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# The fibonacci sequence and the golden ratio #Scichallenge2017

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#SciChallenge2017
In this presentation I would like to show how important mathematics is. It is shows up in everyday life through nature.
"In order to understand the Universe you must know the language which it is written and that is Mathematics." /Galileo Galilei/

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### The fibonacci sequence and the golden ratio #Scichallenge2017

1. 1. # S C I C H A L L E N G E THE FIBONACCI SEQUENCE AND THE GOLDEN RATIO Created by: Szabó Miléna Dóra
2. 2. # S C I C H A L L E N G E FIBONACCI (Leonardo Pisano) • Fibonacci was an Italian mathematician considered to be „the most talented Western mathematician of the Middle Ages”. • The name he is commonly called, "Fibonacci" is short for "figlio di Bonacci" ("son of Bonacci")
3. 3. # S C I C H A L L E N G E THE FIBONACCI SEQUENCE The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34,55,89,144 ... The rule: The next number is found by adding up the two numbers before it. (n≥2) xn = xn-1 + xn-2
4. 4. # S C I C H A L L E N G E EXPLICIT FORMULA Explicit formula means, a formula that allows direct computation of any term for a sequence. Fibonacci sequence’s explicit formula:
5. 5. # S C I C H A L L E N G E WHERE DOES THE SEQUENCE COME FROM? Fibonacci considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that: • a single newly born pair of rabbits (one male, one female) are put in a field; • rabbits are able to mate at the age of one month so that at the end of it’s second month a female can produce another pair of rabbits; • rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on.
6. 6. THE RABBITS Month 1st 2nd 3rd 4th 5th …th pair 1 1 2 3 5 …
7. 7. # S C I C H A L L E N G E FIBONACCI SPIRAL Click here! It’s moving
8. 8. # S C I C H A L L E N G E IN NATURE Patterns created by the fibonacci sequence can be found throughout nature. In petal patterns:
9. 9. # S C I C H A L L E N G E IN THE SUNFLOWER: IN FRUITS: IN PLANTS: Solar cell inspired by the sunflower:
10. 10. # S C I C H A L L E N G E THE GOLDEN RATIO We find the golden ratio when we divide a line into two parts so that: the whole length divided by the „a” part is also equal to the „a” part divided by the „b” part.
11. 11. # S C I C H A L L E N G E π φ e Phi φ ≈ 1.6180339887498948420 … This irrational number is the Golden ratio. Similarly as the well known π and e. There is a special relationship between the Golden Ratio and the Fibonacci Sequence. When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio. In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation.
12. 12. # S C I C H A L L E N G E PENTAGRAM The golden ratio hidden inside the pentagram. a/b = 1,618... b/c = 1,618... c/d = 1,618...
13. 13. # S C I C H A L L E N G E IN NATURE The golden ratio is also found in nature. • IN SHELLS:
14. 14. # S C I C H A L L E N G E IN GALAXIES:
15. 15. # S C I C H A L L E N G E IN HUMAN BODY Leonardo Da Vinci: Vitruvius de architectura
16. 16. # S C I C H A L L E N G E IN ART Just as the Golden Section is found in the design and beauty of nature, it can also be used to achieve beauty, balance and harmony in art and design. Hokusai: The great wave off Kangawa Edward Burne Jones: The golden stairsLeonardo Da Vinci: Mona Lisa
17. 17. # S C I C H A L L E N G E IN ARCHITECTURE Notre DameTaj Mahal Parthenon
18. 18. # S C I C H A L L E N G E The End Click on the rabbits!