The mathematics of sunflowers

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On the road near Tahuna this field of sunflowers caught our eye. How could we not stop and snap?

Here’s something I never knew about these summer friends – a mathematical model for the pattern of florets has been devised by H Vogel. Thus:

r = c \sqrt{n},
\theta = n \times 137.5^{\circ},

where θ is the angle, r is the radius or distance from the center, and n is the index number of the floret and c is a constant scaling factor. It is a form of Fermat’s spiral. The angle 137.5° is related to the golden ratio (55/144 of a circular angle, where 55 and 144 are Fibonacci numbers) and gives a close packing of florets. Thank you Wikipedia!

(Does popping a small amount of maths into any writing instantly make it more impressive? Check out what Waikato University physicist Marcus Wilson has to say on the subject… )

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