![]() ![]() 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. 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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