## Sunday, November 2, 2014

### Preparation for Fibonacci Day - Fibonacci Rabbits

Leonardo of Pisa (or Leonardo Fibonacci – the term Fibonacci means “son of Bonacci”) was born around 1170 into the Bonacci family in Pisa.  He worked in his family business and spent a lot of time in North Africa trading.  While there he learned from the North African about their number system and methods of performing calculations.  He found their mathematics was much simpler than the mathematics he learned and used in Pisa.
He later wrote a book called “Liber Abaci” that showed how to use these Hindu-Arabic numerals and to perform calculations with them.  (This book is the reason you are not doing math with Roman numerals.)
In his book he described a mathematical problem about a man who was starting a business raising rabbits.
“A man put a pair of rabbits (a male and a female) in a garden that was enclosed. How many pairs of rabbits can be produced from the original pair within 12 months, if it is assumed that every months each pair of rabbits produce another pair (a male and a female) in which they become productive in the second month and no death, no escape of the rabbits and all female rabbits must reproduced during this period (year)?"
So in the first month you get a pair (male and female) of baby rabbits and put them in your enclosed garden.  In the second month you still have 1 pair of rabbits because they are not old enough to reproduce.  In the third month you have the same pair of rabbits, but they have also had a pair of babies – for a total of 2 pairs.  In the 4th month you have the original pair of rabbits, their first pair of babies, and a second pair of babies from the original pair – for a total of 3 pairs.  The original pair continues to have pairs of babies each month, and as the pairs of babies become two months old they begin to have pairs of babies also.  The diagram below illustrates this process for the first 5 months.
Notice the pattern of numbers produced, counting the numbers of pairs of rabbits, month by month.
Mathematicians became interested in this problem and noticed that there was a pattern for these numbers.  After the first and second months (both showed 1 pair of rabbits), the next number could be obtained by adding the two previous numbers.  The third number would be 1 + 1 = 2.  The fourth number would be 1 + 2 = 3.  And so forth.  These mathematicians called this sequence the Fibonacci sequence (though I think it should have been called the Rabbit Sequence).  They also began to prefer the name “Fibonacci” instead of Leonardo of Pisa”.
It is unfortunate that this man is more remembered for one math problem involving rabbits than for teach us how to us hindu-arabic numbers (the system we use today.  Personally, I don’t think I could have ever learned long division if I had to use Roman numbers.
1, 1, 2, 3, 5, 8, …
Remember the Fibonacci cheer: “Two, three, five, eight, who do we appreciate?  Fibonacci!”

References:
“The Man of Numbers: Fibonacci’s Arithmetic Revolution”, Keith Devlin
“Fibonacci Numbers and Golden Ratio in Mathematics and Science” – T. O. Omotehinwa and S. O. Ramon

David