonacci Sequence It's as easy as 1, 1, 2, 3...

2. What is the Fibonacci Sequence?

The Fibonacci sequence is a series of numbers that follow a unique integer sequence.

3. These numbers generate mathematical patterns that can be found in all aspects of life. 4. The patterns can be seen in everything from the human body to the physiology of plants and animals. 5. How does the Fibonacci Sequence Work?

The Fibonacci sequence is derived from the Fibonacci numbers.The Fibonacci numbers are as follows:

6. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...and so on. 7. These numbers are obtained by adding the two previous numbers in the sequence to obtain the next higher number. 8. Example: 1+1= 2,2+3= 5,5+8= 13... 9. The formula is: Fn = Fn-1 + Fn-2 10. Every third number is even and the difference between each number is .618 with the reciprocal of 1.618. These numbers are know as the golden ratio or golden mean. 11. What is the History of the Fibonacci Sequence?

Theexact origination of theFibonacci sequence is unknown.

12. It is believed that contributions to the theory began in 200 BC by Indian mathematicians whose studies were based on Sanskirt prosody. 13. The sequence was introduced to Western European mathematics in 1202 by Leonardo of Pisa, aka Fibonacci 14. His study of the sequence began with the breeding patterns of rabbits. In which he found rabbit generations duplicated inaccordance with the Fibonacci numbers. 15. Fibonacci in Nature

Patterns created by the Fibonacci sequence can be foundthroughout nature...

16. Fibonacci Sequence in Petal Patterns

The Fibonacci sequence can be seen in most petal patterns.

17. For instance most daisies have 34, 55, or 89 petals. (The 9th, 10th, and 11 thFibonacci numbers) 18. Fibonacci Sequence in Sunflowers

The Fibonacci sequence can be found in a sunflower heads seed arrangement.

19. The arrangement of seed is based upon the golden mean which corresponds to the golden angle of 137.5 degrees. 20. The seeds are arranged in consistent patterns of 137.5 degrees 21. This gives the flower the optimal filling ratio for its seeds. 22. Fibonacci Sequence in Seashells

The Fibonacci numbers directly correspond to the spiral found in seashells.

23. The numbers form what are called Fibonacci rectangles or golden rectangles 24. The rectangles are unique because each rectangle has sides equal to the length of the Fibonacci numbers. 25. Within these rectangles we can create a spiral withcross sections equal to exactly 1.618 (the goldenmean with the corresponding angle of 137.5 degrees 26. Fibonacci Review

What are the Fibonacci numbers and how are they obtained?

27. Where did the study of the sequence begin? 28. Who introduced the numbers to Western European mathematics? 29. What is the golden ratio/golden mean and how is it related to the Fibonacci sequence? 30. Where can the Fibonacci sequence be found? 31. What are some natural phenomena created by using the Fibonacci sequence?