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- 1. The Fibonacci Sequence It's as easy as 1, 1, 2, 3...
- 2. What is the Fibonacci Sequence? <ul><li>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. </li></ul>
- 5. How does the Fibonacci Sequence Work? <ul><li>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.” </li></ul>
- 11. What is the History of the Fibonacci Sequence? <ul><li>The exact origination of the Fibonacci 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 in accordance with the Fibonacci numbers. </li></ul>
- 15. Fibonacci in Nature <ul>Patterns created by the Fibonacci sequence can be found throughout nature... </ul>
- 16. Fibonacci Sequence in Petal Patterns <ul><li>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 th Fibonacci numbers) </li></ul>
- 18. Fibonacci Sequence in Sunflowers <ul><li>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. </li></ul>
- 22. Fibonacci Sequence in Seashells <ul><li>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 with cross sections equal to exactly 1.618 (the “golden mean” with the corresponding angle of 137.5 degrees </li></ul>
- 26. Fibonacci Review <ul><li>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? </li></ul>

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