Diapositiva 1

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Have you ever observed the head of a sunflower?
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• We can notice the presence of spirals that go in
  opposite directions
• . 34 counter-clockwise
• . 55 clockwise
• Starting from this observation we wondered if the
  development of the head is guided by some sort of
  mathematic law.

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To answer this question, we supposed that the law
discovered in the development of the other
flowers we examinated could be applied to the
sunflower development too we actually supopsed
that every seed of the head developed every 140
and that every seed had less distance from the
center than the previous. Then we verified our
supposition with a simulation.
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Let's consider a circumference that will
represent the final head of our sunflower. Let's
mark the position of the first seed developed- In
the conclusive phase it will be on the border of
the head.
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Let's suppose that the second seed develops at a
140 distance from the previous. In the
conclusive phase it will be 140 distant from the
first seed and it will be distant ?L from the
border of the head. With the same principle we
can obtain the position of the other seeds.
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a 140
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a1140
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Cambiando i valori dellangolo
By assigning different values to the angle that
separates the seed we can verify that the angle
that gives us the real structure of the head (34
and 55 spirals) is of 137. With some calculation
we discover that a 137 360- 360/?
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If we try to vary the step of the angle we find
out that the graph assumes different
conformations that remind the development of some
plants like the rose (143 angle), or of a galaxy
(153 angle)
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