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| − | Fibonacci was an Italian mathematician. The Fibonacci numbers are so called because they were made popular by Fibonacci in 1202 A.D in his book Liber Abaci when he posed a puzzle and its solution <sup>[ | + | =Counting Rabbits= |
| + | <p>Fibonacci was an Italian mathematician. The Fibonacci numbers are so called because they were made popular by Fibonacci in 1202 A.D in his book Liber Abaci when he posed a puzzle and its solution <sup>[3]</sup>. No discussion of Fibonacci numbers can be complete without the study of this puzzle.</p><p>The puzzle is to count the number of pairs of rabbits as rabbit population grows.</p> | ||
Make the following assumptions: rabbits never die, a female rabbit always produces a pair of male and female offsprings and it takes one month for a female rabbit to produce a pair of offsprings. We start with 1 pair of rabbits.<br> | Make the following assumptions: rabbits never die, a female rabbit always produces a pair of male and female offsprings and it takes one month for a female rabbit to produce a pair of offsprings. We start with 1 pair of rabbits.<br> | ||
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http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibrab.gif<br> | http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibrab.gif<br> | ||
| − | <i>Fibonacci's Rabbits<sup> | + | <i>Fibonacci's Rabbits<sup>5</sup> </i></center> |
| − | This process continues and the number of pairs of rabbits at the end of each month is:<b><i> 1, 1, 2, 3, 5, 8, 13, …</i></b>. The reader may notice that this is the Fibonacci sequence discussed at the beginning of this paper. | + | This process continues and the number of pairs of rabbits at the end of each month is:<b><i> 1, 1, 2, 3, 5, 8, 13, …</i></b>. The reader may notice that this is the Fibonacci sequence discussed at the beginning of this paper.<br> |
| + | [[Walther MA279 Fall2018 topic1|Back to Home]] | ||
<br><br>[[Category:MA279Fall2018Walther]] | <br><br>[[Category:MA279Fall2018Walther]] | ||
Latest revision as of 16:40, 2 December 2018
Counting Rabbits
Fibonacci was an Italian mathematician. The Fibonacci numbers are so called because they were made popular by Fibonacci in 1202 A.D in his book Liber Abaci when he posed a puzzle and its solution [3]. No discussion of Fibonacci numbers can be complete without the study of this puzzle.
The puzzle is to count the number of pairs of rabbits as rabbit population grows.
Make the following assumptions: rabbits never die, a female rabbit always produces a pair of male and female offsprings and it takes one month for a female rabbit to produce a pair of offsprings. We start with 1 pair of rabbits.
- Suppose a pair of rabbits mate in month 1. Observe that there is 1 pair of rabbits at the end of the 1st month.
- The female rabbit produces a pair of offspring in month 2. Observe that there are now 2 pairs of rabbits at the end of month
- The female rabbit from the original pair produces a new pair of offsprings in month 3. Observe that there are now 3 pairs of rabbits at the end of month
- The female rabbit from the original pair produces a new pair of offsprings in month 5. Also, the female rabbit from the pair of offspring produced at the end of month 2 produces a pair of offsprings as well. There are now 5 pairs of rabbits at the end of month 3.
This process continues and the number of pairs of rabbits at the end of each month is: 1, 1, 2, 3, 5, 8, 13, …. The reader may notice that this is the Fibonacci sequence discussed at the beginning of this paper.
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