The document discusses relationships between DNA and the golden ratio/Fibonacci sequence. It notes that the dimensions of the DNA double helix spiral, including the major and minor grooves, exhibit ratios that approximate phi. DNA sequences can be divided into sections of Fibonacci lengths that exhibit resonant proportions. The golden ratio appears throughout nature, including in pentagonal symmetry and patterns in plants and marine life.

1. DNA and Golden mean
 Information-package/condensed
 Modules used to make the whole
 Configuration of system- Ratio and
proportion*
 Process Impowered
 Motion
 Metamorphosis
physical, chemical, time duration
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2. Self-Reproduction
-Copy of the original
-Imitation
-Reflection
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3.  The DNA molecule measures 34 DNA
angstroms long by 21 angstroms wide for
each full cycle of the double helix spiral.
34 and 21 are Fibonacci numbers and
their ratio closely approximates phi. DNA
has two grooves in its spirals, with a phi
ratio between the major groove and the
minor groove (roughly 21 angstroms to
13 angstroms).
*A number series closely related to the golden section is the Fibonacci sequence: it begins with 0 and
1, and each subsequent number is generated by adding the two preceding numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ...
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4. Golden section ratio
 A Phi is something to look for such
self reproducing machine.
The golden section is an irrational,
or transcendental, number,
meaning that it never repeats and26/10/09

5. If we take these numbers two
at a time, and divide the larger
one by the smaller one, the
value will oscillate alternately
above and below the golden
section, while gradually
converging on it. If we divide the
smaller number by the larger
number, the value converges on
1/φ (0.618.)

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7. SC
ALE
DISTAN
CE
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8. INCLINAT
Xº
ION
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9. Golden Ruler
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10. Fibonacci Fraction:leaves/spirals
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11. Arrangements
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12. Conclusion
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13. Self reproducing
machine
The object has a shape that has the same shape with inner side and the molecules will be distributed
when the main object grows like a plant. I don't know how this should work or be done. But the
idea is to make some thing which will grow filling the molecules and duplicating it self. I don’t
want to say these are the molecules, method/casting, movements -I think this is something to
discover through time.
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14. Exploring

Nature
The golden ratio appears in
pentagonal forms of symmetry,
notably in the five-pointed star
(or pentagram), which was the
emblem of the Pythagorean
brotherhood. Pentagonal
symmetry abounds in living
organisms, especially plants
and marine animals (e.g.
starfishes, jellyfishes, sea
urchins). Flowers with 5 petals
(or multiples of 5) include all
fruit blossoms, water lilies,
roses, honeysuckles,
carnations, geraniums,
primroses, orchids, and
passionflowers .
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15. Platonic isohedral
configuration
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16. DNA and Golden Proportion
 Anywhere in a sequence of DNA, a contig of bases TCAG of which the
length is a number of Fibonacci : for example 144 bases.
 If this section is subdivided, for the example treated here, in 55
bases T and 89 bases A or C or G... We will thus say that this unit
constitutes a " re
 " A resonance is thus a proportion between 3 successive numbers of
Fibonacci. "
 All combinative of other combinations is possible:
 C versus AGT, A versus TCG, or G versus TCA by example.
 One will insist on the fact that the relative positions of the bases
inside this section are indifferent. It is before a a whole question of
RATIO and relative PROPORTION.
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17. Shapes and conversion
Convertor
Copy
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