Successfully reported this slideshow.
NATURE BY NUMBERS
Created by Gerda Šidlauskytė
CONTENT
Rabbits and Bees Family Trees
Fibonacci Numbers and the Golden Number
Fibonacci Numbers and Plants
Always Fibonacc...
RABBITS AND BEES FAMILY
TREES
FIBONACCI’S RABBITS
 A newly-born pair of rabbits in a field
 Our rabbits never die
 The female always produces one new...
FIBONACCI’S RABBITS
FIBONACCI SEQUENCE
 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
 f(1) = 1
 f(2) = 1
 f(n) = f(n−1) + f(n−2) if n > 2
HONEYBEES
 One special female called the queen.
 Many female worker bees but they produce no
eggs.
 Male drone bees do ...
HONEYBEE’S FAMILY TREES
FIBONACCI NUMBERS AND
THE GOLDEN NUMBER
FIBONACCI RECTANGLES
THE EQUIANGULAR SPIRAL
THE GOLDEN NUMBER
618.1
)1(
)(
lim ≈=
−∞→
Phi
iF
iF
i
618.0
)(
)1(
lim −≈−=
−
∞→
phi
iF
iF
i
FIBONACCI NUMBERS AND
PLANTS
PETALS ON FLOWERS
3 petals: lily, iris
PETALS ON FLOWERS
5 petals: buttercup, wild rose, larkspur, columbine
(aquilegia), pinks
PETALS ON FLOWERS
8 petals: delphiniums
PETALS ON FLOWERS
13 petals: ragwort, corn marigold, cineraria, some
daisies, black-eyed susan
PETALS ON FLOWERS
21 petals: aster, chicory
PETALS ON FLOWERS
34 petals: plantain, pyrethrum
PETALS ON FLOWERS
55, 89 petals: michaelmas daisies, the asteraceae family.
SEED HEADS
SEED HEADS
PINE CONE
VEGETABLES
LEAF ARRANGEMENTS
ALWAYS FIBONACCI?
FIBONACCI FINGERS?
 2 hands
 5 fingers
 3 parts
 2 knuckles
ALWAYS FIBONACCI?
LUCAS NUMBERS
 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521,
843 ...
 f(1) = 2
 f(2) = 1
 f(n) = f(n−1) + f(n...
YOUR QUESTIONS ARE
WELCOME
Upcoming SlideShare
Loading in …5
×

Mathematics in nature

1,910 views

Published on

Published in: Education, Technology, Business
  • Be the first to comment

Mathematics in nature

  1. 1. NATURE BY NUMBERS Created by Gerda Šidlauskytė
  2. 2. CONTENT Rabbits and Bees Family Trees Fibonacci Numbers and the Golden Number Fibonacci Numbers and Plants Always Fibonacci?
  3. 3. RABBITS AND BEES FAMILY TREES
  4. 4. FIBONACCI’S RABBITS  A newly-born pair of rabbits in a field  Our rabbits never die  The female always produces one new pair (one male, one female) every month from the second month on  How many pairs will there be in one year?
  5. 5. FIBONACCI’S RABBITS
  6. 6. FIBONACCI SEQUENCE  1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...  f(1) = 1  f(2) = 1  f(n) = f(n−1) + f(n−2) if n > 2
  7. 7. HONEYBEES  One special female called the queen.  Many female worker bees but they produce no eggs.  Male drone bees do no work.  Females have two parents.  Male bees only have a mother but no father!
  8. 8. HONEYBEE’S FAMILY TREES
  9. 9. FIBONACCI NUMBERS AND THE GOLDEN NUMBER
  10. 10. FIBONACCI RECTANGLES
  11. 11. THE EQUIANGULAR SPIRAL
  12. 12. THE GOLDEN NUMBER 618.1 )1( )( lim ≈= −∞→ Phi iF iF i 618.0 )( )1( lim −≈−= − ∞→ phi iF iF i
  13. 13. FIBONACCI NUMBERS AND PLANTS
  14. 14. PETALS ON FLOWERS 3 petals: lily, iris
  15. 15. PETALS ON FLOWERS 5 petals: buttercup, wild rose, larkspur, columbine (aquilegia), pinks
  16. 16. PETALS ON FLOWERS 8 petals: delphiniums
  17. 17. PETALS ON FLOWERS 13 petals: ragwort, corn marigold, cineraria, some daisies, black-eyed susan
  18. 18. PETALS ON FLOWERS 21 petals: aster, chicory
  19. 19. PETALS ON FLOWERS 34 petals: plantain, pyrethrum
  20. 20. PETALS ON FLOWERS 55, 89 petals: michaelmas daisies, the asteraceae family.
  21. 21. SEED HEADS
  22. 22. SEED HEADS
  23. 23. PINE CONE
  24. 24. VEGETABLES
  25. 25. LEAF ARRANGEMENTS
  26. 26. ALWAYS FIBONACCI?
  27. 27. FIBONACCI FINGERS?  2 hands  5 fingers  3 parts  2 knuckles
  28. 28. ALWAYS FIBONACCI?
  29. 29. LUCAS NUMBERS  2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843 ...  f(1) = 2  f(2) = 1  f(n) = f(n−1) + f(n−2) if n > 2  618.1 )1( )( lim ≈= −∞→ Phi iF iF i
  30. 30. YOUR QUESTIONS ARE WELCOME

×