The Fibonacci Sequence

and the Golden Ratio

Leonardo da Pisa – Fibonacci Fibonacci is the greatest European mathematician of the middle ages

Born in 1170 and died in 1240

He introduced the Arabic number system in Europe

Fibonacci Sequence The sequence in which each number is the SUM of the two preceding numbers

+ + + + + + + +++

1 2 3 5 8 13 21 34 55 89 233

1441+

The Fibonacci sequence in nature: Flowers

1 Petal 5 Petals3 Petals

8 Petals 13 Petals

The Fibonacci sequence in nature: Spirals

Nautilus ShellCauliflower

Pine Conehttps://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html

Why do we find the Fibonacci sequence in nature?

Does nature study mathematics?

HurricaneGalaxy

The Golden Ratio

: : ::

55 89 144 233 377

Every number of the Fibonacci sequence divided for the preceding one is always:

1.61801.61801.61801.6180

The Golden Ratio

The Golden Rectangle

The Golden Rectangle: Nature and architecture

Ear Egg

Rose

Parthenon

The Fibonacci Sequence: Music

In an octave there are 13 keys: 8 are white and 5 are black

To sum up

The Fibonacci sequence:A sequence in which every number is the SUM of the preceding two

The Golden Rectangle:A rectangle built according to the Fibonacci sequence

The Golden Ratio:The number you get DIVIDING a number of the Fibonacci sequence for the preceding one:1.6180