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# Mathematics in nature

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### 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.