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    pdf_fibo_series

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    pdf_fibo_series

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    Fibonacci Sequence: Magic, Myth, or Just Math

    Have you ever wondered what might be the common factor between DNA, sunflower
    petals, galaxy spirals, and the family tree of a bee? It is the Fibonacci sequence.
    This sequence, consisting of just a set of integers which are basically the summation
    of the previous 2 integers, can lead us to profound insights about the natural and human-
    made world. So let me introduce you to the fascinating universe of the Fibonacci sequence.
    This astonishing series, which has baffled mathematicians and artists for millennia,
    was noted by the medieval Italian mathematician Fibonacci (Leonardo Pisano) in his
    book Liber Abaci (1202).

    History and Context


    Contrary to popular belief, Fibonacci was not the first person to notice and study the
    sequence. Its origin traces back to Indian mathematicians. By the 6th century, math-
    ematicians like Virahanka and Gopala were studying the sequence in connection with
    Sanskrit poetry and meter. These sequences were used to count rhythmic syllables.
    In the book Liber Abaci, Fibonacci introduced the Hindu-Arabic counting method
    to Europe, which was a revolution as using the Roman counting system in complex
    arithmetic was pretty hectic. It also contained the rabbit problem:

    ”Suppose a pair of rabbits is put in a field to breed. They mature in a month,


    and each month, they produce another pair of rabbits. If each pair of rabbits
    reproduces in the same manner, how many pairs will there be in a year?”

    (Add a diagram here.)


    To solve this problem, Fibonacci demonstrated the sequence we now know by his
    name:
    0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, . . .

    Real-Life Implementation and the Logic Behind It


    Out of all the places you would expect the Fibonacci sequence to appear, a family tree
    would be the last thing to come to your mind. Yes, the Fibonacci sequence appears in
    the family tree of a beehive.
    To understand this phenomenon, you first need to understand the science behind bee
    reproduction. Only the queen bee of the hive is able to lay eggs. The other females are
    worker bees. The male bees are called drones.

    1
    If an egg is fertilized by a drone after being laid, it hatches into a female worker bee.
    If it is not fertilized, it hatches into a drone. This means a drone only has one parent (a
    mother), and a female bee has two.
    So let’s say we have a drone bee named Bif. Bif has one parent, his mother. His
    mother has two parents: a queen and a drone. In the next generation, Bif’s grandparents
    include one male and two females, making three ancestors. Continuing further, his great-
    grandparents total five, and the numbers keep increasing as 8, 13, 21, and so on.
    If we lay out these numbers, they form the Fibonacci sequence:

    1, 1, 2, 3, 5, 8, 13, 21, . . .

    (Add a diagram showcasing the phenomenon here.)

    The Fibonacci sequence is often found in nature in the form of spirals. This is visible
    in the number of flower petals, in spirals of seed heads in sunflowers, pinecones, and
    pineapples. This spiraling pattern is also visible in the branching of certain types of
    trees.
    If you are wondering why, the simple answer would be evolution. All these plants
    want to maximize sunlight exposure in order to produce more food. So they need to
    organize the leaves and seeds in such a way so that they receive the most sunlight by
    using as few resources as possible.
    (Add diagram showcasing the phenomenon here.)
    The Golden Ratio, derived from the Fibonacci sequence, also appears in many unex-
    pected places. You can find it in art masterpieces, the structure of DNA, the spirals of
    galaxies, and even in computer algorithms.

    Conclusion
    The Fibonacci sequence is a series consisting only of simple integers, yet it tells a lot
    about our natural world. It transcends the realm of the mathematical world. It is just
    an awesome example of how mathematics is deeply intertwined with our natural world.

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