https://en.wikipedia.org/wiki/Fibonacci_number This would make in interesting article, btw
But the number comes from sunflower patters
Fibonacci sequences appear in biological settings, id="cite_ref-S._Douady_and_Y._Couder_1996_255.E2.80.93274_9-1"
class="reference">href="https://en.wikipedia.org/wiki/Fibonacci_number#cite_note-S._Douady_and_Y._Couder_1996_255.E2.80.93274-9">[9]
in two consecutive Fibonacci numbers, such as branching in
trees, title="Phyllotaxis">arrangement of leaves on a stem, the
fruitlets of a href="https://en.wikipedia.org/wiki/Pineapple"
title="Pineapple">pineapple, id="cite_ref-Jones_2006_544_10-1" class="reference">href="https://en.wikipedia.org/wiki/Fibonacci_number#cite_note-Jones_2006_544-10">[10]
the flowering of href="https://en.wikipedia.org/wiki/Artichoke"
title="Artichoke">artichoke, an uncurling fern and the
arrangement of a href="https://en.wikipedia.org/wiki/Pine_cone" title="Pine
cone" class="mw-redirect">pine cone, id="cite_ref-A._Brousseau_1969_525.E2.80.93532_11-1"
class="reference">href="https://en.wikipedia.org/wiki/Fibonacci_number#cite_note-A._Brousseau_1969_525.E2.80.93532-11">[11]
and the family tree of honeybees. class="reference"> href="https://en.wikipedia.org/wiki/Fibonacci_number#cite_note-56">[56]
However, numerous poorly substantiated claims of Fibonacci
numbers or href="https://en.wikipedia.org/wiki/Golden_section"
title="Golden section" class="mw-redirect">golden sections
in nature are found in popular sources, e.g., relating to the
breeding of rabbits in Fibonacci's own unrealistic example, the
seeds on a sunflower, the spirals of shells, and the curve of
waves. href="https://en.wikipedia.org/wiki/Fibonacci_number#cite_note-57">[57]
href="https://en.wikipedia.org/wiki/Przemys%C5%82aw_Prusinkiewicz"
title="Przemys?aw Prusinkiewicz">Przemys?aw Prusinkiewicz
advanced the idea that real instances can in part be understood
as the expression of certain algebraic constraints on href="https://en.wikipedia.org/wiki/Free_group" title="Free
group">free groups, specifically as certain href="https://en.wikipedia.org/wiki/L-system" title="L-system">Lindenmayer
grammars. href="https://en.wikipedia.org/wiki/Fibonacci_number#cite_note-58">[58]
A model for the pattern of href="https://en.wikipedia.org/wiki/Floret" title="Floret"
class="mw-redirect">florets in the head of a href="https://en.wikipedia.org/wiki/Sunflower"
title="Sunflower" class="mw-redirect">sunflower was
proposed by H. Vogel in 1979. class="reference"> href="https://en.wikipedia.org/wiki/Fibonacci_number#cite_note-59">[59]
This has the form
![\theta<BR> = \frac{2\pi}{\phi^2} n,\ r = c \sqrt{n}]()
src="cid:part18.08040504.01020402-at-panix.com">
where n is the index number of the floret and c
is a constant scaling factor; the florets thus lie on href="https://en.wikipedia.org/wiki/Fermat%27s_spiral"
title="Fermat's spiral">Fermat's spiral. The divergence
angle, approximately 137.51°, is the href="https://en.wikipedia.org/wiki/Golden_angle"
title="Golden angle">golden angle, dividing the circle in
the golden ratio. Because this ratio is irrational, no floret
has a neighbor at exactly the same angle from the center, so the
florets pack efficiently. Because the rational approximations to
the golden ratio are of the form F(j):F(j + 1),
the nearest neighbors of floret number n are those at n ± F(j)
for some index j, which depends on r, the
distance from the center. It is often said that sunflowers and
similar arrangements have 55 spirals in one direction and 89 in
the other (or some other pair of adjacent Fibonacci numbers),
but this is true only of one range of radii, typically the
outermost and thus most conspicuous. class="reference"> href="https://en.wikipedia.org/wiki/Fibonacci_number#cite_note-60">[60]
On 02/15/2015 01:09 PM, Kamran wrote:
