Upcoming SlideShare
×

# Fibonacci gold number

4,261 views

Published on

Presentación acerca de Fibonacci y el número áureo.

8 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total views
4,261
On SlideShare
0
From Embeds
0
Number of Embeds
387
Actions
Shares
0
213
0
Likes
8
Embeds 0
No embeds

No notes for slide

### Fibonacci gold number

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 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. 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. 4. Which are these numbers?... <ul><li>By definition, the first two Fibonacci numbers are 0 and 1 </li></ul>These numbers are a numeric serie made with a simple rule of formation: <ul><li>Each remaining number is the sum of the previous two </li></ul>
5. 5. <ul><li>By definition, the first two Fibonacci numbers are 0 and 1 </li></ul><ul><li>Each remaining number is the sum of the previous two </li></ul><ul><li>And then, the 15 first terms are… </li></ul>Which are these numbers?... These numbers are a numeric serie made with a simple rule of formation: (Of course, there are infinite terms...)
6. 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. 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. 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. 9. The Fibonacci numbers and The Golden Ratio <ul><li>Mathemathics </li></ul><ul><li>Science </li></ul><ul><li>Architecture </li></ul><ul><li>Painting </li></ul><ul><li>Music </li></ul><ul><li>Nature </li></ul><ul><li>Astronomy </li></ul><ul><li>Sculpture </li></ul>
10. 10. One plant in particular shows the Fibonacci numbers in the number of &quot;growing points&quot; 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. 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. 12. Fuchsia 4 petals… it isn’t a Fibonacci number! Nature Petals on flowers
13. 13. 1 1 2 3 5 8 13 <ul><li>Add another square below this, with a size of 1 unit </li></ul><ul><li>Add another to the left with a size of 2 unit </li></ul><ul><li>Add another on top, with a size of 3 unit </li></ul><ul><li>Add another to the right, with a size of 5 unit </li></ul><ul><li>Repeat these operations with 8, 13, 21... </li></ul><ul><li>Draw a square, with a size of 1 unit </li></ul><ul><li>Then, draw an spiral, starting from the outer edge to the opposite… </li></ul>Nature Spirals in the Nature
14. 14. Nature Spirals in the Nature Sunflower seeds Hurricane Galaxy Sea shells
15. 15. Nature Human body Human ear: Fibonacci spiral Human arm: Golden ratio Human phalanx: Fibonacci numbers
16. 16. You can find many Golden Ratios in the human body Nature Human body φ =
17. 17. Science DNA doble helix a b
18. 18. Architecture Buildings & towers Eiffel tower: Golden ratio the Parthenon, in the Acropolis in  Athens
19. 19. <ul><li>Three examples of Gold Ratio: </li></ul><ul><li>Man of Vitruvio </li></ul><ul><li>The Mona Lisa </li></ul><ul><li>Birth of Venus </li></ul>Arts Painting
20. 20. Cards Credit cards a b
21. 21. Cards Identity card