Nature's Mathmatics
A model for the pattern of florets in the head of a sunflower was proposed by H. Vogel in 1979, This is expressed in polar coordinates
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. This model has been used to produce computer graphics representations of sunflowers. en.wikipedia.org/wiki/Sunflower
I'm no mathmetician, but the graphic looks pretty close to the center of the sunflower.
Thanks for your visit and all of your support. Hope everyone has a great weekend.
© Melissa Post 2013 All rights reserved. Please respect my copyright and do not copy, modify or download this image to blogs or other websites without obtaining my explicit written permission.
Nature's Mathmatics
A model for the pattern of florets in the head of a sunflower was proposed by H. Vogel in 1979, This is expressed in polar coordinates
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. This model has been used to produce computer graphics representations of sunflowers. en.wikipedia.org/wiki/Sunflower
I'm no mathmetician, but the graphic looks pretty close to the center of the sunflower.
Thanks for your visit and all of your support. Hope everyone has a great weekend.
© Melissa Post 2013 All rights reserved. Please respect my copyright and do not copy, modify or download this image to blogs or other websites without obtaining my explicit written permission.