Mathematical Model of Floret Arrangement
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
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.
Read more about this topic: Sunflower
Famous quotes containing the words mathematical, model and/or arrangement:
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
“The Battle of Waterloo is a work of art with tension and drama with its unceasing change from hope to fear and back again, change which suddenly dissolves into a moment of extreme catastrophe, a model tragedy because the fate of Europe was determined within this individual fate.”
—Stefan Zweig (18811942)
“The best protection parents can have against the nightmare of a daycare arrangement where someone might hurt their child is to choose a place that encourages parents to drop in at any time and that facilitates communication among parents using the program. If parents are free to drop in and if they exercise this right, it is not likely that adults in that place are behaving in ways that harm children.”
—Gwen Morgan (20th century)