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    Fibonacci Numbers

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    Iga Gollum
    The Fibonacci sequence is an infinite sequence of numbers where each subsequent number is the sum of the previous two. It begins with 1, 1, and then 2, 3, 5, 8, etc. The sequence is named after Italian mathematician Leonardo Fibonacci who first studied the pattern of rabbit breeding. Many patterns in nature follow the Fibonacci sequence, including the number of petals on flowers, the spirals in seashells and sunflowers, and the arms of spiral galaxies.

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    Fibonacci Numbers

    Uploaded by

    Iga Gollum
    32 views2 pages
    The Fibonacci sequence is an infinite sequence of numbers where each subsequent number is the sum of the previous two. It begins with 1, 1, and then 2, 3, 5, 8, etc. The sequence is named after Italian mathematician Leonardo Fibonacci who first studied the pattern of rabbit breeding. Many patterns in nature follow the Fibonacci sequence, including the number of petals on flowers, the spirals in seashells and sunflowers, and the arms of spiral galaxies.

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    Fibonacci numbers

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    The Fibonacci sequence is an infinite sequence of numbers where each subsequent number is the sum of the previous two. It begins with 1, 1, and then 2, 3, 5, 8, etc. The sequence is named after Italian mathematician Leonardo Fibonacci who first studied the pattern of rabbit breeding. Many patterns in nature follow the Fibonacci sequence, including the number of petals on flowers, the spirals in seashells and sunflowers, and the arms of spiral galaxies.

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    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    32 views2 pages

    Fibonacci Numbers

    Uploaded by

    Iga Gollum
    The Fibonacci sequence is an infinite sequence of numbers where each subsequent number is the sum of the previous two. It begins with 1, 1, and then 2, 3, 5, 8, etc. The sequence is named after Italian mathematician Leonardo Fibonacci who first studied the pattern of rabbit breeding. Many patterns in nature follow the Fibonacci sequence, including the number of petals on flowers, the spirals in seashells and sunflowers, and the arms of spiral galaxies.

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    The Fibonacci sequence

    The Fibonacci sequence is an infinite sequence of natural numbers which starts with numbers 1 and
    1. Each term is obtained by adding the two numbers before it:

    1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1.597…

    The elements of this sequence are called the Fibonacci numbers. A mainstay of high-school and
    undergraduate classes, it's been called "nature's secret code," and "nature's universal rule."

    Fibonacci numbers are named after Italian mathematician Leonardo of Pisa, later known as
    Fibonacci. As well as being famous for the Fibonacci Sequence, he helped spread Hindu-Arabic
    Numerals (like our present numbers 0,1,2,3,4,5,6,7,8,9) through Europe in place of Roman Numerals
    (I, II, III, IV, V, etc).

    The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could
    breed in ideal circumstances. 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. How
    many pairs will there be in one year?

    1. At the end of the first month, they mate, but there is still only 1 pair.
    2. At the end of the second month the female produces a new pair, so now there are 2 pairs of
    rabbits in the field.
    3. At the end of the third month, the original female produces a second pair, making 3 pairs in
    all in the field.
    4. At the end of the fourth month, the original female has produced yet another new pair, the
    female born two months ago produces her first pair also, making 5 pairs.

    Golden spiral
    In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is,
    a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.
    It grows such that the angle of a line from the center of the spiral to the tangent to the curve at that
    point is constant.
    Examples of the Fibonacci sequence in nature
     The number of petals in a flower consistently follows the Fibonacci sequence.
     The fibonacci spiral appears in the perfect nautilus shell.
     The composition of seeds in the center of a sunflower looks like spiral patterns curving left
    and right. Amazingly, if you count these spirals, your total will be a Fibonacci number.
     The Fibonacci Sequence evolves out of the trunk and spiral and grows the taller and larger
    the tree becomes. Some truly majestic trees are in existence today, utilizing this pattern.
     Not surprisingly, spiral galaxies also follow the familiar Fibonacci pattern. The Milky Way has
    several spiral arms, each of them a logarithmic spiral of about 12 degrees.

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