Fibonacci Sequence 3

Fibonacci´s Project
IES Sierra de Santa Barbara.
By: Daniel Galván, Red colour; Alejandro Bodeguero, Blue
colour; Francisco Javier Muñoz, Green colour.
English and Mathematics 2ºB.

Summary
● Fran: -sunflower
-Bibliography
-Summary of the book
● Dani: -pineapple
-index
-Leonardo´s biography
● Alex: -daisy
-summary
-conclusion

FIBONACCI'S SEQUENCE IN THE SUNFLOWERS
The sunflowers are beautiful flowers recognised
because of the form in that its yellow heads are
seen against the blue sky.
Nevertheless, Have you ever seen the pattern of
the seeds in the centre of those flowers?
The sunflowers, apart from being beautiful,
contain maths. The pattern of the seeds follows
the fibonacci sequence
(0,1,1,2,3,5,8,13,21,34,55,89,144,233...)
Each number of the sequence is the addition of
the two last numbers.
Los girasoles son hermosas flores reconocidas por la
forma en que sus cabezas amarillas se ven contra el cielo
azul. Y por supuesto, a muchos también les gusta
masticar sus semillas.
Sin embargo, ¿te has detenido a observar el patrón de las
semillas al centro de estas flores?
Los girasoles son, además de una bella imagen o una
maravilla matemática. El patrón de las semillas dentro del
girasol sigue la sucesión de Fibonacci o 1, 2, 3, 5, 8, 13,
21, 34, 55, 89, 144… Cada número de la secuencia es la
suma de los dos números anteriores.
En los girasoles, las espirales que se ven en el centro se
generan a partir de esta secuencia -hay dos series de
curvas sinuosas en direcciones opuestas, comenzando
en el centro y extendiéndose hacia los pétalos, con cada
semilla en un ángulo particular de la vecina para así crear
el espiral.

FIBONACCI´S SEQUENCE IN THE
SUNFLOWERS
In the sunflowers the spirals that we can see in the
centre are generated following this sequence. There
are 2 series of curves in opposite direction, starting
in the centre and spreading out towards petals, with
each seed in a particular angle of the next one for
creating the spiral

Fibonacci`s biography
Leonardo de Pisa, also known as
“Fibonacci”, was born in Pisa, Italy
in the year 1175 and he died in 1240,
He was an Italian mathematician that
spread the knowledge of the
mathematics throughout all the
west, he popularized
the use of the Arabic figures
and exposed the beginning
of the trigonometry and he
discovered a very
important sequence.
Leonardo de Pisa también conocido
como “Fibonacci”, nació en Pisa,
Italia, en el año 1175 y murió en
1240, fué un matemático Italiano
que difundió los conocimientos
matemáticos por todo occidente,
popularizó el uso de las
cifras árabes y expuso los
principios de la
trigonometría, y descubrio
una sucesión muy
importante.

Fibonacci's sequence in the
daisy
There are many types of flowers with these numbers of
petals: 1,2,3,5,8
And the list is endless. Black-eyed Susans have 13
petals, daisies have 21 to 34 petals. Above all we see a
pattern of: 1, 2, 3, 5, 8, 13, 21, 34 and so on. This is a
clear example of the Fibonacci sequence from 1.
However, you can also find the Fibonacci sequence from
13 through an ordinary daisy field. There are daisies with
13, 21, 34, 55 and even 89 petals, which are all
examples of the Fibonacci sequence.
Hay muchos tipos de flores con pétalos:1,2,3,5,8…
Y la lista es interminable. Hay Susans Black-eyed con
13 pétalos, margaritas con 21 y 34 pétalos. En general
vemos un patrón de:1, 2, 3, 5, 8, 13, 21, 34 y así
sucesivamente.Este es un claro ejemplo de la sucesión
de Fibonacci a partir de 1. Sin embargo también se
puede encontrar la secuencia de Fibonacci a partir del
13 en las margaritas. Hay margaritas con 13, 21, 34, 55
y hasta 89 pétalos, que son todos ejemplos de la
secuencia de Fibonacci.

Fibonacci sequence in the daisy
If you draw lines through the flower’s axils, you’ll see that the number of branches up each level represents the
Fibonacci number sequence
The number of leaves up each level, also represents the Fibonacci Sequence!

SUMMARY OF THE BOOK
The town of Chee was famous because there were big green gardens and the Pied Piper
lived there. The people thought that there was all this food thanks to the wizard that
lived at the top of the mountain. One day when they were carrying the food to the
wizard the Pied Piper stopped and said that he wouldn't give more food to the wizard.
That night the wizard got angry and said that the people of Chee would pay for the fib.
The next day a girl called Amanda went to the gardens to take the food and she saw
two little rabbits, on Tuesday she saw that the rabbits were bigger, and on Wednesday
there were the rabbits with two babies. The rabbits grew faster and they had more
sons.The mayor of Chee made a meeting to solve the problem. The Pied Piper tried to
solve it. His idea consisted on playing his flute and the rabbits would follow him.
Amanda saw that the rabbits grew and had sons following a pattern, she told this to the
wizard and he gave her a flute to take the rabbits out.When Amanda played the flute
the rabbits followed her and she solved the problem of the rabbits.

Fibonacci's sequence in the pineapple
Pineapples match with two terms of
the sequence of Fibonacci: 8 and 13;
or 5 and 8. These numbers are the
numbers of the spirals of the
pineapple. The bigger number is
always the number of the spirals to
the left, and the smaller number is
always the number of the spirals
to the right. For example: One
pineapple of medium age has got
8 spirals to the right and 13
spirals to the left.
Coinciden con dos términos de la
sucesión de Fibonacci: 8 y 13; o 5 y
8. Estos números son los números the
espirales que tiene la piña.
Siempre el número más grande es el
número de espirales que tiene la
piña hacía la izquierda, y el número
más pequeño es el número de
espirales que tiene la piña
hacía la derecha. Por ejemplo:
una piña de mediana edad tiene
8 espirales a la derecha y 13
espirales a la izquierda.

We have found information
in:
-Edmodo.
-Teacher´s suggestions.
-Internet.
-The book: Rabbits, Rabbits
Everywhere.
-Dictionary.
Nosotros hemos encontrado
información en:
-Edmodo.
-Consejos de los profesores.
-Internet.
-El libro: Rabbits, rabbits
everywhere.
-Diccionario.
BIBLIOGRAPHY

Fibonacci Sequence 3

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