The mathematics of sunflowers

January 31, 2013February 4, 2013 Annette Taylor 2 Comments summer scenes, Sunflowers, Tahuna

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… )