LydiaLe-EEB308-Assignment Tasks: Question 1-Fibonacci's Rabbit Problem

Fibonacci’s rabbit problem

1-How many pairs of rabbits will there be after a year if it is assumed that every month each pair produces one new pair, which begins to bear two young two months after its own birth? Assume we start the year with one newborn pair.

A-Solution:

In solving this problem, I believe that understanding the Fibonacci's sequence, and applying techniques of determining boundaries of the start and the end of rabbits' identification hold extremely important roles. My work divides finding information into two main steps as below.

Step 1-Understanding of Fibonacci Number, or Fibonacci's sequence.

It is crucial to understand the notion of Fibonacci Number or Fibonacci's sequence.

This Fibonacci’s sequence can be illustrated in an image as below.

https://sites.google.com/site/lydiale2016eeb308csu/fibonacci-s-rabbit-problem

AboutEducation-Russell (2016) considers this sequence is a recursive sequence.
In practice, it is obviously that the Fibonacci's sequence formula is used to determine a series of numbers in which each current or given number is the sum of the two numbers preceding it.
In my work for this problem, these two numbers namely the first predecessor, and the second predecessor. Setting the 'n' as the current or given number, then its first predecessor number is 'n-1', and its second predecessor number is 'n-2'. Traditionally, as mentioned, the Fibonacci's sequence formula is expressed as follows. F(n)=F(n-1)+F(n-2)

This formula will be used to find out numbers of pairs of rabbits. These rabbits need to be identified at the start and at the end of each month, in the following step.

Step 2-Setting and determining the boundaries towards the identification of rabbits.

The identity of rabbits is crucial in a process of finding the numbers of rabbits. This process begins with a setting to determining the pivotal points of boundaries. According to Walker (2013) 'boundaries identify where something starts and where something ends, and anything that has no Boundary has no identity’. Therefore, I believe that one core activity of this exercise is to set and determine the boundaries by determining the start and the end of the boundaries between months when the rabbits are identified for their identities. In other words, the boundaries of this exercise refer to the points of the start and the end of each month where all pairs of rabbits need to be counted.

My application of the 'Walker's boundaries ' to identify Fibonacci's rabbits is as follows:

Let's set:

F0 = Month (0) ==> starts with a rabbit baby pair

F1 = Month (1) ==> continues with a rabbit youth pair

F2 = Month (2) ==> continues with a rabbit adult pair

F(n) = Month (n)

In this case, Fibonacci’s [sequence] numbers occur from F3 , i.e [Fibonacci] Month(3).

Each subsequent number is the sum of the two preceding it. Using Microsoft Excel is my tool to find the figures as below.

In adding images of Adult, Baby, and Youth rabbits into my Microsoft Excel 2013 file, and using its relevant functions for calculating and drawing, my figures of pairs of rabbits for each month and the end of 12 months are visually and mathematically calculated, found and illustrated as follows.

The information above shows that after a year, there will be 233 [89+89+55] pairs[i.e. 466] of rabbits including 89 adult pairs, 89 baby pairs, and 55 youth pairs.

Therefore, there will be 233 pairs of rabbits after a year.

My notes:

Arguably, this question has being embedded the absurdity of real life, therefore it causes to raise further questions and problems since it has been called so. In addition, the question guides and focuses on the Fibonacci's sequence dealing with a single influence of the Fibonacci's issue. In fact, I believe that if at the beginning, the boundary's notion is provided and considered, then the solution can be easily found, and this Fibonacci's issue would no longer be problem.
However, I believe that with raising viewpoints from different edges of an issue will help learners gain more knowledge and develop their critical thinking skills.