The chambered nautilus (Nautilus pompilius) is a specific example of one of the marine creatures whose structure represents a spontaneous logarithmic spiral growth pattern. In addition, the growth patterns of natural shells like Conch Shell, Moon Snail Shell, and Atlantic Sundial Shell show logarithmic spiral growth patterns of Golden Section properties or golden spiral form (Akhtaruzzaman and Shafie). Akhtaruzzaman says “has a close intimacy with Golden Ratio.”
For example, the sea star (Astropecten Aurantiacus), the star fish (Ophiotrix capillaris) and the sand dollar (Echinarachnius parma) exhibit five-fold symmetry (Trinajstic) which Md.
A wide variety of sea creatures also exhibit pentagonal symmetry.
For example, they describe the body of the Rainbow Trout fish as having a shape on which “three Golden Rectangles together can be fitted” and “the tail fin falls in the reciprocal Golden Rectangles and square.” Additionally, the individual fins also have the Golden Section properties” (Akhtaruzzaman and Shafie). Akhtaruzzaman and Shafie mention many sea creatures which exhibit the Golden Proportion in one form or another.
GOLDENRATIO PROTEIN FULL
These claims should be viewed with a “healthy degree of skepticism in the absence of full and replicated scientific reports,” however (Green). It must be noted, however, that many contemporary scholars dismiss such (and similar) claims by Golden Ratio adherents like Ghyka, the Romanian novelist, mathematician, historian, and philosopher who said, “Diagrams of proportions, however diversely arranged, can be deciphered by the same key.” Ghyka, for example, offered a “harmonic analysis” of a thoroughbred horse which showed that ratios between the length of the leg to the vertical thickness of the body are φ. Animal biology would seem to follow the same spontaneous growth patterns exhibited by plants. Some see the Golden Spiral in the shape of the horns of both the ram and the kudu and in the curvature of elephant tusks (Boeyens and Thackeray Masran D’Agnese). For example, the natural design of a Peacock’s feather hints at the Golden Ratio, the eye, fins and tail of a dolphin appear to fall at Golden Sections of the length of its body, and a penguin body exhibits Golden Ratio properties (Akhtaruzzaman and Shafie). He observed that there are a lot of examples of the Golden Section or Divine Proportion found in animals, fishes, and birds, in addition to insects and snails. German psychologist Adolf Zeising (1810–1876) studied the skeletons of animals and the branching of their veins and nerves.
GOLDENRATIO PROTEIN SERIES
Some investigators argue that microtubules are more efficient “information processors” because they are structured this way rather than with other possible structures however, Livio admits that “the apparent connection with the Fibonacci series may be coincidental” (Livio). This is the structure that “gives shape to the cell and also appears to act as a kind of cell ‘nervous system.’ Each mammalian microtubule is typically made up of thirteen columns, arranged in five right-handed and eight left-handed structures (5, 8, and 13 are all Fibonacci numbers).” Occasionally there are double microtubules with an outer envelope consisting of 21 columns, the next Fibonacci number. These structures are “hollow cylindrical tubes of a protein polymer” which make up the cytoskeleton. Livio says Fibonacci numbers are “a kind of Golden Ratio in disguise,” as they are found in even microscopic places, such as in the microtubules of an animal cell. The ubiquity of logarithmic spirals in the animal, bird, and plant kingdoms presents a convincing case for a cosmic character of the Golden Ratio (Boeyens and Thackeray). (Previous Section: Fibonacci and Insects) Buy Now on Amazon All citations are catalogued on the Citations page. This is an excerpt from Master Fibonacci: The Man Who Changed Math.
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