Fibonacci y el numero de Oro

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Fibonacci y el numero de Oro

  1. 1. FIBONACCI &THE GOLD NUMBER
  2. 2. Who was Fibonacci?... “The greatest European mathematician of the middle ages“ was born in Pisa, Italy, in 1170 and died in 1250He was known like Leonardo dePisa, Leonardo Pisano orLeonardo Bigollo, but he wasalso called “Fibonacci”(fillius of Bonacci, his father’snickname)
  3. 3. What did Fibonacci?... He was one of the first people to introduce the Hindu-Arabic number system into Europe, the positional system we use today. It’s based on the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 with its decimal point and a symbol for zero (not used till now) For example: two thousand and thirtysixRoman numeral Positional system MMXXXVI 2036 But the most transcendental thing why he was known is by: The Fibonacci numbers
  4. 4. Which are these numbers?...These numbers are a numeric serie made with a simple rule of formation: By definition, the first two Fibonacci numbers are 0 and 1 Each remaining number is the sum of the previous two
  5. 5. Which are these numbers?...These numbers are a numeric serie made with a simple rule of formation: By definition, the first two Fibonacci numbers are 0 and 1 Each remaining number is the sum of the previous two And then, the 15 first terms are… (Of course, there are infinite terms...)
  6. 6. But...why are so special these numbers?...Please!, choose the most aesthetic rectangle between the seven onesbelow… 7 1 6 5 4 2 3
  7. 7. But...why are so special these numbers?... a a b = 1,6180...( ϕ ) bThis rectangle is made using a special ratio between its long and its wide:The Golden Ratio also called φ (phy).At least since the Renaissance, many artists and architects have been usingthis Golden Ratio in their works, believing this proportion to be aestheticallypleasing.
  8. 8. But...why are so special these numbers?...If we divide each term by the number before it, we will find thefollowing numbers: From now onwards, the ratio is nearly constant, and equals…1,6180… The Golden Ratio! (can you believe it?)
  9. 9. The Fibonacci numbers and The Golden RatioMathemathics ArchitectureScience PaintingNature MusicAstronomy Sculpture
  10. 10. Nature The plant branchingOne plant in particular shows the Fibonacci numbers in the number of"growing points" that it has.Suppose that when a plant puts out a new shoot, that shoot has to grow twomonths before it is strong enough to support branching. If it branches everymonth after that at the growing point, we get the picture shown here. 13 8 5 3 2 1 1 Achillea ptarmica (“sneezewort”)
  11. 11. Nature Petals on flowers On many plants, the number of petals is a Fibonacci number:white calla lily Euphorbia Trillium Columbine 1 petal 2 petals 3 petals 5 petals Bloodroot black-eyed susan shasta daisy field daisies 8 petals 13 petals 21 petals 34 petals
  12. 12. Nature Petals on flowers Fuchsia 4 petals… it isn’t a Fibonacci number!
  13. 13. Nature Spirals in the NatureDraw a square, with a size of 1 unitAdd another square below this, with a size of 1 unitAdd another to the left with a size of 2 unitAdd another on top, with a size of 3 unitAdd another to the right, with a size of 5 unitRepeat these operations with 8, 13, 21...Then, draw an spiral, starting from the outer edge to the opposite… 3 5 1 2 1 13 8
  14. 14. Nature Spirals in the Nature Sea shellsSunflower seeds Hurricane Galaxy
  15. 15. Nature Human body Human arm: Golden ratioHuman phalanx: Fibonacci numbers Human ear: Fibonacci spiral
  16. 16. Nature Human bodyYou can find many Golden Ratios in the human body φ=
  17. 17. Science DNA doble helixa a = 1,6180... bb
  18. 18. Architecture Buildings & towers Eiffel tower: Golden ratiothe Parthenon, in the Acropolis in Athens
  19. 19. Arts PaintingThree examples of Gold Ratio: Man of Vitruvio The Mona Lisa Birth of Venus
  20. 20. Cards Credit cards ab
  21. 21. Cards Identity card

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