Independent Study in Music

Math Project 2011

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References –
1) http://www.Math.about.com/od/Mathematicians/a/fibonacci.htm
2) http://www.maths.surrey.ac.uk/hosted-sites/r.knott/fiboncci/fibbio.htm
3) http://www.lifeinitaly.com/heroes-villans/fibonacci.asp
4) http://en.wikipedia.org/wiki/Fibonacci

      Filius Bonacci was the single greatest mathematician of the middle ages. His full name was Leonardo Pisano but most modern authors and people that speak of him call him Fibonacci. He was born in Pisa, Italy approximately 1170 ad and he died in 1250 ad. Fibonacci was born in Italy and obtained his education in North Africa were he learned the Hindu – Arabic Numbering System. He learned this system from merchants and people while he was in North Africa traveling at the age of 32. He used Hindu – Arabic (0-9) symbols instead of roman symbols which didn’t have 0’s and lacked place value.
      Fibonacci brought back what he learned from North Africa to Europe and proved the superiority of using the Hindu – Arabic number system instead of the roman numeral system. He wrote a book called “Liber Abaci” which translates in English “The book of calculation”. The book was about everything he learned from the Mediterranean. His Book became famous because of the rabbit problem that was in his book the question says “A certain man put a pair of rabbits in place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that par in a year if it is supposed that every month each pair begets a new pair, which from the second month on becomes productive?”
      It was that problem that led Fibonacci to invent the Fibonacci sequence which is still used today. The sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… this sequence, shows that each number is the sum of the two preceding numbers. This sequence is used in many different areas of math & science
It is an example of a recursive sequence.

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Fibonacci most famous contributions to the number theory include...