The document discusses the relationship between DNA structure and the golden ratio, highlighting how key measurements of DNA correspond with Fibonacci numbers and ratios. It explains the significance of these mathematical relationships in the context of natural patterns, such as those found in pentagonal symmetry in organisms and botanical structures. Additionally, it introduces the concept of 'resonance' in sequences of DNA, emphasizing the importance of ratios and proportions in biological configurations.

1. DNA and Golden meanInformation-package/condensedModules used to make the wholeConfiguration of system- Ratio and proportion*Process ImpoweredMotionMetamorphosis physical, chemical, time duration

2. Self-Reproduction-Copy of the original-Imitation-Reflection

3. DNA The DNA molecule measures 34 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 ...

4. Golden section ratioA Phi is something to look for such self reproducing machine.The golden section is an irrational, or transcendental, number, meaning that it never repeats and never ends.

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.)

7. SC ALEDISTANCE

8. INCLINATIONXº

9. Golden Ruler

10. Fibonacci Fraction:leaves/spirals

11. Arrangements

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.

15. ConvertorCopy

16. Platonic isohedral configuration

17. ProportionHuman proportionThe human body clearly expresses the pentad’s symmetry in its five senses and five extensions from the torso, each limb ending in five fingers or toes.DNA and Golden ProportionAnywhere 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 " resonance "." 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.

19. Human Face-proportion