Dr. Carrie Wright presented Exploring the Fibonacci Sequence
February 10, 2011
Carrie introduced the history of the Fibonacci Sequence without stating what the sequence is. Participants in groups were given the Fibonacci Rabbits Problem:
Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was...
How many pairs of rabbits will there be in one year?
Participants shared their solutions and their techniques for solving. They then explored three more related problems...
1. How many ways can an elf climb a staircase with n stairs if the elf is able to go up either one or two stairs for each step he takes?
2. Click here to find the Drone Bee Problem.
3. How many ways can a sequence of n numbers be written if only 1's and 2's are allowed?
After dinner, Carrie showed numerous places where the Fibonacci occur in nature...
Carrie then illustrated how we can create the golden spiral using grid paper. Participants follow the diractions & each created the spiral.
Click on any photo below to see a larger image.
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| Carrie Wright introduced the history Leonardo of Pisa who has come to be known as Fibonacci. | Michael Warrick shared his method for organizing the rabbit data and his solution. | Chris Loria shared her table for organizing the rabbit data and her solution. |
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| Carrie illustrated the recursive formula for the "nth" term of the Fibonacci sequence. | Brett Wilmore explained his reasoning in solving a problem. |
