Fibonacci

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This is about Fibonacci, a famous mathematician who lived hundreds of years ago. He discovered number patterns in all aspects of nature.

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Fibonacci

  1. 1. Fibonacci Sequence of Numbers Stage 2 Integrated Unit Patterns and Life Cycles in our World
  2. 2. Who was Fibonacci? <ul><li>Born in 1180 in Pisa Italy. </li></ul><ul><li>His father was a diplomat in North Africa. </li></ul><ul><li>Travelled with his father. </li></ul><ul><li>Received instruction in accounting. </li></ul><ul><li>Returned to Pisa in 1200. </li></ul>
  3. 3. <ul><li>He wrote books .It was before printing therefore hand-written. </li></ul><ul><li>He wrote a book on commercial arithmetic. </li></ul><ul><li>He was paid a salary by the city </li></ul><ul><li>for his services to the city. </li></ul><ul><li>He introduced the Hindu-Arabic decimal system into Europe. </li></ul><ul><li>He taught others how to convert between various currencies for trade between countries. </li></ul><ul><li>He died in 1250. </li></ul><ul><li>Statue in Pisa, Italy </li></ul>
  4. 4. This is the Fibonacci Sequence <ul><li>1, 1, 2, 3, 5, 8, 13, 21, ………….. </li></ul><ul><li>Can you work out the pattern? </li></ul><ul><li>What are the next two numbers? </li></ul>
  5. 5. Fibonacci Sequence <ul><li>These numbers are to be found everywhere in nature. </li></ul>
  6. 6. Fibonacci Sequence <ul><li>The Nautilus Shell </li></ul>
  7. 7. Fibonacci Sequence <ul><li>The following diagrams are cross-sections of the Nautilus shell. </li></ul>
  8. 8. Fibonacci Sequence
  9. 9. Fibonacci Sequence
  10. 10. Fibonacci Sequence <ul><li>This plant shows this sequence in the number of growing points it has: </li></ul>
  11. 11. Fibonacci Sequence <ul><li>Petals on Flowers </li></ul><ul><li>Many have the Fibonacci sequence: </li></ul><ul><li>3 petals: lily, iris </li></ul><ul><li>5 petals: buttercups, pansies </li></ul><ul><li>8 petals: delphiniums </li></ul><ul><li>13 petals: cineraria, some daisies </li></ul><ul><li>21 petals: aster </li></ul><ul><li>34 petals: plantain </li></ul><ul><li>55, 89 petals: michaelmas daisies </li></ul>
  12. 12. Fibonacci Sequence <ul><li>Back view: </li></ul><ul><li>3 sepals protect the bud </li></ul><ul><li>5 outer green petals </li></ul><ul><li>5 inner lower of paler green petals. </li></ul><ul><li>Passion fruit flower </li></ul>
  13. 13. Fibonacci Sequence <ul><li>Front view: </li></ul><ul><li>2 sets of 5 green petals are outermost </li></ul><ul><li>Array of purple & white stamens </li></ul><ul><li>In centre are 5 greenish stamens (T-shaped) </li></ul><ul><li>Uppermost in centre are 3 deep brown carpels </li></ul>
  14. 14. Pine Cones <ul><li>Pine cones show the Fibonacci </li></ul><ul><li>Spirals clearly. Here is a picture </li></ul><ul><li>of an ordinary pine cone seen </li></ul><ul><li>from its base where the stalk </li></ul><ul><li>connects it to the tree. </li></ul><ul><li>Can you see the two sets of spirals? </li></ul><ul><li>How many are there in each set? </li></ul><ul><li>Complete the sheet on Pine Cones. </li></ul>
  15. 15. Fibonacci Sequence <ul><li>After looking at pine cones, check out </li></ul><ul><li>cauliflowers, </li></ul><ul><li>broccoli, </li></ul><ul><li>lettuce! </li></ul>
  16. 16. Look at this beautiful sunflower! <ul><li>Can you see the spirals? </li></ul>
  17. 17. Fibonacci Sequence <ul><li>Something to do at home: </li></ul><ul><li>Count the number of florets in the spirals on your cauliflower. The number in one direction and in the other will be Fibonacci numbers. </li></ul><ul><li>Take a closer look at a single floret (this is also has spirals). </li></ul>
  18. 18. Fibonacci Sequence <ul><li>Now look at your own hand: </li></ul><ul><li>You have: </li></ul><ul><li>2 hands, each of which has … </li></ul><ul><li>5 fingers, each of which has … </li></ul><ul><li>3 parts separated by … </li></ul><ul><li>2 knuckles </li></ul><ul><li>Co-incidence?? </li></ul>
  19. 19. Fibonacci Sequence <ul><li>The following spirals are Fibonacci sequences: </li></ul>
  20. 28. This is an interesting video … <ul><li>http://www.youtube.com/watch?v=wS7CZIJVxFY </li></ul><ul><li>Make sure your speakers are turned on. </li></ul>
  21. 29. <ul><li>Fibonacci, a mathematician who lived 800 years ago!!! </li></ul>
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