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Math Help - Fibonacci Sequence

  1. #1
    m.c
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    Fibonacci Sequence

    "I thought about the origin of all square numbers and discovered that tthey arise out of the increasing sequence of odd numbers; for the unity is a square and from it is made the first square, namely 1; to this unity is added 3, making the second square, namely 4; if to the sum is added to the third odd number, namely 5, the third square is created, namely 9; an thus sums of consecutive odd numbers and a sequence of squares always arise together in order." -Fibonacci

    1,3,5,7.... the sequence of odd numbers
    1,4,9,16... the sequence of squares

    I am confused and do not see the connection? Is there a formula that connects the relationship of odd numbers and squares?
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  2. #2
    Flow Master
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    Quote Originally Posted by m.c View Post
    "I thought about the origin of all square numbers and discovered that tthey arise out of the increasing sequence of odd numbers; for the unity is a square and from it is made the first square, namely 1; to this unity is added 3, making the second square, namely 4; if to the sum is added to the third odd number, namely 5, the third square is created, namely 9; an thus sums of consecutive odd numbers and a sequence of squares always arise together in order." -Fibonacci

    1,3,5,7.... the sequence of odd numbers
    1,4,9,16... the sequence of squares

    I am confused and do not see the connection? Is there a formula that connects the relationship of odd numbers and squares?
    Add up the odd numbers and you will see:

    1 + 3 =

    1 + 3 + 5 =

    1 + 3 + 5 + 7 =
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