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  • Blog Post 3

    \(1\) \(\underline{\text{Fibonacci Sequence}}\)

    According to some accounts, Fibonacci is regarded as one of the most famous names in mathematics. It was Fibonacci, also known by the name Leonardo Pisano, that helped popularize our modern number system in the Latin-speaking world (Knott, 2013). However, he is more widely recognized for what we now call the Fibonacci Sequence. It was when he was contemplating the reproduction of rabbits, and trying to calculate how many pairs of rabbits there would be in one year, that Fibonacci came across the formula, which will become familiar: \(x_{n+1}=x_n+x_{n-1}\).

    This recurrence relation was used to define the Fibonacci Sequence as such: \(F_n=F_{n-1}+F_{n-2}\) where \(F_1=F_2=1\). Calculating the first few terms we see the numbers \(1,1,2,3,5,8,13,21...\). These numbers are called the Fibonacci numbers.

    These numbers appear in a plethora of areas from nature, art, geometry, etc. A few examples of where these numbers occur include the following:

    • Honeybee colonies

    • Spirals and shells

    • Plants and flowers

    The image (above) shows the presence of Fibonacci numbers in the spirals of seeds.

    Pictured are two more occurrences of Fibonacci numbers.

    It is made clear by the following illustration how these numbers are connected to spirals in particular. When we make squares with the widths equal to the Fibonacci numbers, we obtain a nice spiral: