The Fibonacci numbers by 31MF3W8c

VIEWS: 7 PAGES: 7

									             By Amandine Hegner
                   MS2
                 August 07



                Guiding question:
Who was Fibonacci and how did he change the world?


                   Areas of Focus:
      Global Impact and Approach to Learning




                        1
                         Contents page


Title page ………………………………………………………………………01

Introduction …………………………………………………………………....02

Main Body of Research:

Fibonacci’s life ………………………………………………………………...03

Fibonacci’s names ……………………………………………………………..03

The Fibonacci code ………………………………………………………...04/05

The Fibonacci numbers ………………………………………………………..05

Interpretation of facts ………………………………………………………….05

Conclusion …………………………………………………………………….05

Reflection ……………………………………………………………………..06

Bibliography ………………………………………………………………….06




                                   2
                         Introduction

Leonardo Pisano or Leonardo of Pisa (1170-1250) is better known as Fibonacci.
Fibonacci means “Filius Bonacci”, which means “Son of Bonacci”. He was one
of the most famous mathematicians of the world. Fibonacci invented the
Fibonacci-Code, which is a sequence of numbers, where each number is the sum
of the two previous numbers: 1,1,2,3,5,8,13, …
This sequence is used in many areas of maths and science




Goals in this project:

1. To find out how Fibonacci changed the
   world with his math.

2. To find out who was Fibonacci.
3. To research Fibonacci’s life style.

4. To find out information about
   Fibonacci’s childhood.



How am I going to achieve my goals?

I am going to achieve my goals by:

   1. Searching in different resources, for    A statue of Fibonacci in Pisa
   example the internet, interview people,
   read books, etc.
   2. Working at home and in the school




                                         3
                         Fibonacci’s life



Fibonacci’s Childhood:

Leonardo was born between 1170 and 1180 in Pisa, Italy. His father Guglielmo
nicknamed Bonacci (“good natured”) was a secretary of Pisa and had a
diplomatic post in North Africa, his mother Alessandra Larracocci died when he
was nine.
He followed his father to North Africa when he was a teenager, there he learned
arithmetic.



                                                                 Roman Numerals
                                                                    I   =1
                                                                   V    =5
Then he travelled to Egypt, Syria and Greece where he learned      X    = 10
the Hindu-Arabian way of arithmetic (which is today our            L    = 50
arithmetic) and saw that it is higher level, than the North        C    = 100
African way, later on he saw the advantages of the Hindu-          D    = 500
                                                                   M    = 1000
Arabian number system in comparison with the roman system.


His names:

There are many different names of him, for example:

   1. Fibonacci, that means son of Bonacci and Bonacci means “good natured”.
      He was called or nicknamed Fibonacci, because his father was called
      Bonacci
   2. Leonardo of Pisa, he was called like this because his was born in Pisa.
   3. Leonardo Pisano, it’s the Latin way of Leonardo of Pisa. Scientist are not
      sure if he was really called Leonardo Pisano.




                                       4
                   The Fibonacci code

Leonardo of Pisa invented the Fibonacci code. Many people don’t know for
what he used. Fibonacci used the code to solve a difficult text and logic
problem. The original problem he investigated (in the year 1202) was about how
fast rabbits reproduce.

Suppose that a pair of newly-born rabbits, one male and one
female were put in a field. Rabbits are able to reproduce at the
age of one month, so that a female rabbit can produce another
pair of rabbits at the end of the second month. Suppose that
the rabbits never die and that the female always produces
one pair (one female and one male) every month from the
second month on.
Fibonacci’s problem was:
How many pairs of rabbits will there be in one year?

   1. At the end of the first month the mate, but they get no babies, so there is
      still one pair of rabbits.
   2. At the end of the second month the female rabbit gets a new pair of
      rabbits so there are two pairs of rabbits in the field.
   3. At the end of the third month the original female produces a second pair
      of rabbits so there are three pairs in the field, because the second female
      can’t produce yet.
   4. At the end of the fourth month the original female gets a pair of rabbits
      and the second female too so there are five pairs in the field.




                                         5
                                  The Fibonacci numbers



Fibonacci used the Fibonacci code to solve this problem:
                                                                   Month Amount of
                                                                         pairs
1,1,2,3,5,8,13,21,34,55,89,144,
                                                                   1     1
                                                                   2     1
Each number of the Fibonacci sequence is
                                                                   3     2
the sum of the two previous numbers.
                                                                   4     3
                                                                   5     5
The rabbit problem of Fibonacci is not
                                                                   6     8
very realistic, it says that brother and sister mate. It is also
                                                                   7     13
not true that a female gets exactly two rabbits, a female
                                                                   8     21
and a male, but in Fibonacci’s problem it says that we
                                                                   9     34
should suppose.
                                                                   10    55
                                                                   11    89
                                                                   12    144


Interpretation of facts

I think that Leonardo Pisano was a great Mathematician in the middle ages,
because he discovered many things, for example: the Fibonacci code, the golden
ratio, the shell spirals, the golden section and the Fibonacci rectangles.
He learned many things through traveling so if people travel they maybe become
smarter. A big advantage was that Fibonacci learned the Arabic numbers, which
are the present number system.

Conclusion

My guiding question for this project was: Who was Fibonacci and how did he
change the world? My areas of focus were Global impact and Approach to
Learning (ATL). I think that Fibonacci changed the math world quite a lot,
because he invented the Fibonacci code that is today used in many different
areas of science and math. Fibonacci’s text problem shows that the people and
mathematicians in the middle ages were already studying and solving text and
logic problems.




                                            6
Reflection

I learned very much about math, especially about the Fibonacci code and the
golden ratio. I did not really understand the golden ration, golden section and the
shell spiral, that’s why I didn’t write about them. I looked at a video on you tube
that helped me to understand it but it was not clear enough. Next time I would
write more in my Interpretation of facts.

I learned…

….to concentrate on a mathematician

…. the Fibonacci code

….for what Fibonacci used the Fibonacci code

….very much about his childhood


Bibliography

My Pictures:
  1. lahabra.seniorhigh.net/.../MmiddleAges.html
  2. faculty.evansville.edu/ck6/bstud/fibo.html
  3. www.sfusd.k12.ca.us/.../ScienceMath/Math.html
  4. blog.ewanscorner.com/archives/2005/03/rabbits.php
  5. www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
My information:
  1. www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
  2. www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/fibonacci2.html
  3. milan.milanovic.org/math/english/leonardo/leonardo.html
  4. www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibBio.html
  5. perso.orange.fr/bernard.langellier/english/fibonacci.html
  6. www.traderslog.com/biography-and-fibonacci.htm




1018 Words




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