Fibonacci was an Italian mathematician born in 1170 who introduced the Hindu-Arabic numeral system to Europe. He is most known for the Fibonacci sequence, where each number is the sum of the previous two, starting with 0 and 1. These numbers appear often in nature, such as the spiral of a nautilus shell or the petals of flowers. The ratios of numbers in the Fibonacci sequence approach the golden ratio, about 1.6, which has been considered aesthetically pleasing, appearing in architecture, art, and the human body.

1. FIBONACCI & THE GOLD NUMBER

2. Who was Fibonacci?... “ The greatest European mathematician of the middle ages“ was born in Pisa, Italy, in 1170 and died in 1250 He was known like Leonardo de Pisa , Leonardo Pisano or Leonardo Bigollo , but he was also called “Fibonacci” (fillius of Bonacci , his father’s nickname)

3. 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) But the most transcendental thing why he was known is by: The Fibonacci numbers Roman numeral Positional system 2036 MMXXXVI For example : two thousand and thirtysix What did Fibonacci?...

4. Which are these numbers?... By definition, the first two Fibonacci numbers are 0 and 1 These numbers are a numeric serie made with a simple rule of formation: Each remaining number is the sum of the previous two

5. 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… Which are these numbers?... These numbers are a numeric serie made with a simple rule of formation: (Of course, there are infinite terms...)

6. 1 3 4 6 7 2 5 Please!, choose the most aesthetic rectangle between the seven ones below… But...why are so special these numbers?...

7. This 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 using this Golden Ratio in their works, believing this proportion to be aesthetically pleasing. But...why are so special these numbers?... a b

8. If we divide each term by the number before it, we will find the following numbers: From now onwards, the ratio is nearly constant, and equals… But...why are so special these numbers?... 1,6180 … The Golden Ratio! (can you believe it?)

9. The Fibonacci numbers and The Golden Ratio Mathemathics Science Architecture Painting Music Nature Astronomy Sculpture

10. One 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 two months before it is strong enough to support branching. If it branches every month after that at the growing point, we get the picture shown here. Nature The plant branching 1 1 2 3 5 8 13 Achillea ptarmica (“sneezewort”)

11. On many plants, the number of petals is a Fibonacci number: Nature Petals on flowers white calla lily 1 petal Euphorbia 2 petals Trillium 3 petals Columbine 5 petals Bloodroot 8 petals black-eyed susan 13 petals shasta daisy 21 petals field daisies 34 petals

12. Fuchsia 4 petals… it isn’t a Fibonacci number! Nature Petals on flowers

13. 1 1 2 3 5 8 13 Add another square below this, with a size of 1 unit Add another to the left with a size of 2 unit Add another on top, with a size of 3 unit Add another to the right, with a size of 5 unit Repeat these operations with 8, 13, 21... Draw a square, with a size of 1 unit Then, draw an spiral, starting from the outer edge to the opposite… Nature Spirals in the Nature

14. Nature Spirals in the Nature Sunflower seeds Hurricane Galaxy Sea shells

15. Nature Human body Human ear: Fibonacci spiral Human arm: Golden ratio Human phalanx: Fibonacci numbers

16. You can find many Golden Ratios in the human body Nature Human body φ =

17. Science DNA doble helix a b

18. Architecture Buildings & towers Eiffel tower: Golden ratio the Parthenon, in the Acropolis in Athens

19. Three examples of Gold Ratio: Man of Vitruvio The Mona Lisa Birth of Venus Arts Painting

20. Cards Credit cards a b

21. Cards Identity card