Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.



Published on

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

  • Be the first to comment


  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> </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>