In the Beech we make one
turn of the stem before reaching the third leaf which stands over the
first. In the Apple the thread will wind twice about the stem, before
coming to the sixth leaf, which is over the first.
Another arrangement, not very common, is found in the Magnolia, the Holly,
and the radical leaves of the common Plantain and Tobacco. The thread
makes three turns of the stem before reaching the eighth leaf which stands
over the first. This is the 3/8 arrangement. It is well seen in the
Marguerite, a greenhouse plant which is very easily grown in the house.
Look now at these fractions, 1/2, 1/3, 2/5, and 3/8. The numerator of
the third is the sum of the numerators of the first and second, its
denominator, the sum of the two denominators. The same is true of the
fourth fraction and the two immediately preceding it. Continuing the
series, we get the fractions 5/13, 8/21, 13/34. These arrangements can
be found in nature in cones, the scales of which are modified leaves and
follow the laws of leaf-arrangement.[1]
[Footnote 1: See the uses and origin of the arrangement of leaves in
plants. By Chauncey Wright. Memoirs Amer. Acad., IX, p. 389. This essay
is an abstruse mathematical treatise on the theory of phyllotaxy. The
fractions are treated as successive approximations to a theoretical angle,
which represents the best possible exposure to air and light.
Modern authors, however, do not generally accept this mathematical view of
leaf-arrangement.
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