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Lin-Hsin-Hsin-Sunflower-Mathematical Properties





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Mathematical Properties





    Each floret is oriented toward the next by approximately a golden angle, 137.5° (golden ratio) producing a pattern of interconnecting spirals -- a form of Fermat's spiral where the number of left spirals and the number of right spirals are successive Fibonacci number


    Typically,
    there are 34 spirals clockwise
    and 55 anticlockwise


    Very large sunflower head,
    there could be 89 clockwise
    144 anticlockwise


    This pattern produces the most efficient packing of seeds mathematically possible within the flower head


    55/144 of a circular angle
    55 & 144 = Fibonacci number


    r= c √n
    θ = n x 137.5°


    where
    θ = angle
    r = radius or distance from the center
    n = index number of the floret
    c = constant scaling factor


    Fibonacci Sequence


    is a sequence in which each number is the sum of the two preceding ones


    Fibonacci Numbers


    are the individual numbers therein


    The first 20 numbers

    of

    Fibonacci Sequence


         
    F0  F1  F2  F3  F4  F5  F6  F7  F8  F9  F10  F11  F12  F13  F14  F15  F16  F17   F18   F19  
    0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597  2584  4181 









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