descr

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. 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 thirtysix
Roman numeral Positional system
MMXXXVI 2036
But the most transcendental thing why he was known is by:
The Fibonacci numbers

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

7. But...why are so special these
numbers?...
a
a
b = 1,6180...( ϕ )
b
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.

8. But...why are so special these
numbers?...
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…
1,6180… The Golden Ratio! (can you believe it?)

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

10. Nature The plant branching
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.
13
8
5
3
2
1
1
Achillea ptarmica (“sneezewort”)

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

13. Nature Spirals in the Nature
Draw a square, with a size of 1 unit
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...
Then, draw an spiral, starting from the outer edge to the opposite…
3
5
1
2
1
13
8

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

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

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

17. Science DNA doble helix
a a
= 1,6180...
b
b

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

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

20. Cards Credit cards
a
b

21. Cards Identity card