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    Fibonacci

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    Seema Gupta
    The Fibonacci sequence is the sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, etc. where each number is the sum of the two preceding ones. The Fibonacci sequence appears frequently in nature, such as in the arrangement of leaves and petals on plants and the spirals of sunflowers and pinecones. It is also seen in the branching patterns of some plants and vegetables. The ratio of successive Fibonacci numbers approaches the golden ratio, an important number in mathematics and aesthetics seen in architecture and art.

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    Fibonacci

    Uploaded by

    Seema Gupta
    186 views46 pages
    The Fibonacci sequence is the sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, etc. where each number is the sum of the two preceding ones. The Fibonacci sequence appears frequently in nature, such as in the arrangement of leaves and petals on plants and the spirals of sunflowers and pinecones. It is also seen in the branching patterns of some plants and vegetables. The ratio of successive Fibonacci numbers approaches the golden ratio, an important number in mathematics and aesthetics seen in architecture and art.

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    The Fibonacci sequence is the sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, etc. where each number is the sum of the two preceding ones. The Fibonacci sequence appears frequently in nature, such as in the arrangement of leaves and petals on plants and the spirals of sunflowers and pinecones. It is also seen in the branching patterns of some plants and vegetables. The ratio of successive Fibonacci numbers approaches the golden ratio, an important number in mathematics and aesthetics seen in architecture and art.

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    © All Rights Reserved
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    186 views46 pages

    Fibonacci

    Uploaded by

    Seema Gupta
    The Fibonacci sequence is the sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, etc. where each number is the sum of the two preceding ones. The Fibonacci sequence appears frequently in nature, such as in the arrangement of leaves and petals on plants and the spirals of sunflowers and pinecones. It is also seen in the branching patterns of some plants and vegetables. The ratio of successive Fibonacci numbers approaches the golden ratio, an important number in mathematics and aesthetics seen in architecture and art.

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    The Fibonacci numbers are 0,

    1, 1, 2, 3, 5, 8, 13, ... (add the


    last two to get the next)

    It is called the Fibonacci


    series after Leonardo
    Fibonacci.
    The "shallow diagonals" of Pascal's
    triangle
    sum to Fibonacci numbers.
    The Fibonacci numbers are
    studied as part of number
    theory and have applications
    in the counting of
    mathematical objects such as
    sets, permutations and
    sequences and to computer
    science.
    FIBONACCI SEQUENCE IS
    ALSO SEEN IN RABIT
    MULTIPLICATION
    Fibonacci Fingers?

    Every human has two hands, each one of


    these has five fingers, each finger has
    three parts which are separated by two
    knuckles. All of these fit into the sequence.
    The Fibonacci numbers are Nature's
    numbering system.
    They appear everywhere in Nature, from
    the leaf arrangement in plants, to the
    pattern of the florets of a flower,
    pinecone, or the scales of a pineapple.
    The Fibonacci numbers are therefore
    applicable to the growth of every living
    thing, including a single cell, a grain of
    wheat, a hive of bees.
    If we take the ratio of two successive
    numbers in Fibonacci's series, (1, 1, 2, 3,
    5, 8, 13, ..) and we divide each by the
    number before it, we will find the
    following series of numbers:
    1/1 = 1, 2/1 = 2, 3/2 = 15, 5/3 =
    1666..., 8/5 = 16, 13/8 = 1625, 21/13
    = 161538... The ratio is called the golden
    ratio. It has a value of approximately
    1618034 and is denoted by the Greek
    letter phi.
    Flowers often have a Fibonacci number of petals,
    daisies can have 34, 55 or even as many as 89
    petals!
    Sunflower
    head
    displaying
    florets in
    spirals of
    34 and 55
    around the
    outside

    The beautiful spirals of the sun flower


    head reveal the astonishing double
    connection with the Fibonacci series
    One-petalled

    Two-petalled flowers
    Three petals

    Five petals - there are


    hundreds of species,
    both wild and
    cultivated, with five
    petals.
    Eight-petalled flowers are not
    so common as five-petalled,
    but there are quite a number
    of well-known species with
    eight petals.
    Thirteen, ...

    Twenty-one

    34 petals
    The florets within this cluster are
    arranged spirally. Typically each floret
    is oriented toward the next by
    approximately the golden angle,
    producing a pattern of interconnecting
    spirals where the number of left
    spirals and the number of right spirals
    are successive Fibonacci numbers.
    Fibonacci numbers can also be seen
    in the arrangement of seeds on flower heads.

    This poppy seed head has 13 ridges on top.


    some plants
    branch in such
    a way that they
    always have a
    Fibonacci
    number of
    growing points.
    FIBONACCI SEQUENCE IN PLANTS

    many plants show


    the Fibonacci
    numbers in the
    arrangements of
    the leaves around
    their stems.
    Pine cones show the Fibonacci Spirals
    The scales are
    spirally
    arranged in
    fibonacci
    number ratios.
    Here is a curve which crosses the X-
    axis at the Fibonacci numbers
    FIBONACCI SEQUENCE IN VEGETABLES
    The Fibonacci numbers play a significant
    role in nature and in art and architecture.
    The adjacent picture
    shows a design
    featuring the
    pentagons and
    hexagons used in the
    Mosque. which were
    developed out of the
    connections between
    the Fibonacci
    series,and the Golden
    Proportion.
    The sequence has been used in the
    design of a building,
    The series can be extended and the numbers can be found directly by applying this
    formula-Fn-2=Fn-Fn-1

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