clarification of phyllotaxis

Bob Vickery vickery at MPX.COM.AU
Fri Nov 21 00:42:47 EST 1997

>Hi all,
> I am hoping one of you can enlighten an ignorant soul. I have been
>teaching my class about phyllotaxis using  the text "Botany' by Moore et
>al. They define phyllotaxis as the number of turns of a spiral/number of
>leaves BETWEEN successive leaves of an orthostichy. As I went to expand on
>this subject by giving an example from Esau's "Anatomy of Seed Plants", I
>discovered that she describes 5/13 phyllotaxy as "five windings about the
>axis include 13 leaves with leaves n and n plus 13 located one above the
>other". That is there are only 12 leaves BETWEEN successive leaves of the
>orthostichy. These two definitions are slightly different but important.
>The other surprise was that the phyllotaxis was 5/13 not 8/13, which is
>what I expected based on the Fibonacci series and how it is explained in
>Moore et al.
>My question is "What is the correct definition of phyllotaxis" or is there
>no agreement on this?
>Grant R. Cramer
>Associate Professor
>Department of Biochemistry, Mail Stop 200
>University of Nevada,
>Reno, NV 89557
>Phone (702) 784-4204
>Fax (702) 784-1650
>email: cramer at

Esau's definition is correct if you think of phyllotaxy as the angle between=
 successive leaves.  In her example,  5/13 of a circle =3D 137.5 degrees =3D=
 360 - 222.5 degrees.  But, 222.5 degrees =3D 8/13 of a circle.  Counting=
 along a right-handed helix you get one answer, counting along a left-handed=
 helix you get the other.


Bob Vickery
bob at
vickery at

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