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# Fibonacci Sequence 3

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• 1. 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.
• 2. Summary ● Fran: -sunflower -Bibliography -Summary of the book ● Dani: -pineapple -index -Leonardo´s biography ● Alex: -daisy -summary -conclusion
• 3. 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.
• 4. 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
• 5. 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.
• 6. 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.
• 7. 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!
• 8. 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.
• 9. 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.
• 10. 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