Fibonacci sequence - DOC by wanghonghx


									Fibonacci sequence

The Fibonacci Sequence is a series of numbers where each consecutive number is
equal to the total of the previous two. It begins with the numbers 0, 1. When these
numbers are added the answer is again 1, so the sequence becomes 0, 1, 1. This
process is repeated and the sequence becomes 0, 1, 1, 2, 3, 5, 8, 13 and so on.

Connections have been found between the Fibonacci numbers and aspects of
engineering, architecture, painting and music. They occur regularly within nature
from the petals on a flower to the spirals of a pinecone. Trace back a honeybee’s
family tree and each generation will represent a Fibonacci number. You can even
see what is known as a Fibonacci spiral in the formation of galaxies.

The Discovery the Fibonacci Sequence

Tthe first written record of the Fibonacci Sequence was in the book Liber Abaci,
written by Leonardo of Pisa and published in 1202. The Arabic number system was
not commonly used in Europe at this time and it was noted by Banks that Leonardo
may have acquired his knowledge while studying in North Africa.

Experiences and Outcomes

The Fibonacci Sequence allows gifted and talented students to experience the
seemingly magical properties of numbers. By applying simple equations to this
number sequence students will uncover unexpected connections. Opportunities are
provided to generate and manipulate large numbers, to predict answers and to
locate patterns within and between sequences of numbers.

         Begin with 0, 1. Use the formula of adding the last two numbers in the
          sequence to generate the first 26 numbers in the Fibonacci Sequence.
         For each number in the Fibonacci Sequence, add all the previous Fibonacci
          numbers. Is there a pattern to the results?
         Add alternate Fibonacci numbers starting with 0, 1 and with 1, 2. Compare the
         Create a table to record the following results. Multiply each Fibonacci number
          with the next one in the sequence. Multiply each Fibonacci number with itself.
          Add the squared Fibonacci numbers. Compare the results.
         Create a table or list the first 30 numbers in the Fibonacci Sequence. Use
          different colours to shade the multiples of the Fibonacci numbers 2, 3, 5 and
          8. Does a pattern emerge?

Ideas for Research Projects

Choose one of the research topics below and discover how it relates to the Fibonacci

         The Golden Ratio
         The Lucas Sequence
       Perfect Rectangles
       Fibonacci Spirals
       The Mona Lisa
       Music - Bartok's Dance Suite
       Fibonacci's Rabbit Problem


       Find flowers images on the net that have a Fibonacci number of petals. See
        how many of the Fibonacci numbers you can find, and display your images on
        a page with the number of petals indicated with each flower.
       Count the number of spirals on a pinecone. Do they represent a Fibonacci
       Create ten perfect rectangles using squares the length of Fibonacci numbers.
       Female honeybees have both a mother and a father. Male honeybees have
        only a mother. Create a honeybee family tree to show how the number of
        family members in each generation is always a Fibonacci number.

Extension: When you are finished, find out more about Perfect Numbers.

Read more at Suite101: The Fibonacci Sequence in Gifted Classes: Math Extension Activities For Gifted
and Talented Students | http://primary-school-lesson-

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