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 Write-up

Title
Multiplying Rabbits

Problem Statement
A newborn rabbit is capable of reproducing at maturity which is one month old.  If the rabbit never dies and continues reproducing each month is there a sequence that describes the number of members in the rabbit’s family.

Problem setup

Explain how the Fibonacci sequence (1,1,2,3,5,8,13,21,...) describes the number of members in the rabbit's family at each month.

Plans to Solve/Investigate the Problem

The problem page provided a graph depicting the rabbit’s birth month and subsequent birth of additional family members.  The initial step included continuing the graph on paper and using an excel spreadsheet to compare the number of family members to the Fibonacci sequence.

Investigation/Exploration of the Problem

The following example is a graph completed by hand on the reproduction of the rabbit’s family.  The graph completed by hand was also reproduced in excel which follows.  N = new rabbit, M=mature rabbit

Months             Fibonacci               Rabbits

0                                          1                         1N

1                                          1                         1M

2                                          2                         1M-IN

3                                          3                         1M-1N, 1M

4                                          5                         1M-1N, 1M, 1M-1N

5                                          8                         1M-1N, 1M, 1M-1N, 1M-1N, 1M

 Term Fibonacci Ratio 1 1 2 1 1 3 2 0.5 4 3 0.666667 5 5 0.6 6 8 0.625 7 13 0.615385 8 21 0.619048 9 34 0.617647 10 55 0.618182 11 89 0.617978 12 144 0.618056 13 233 0.618026 14 377 0.618037 15 610 0.618033 16 987 0.618034 17 1597 0.618034 18 2584 0.618034 19 4181 0.618034

Extensions of the Problem

When the problem was extended to 100 using excel, rounding or truncated errors appeared at number 55.

 53 5.33163e+10 0.618034 54 8.62676e+10 0.618034 55 1.39584e+11 0.618034

Author & Contact
Susan R. Kelly

Link(s) to resources, references, lesson plans, and/or other materials

Golden Exploration Worksheet -
This worksheet from Mathematics Teaching in the Middle School leads students to discover the golden ratio by making various measurements and calculations.
[ web page ]

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