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DATE 2015-02-01

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MESSAGE
DATE 2015-02-15
FROM Ruben Safir
SUBJECT Subject: [LIU Comp Sci] Re: Journal Article
From owner-learn-outgoing-at-mrbrklyn.com Sun Feb 15 21:55:58 2015
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Subject: [LIU Comp Sci] Re: Journal Article
References: <54E08421.9000601-at-panix.com> <54E0C314.2070506-at-my.liu.edu> <54E0C6F0.3020308-at-panix.com> <54E0CE72.3080609-at-my.liu.edu> <54E0DCCD.9030302-at-panix.com> <54E0E0C6.4090807-at-my.liu.edu>
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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:


Forget
about my corrections. Use your variant of my article. I am really
grateful that you are helping me with the article.




On 2/15/2015 12:52 PM, Ruben Safir wrote:


On 02/15/2015 11:50 AM, Kamran wrote:


the data *is* divided





it is "the data is divided"




http://nxg.me.uk/note/2005/singular-data/




Mine is on the website.  It took about 6 hours to edit it, and
I'm not


great at such things, so it still needs to go through the
professional


English editor.











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  99. 2015-02-23 Ruben <ruben.safir-at-my.liu.edu> Subject: [LIU Comp Sci] Study Schedule for Tuesday
  100. 2015-02-24 From: "keisha.sylvester" <keisha.sylvester-at-my.liu.edu> RE: Re: [LIU Comp Sci] Binary tree Excersize
  101. 2015-02-24 Ruben Safir <mrbrklyn-at-panix.com> Re: Re: [LIU Comp Sci] Binary tree Excersize
  102. 2015-02-24 From: "keisha.sylvester" <keisha.sylvester-at-my.liu.edu> RE: Re: [LIU Comp Sci] Study Schedule for Tuesday
  103. 2015-02-24 Maneesh Kongara <maneeshkongara-at-gmail.com> Re: [LIU Comp Sci] Binary tree Excersize
  104. 2015-02-24 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Binary tree Excersize
  105. 2015-02-24 Keisha Sylvester <keisha.sylvester-at-my.liu.edu> Re: [LIU Comp Sci] Study anyone??
  106. 2015-02-24 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Study anyone??
  107. 2015-02-25 Ruben <ruben.safir-at-my.liu.edu> Re: [LIU Comp Sci] Binary tree Excersize
  108. 2015-02-25 Ruben Safir <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Binary tree Excersize
  109. 2015-02-25 Keisha Sylvester <keisha.sylvester-at-my.liu.edu> Re: [LIU Comp Sci] Binary tree Excersize
  110. 2015-02-26 Ruben <mrbrklyn-at-panix.com> Re: [LIU Comp Sci] Binary tree Excersize
  111. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Campus
  112. 2015-02-26 Ruben <ruben.safir-at-my.liu.edu> Subject: [LIU Comp Sci] Fwd: [NYLXS - HANGOUT] Bios
  113. 2015-02-26 Ruben <ruben.safir-at-my.liu.edu> Subject: [LIU Comp Sci] Re: Fwd: [NYLXS - HANGOUT] Bios
  114. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  115. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  116. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  117. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  118. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  119. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  120. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  121. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  122. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  123. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  124. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  125. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Re: Role of functional dependencies in
  126. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [mrbrklyn-at-panix.com: (fwd) Role of functional dependencies in
  127. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [mrbrklyn-at-panix.com: (fwd) Re: [LIU Comp Sci] Need tutoring on
  128. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [mrbrklyn-at-panix.com: (fwd) Re: [LIU Comp Sci] Need tutoring on
  129. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [mrbrklyn-at-panix.com: (fwd) Re: [LIU Comp Sci] Need tutoring on
  130. 2015-02-26 Ruben Safir <mrbrklyn-at-panix.com> Subject: [mrbrklyn-at-panix.com: (fwd) Re: [LIU Comp Sci] Need tutoring on
  131. 2015-02-27 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] a hate this question
  132. 2015-02-27 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Allorithms Midterm
  133. 2015-02-27 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Read the FUCKING NOTES
  134. 2015-02-28 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Allgorithm Examination
  135. 2015-02-28 Ruben <ruben.safir-at-my.liu.edu> Subject: [LIU Comp Sci] Linked List Test Question
  136. 2015-02-28 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] Re: [NYLXS - HANGOUT] Read the FUCKING NOTES
  137. 2015-02-28 Ruben Safir <mrbrklyn-at-panix.com> Subject: [LIU Comp Sci] [prmarino1-at-gmail.com: Re: [NYLXS - HANGOUT] Read the FUCKING NOTES

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