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It is shown that the golden ratio plays a prominent role in the dimensions of all objects which exhibit five-fold symmetry. It is also showed that among the irrational numbers, the golden ratio is the most irrational and, as a result, has unique applications in number theory, search algorithms, the minimization of functions, network theory, the atomic structure of certain materials and the growth of biological organisms.
Richard A. Dunlap
Since ancient times artists and architects have seen in the golden mean the most aesthetically satisfying geometric ratio.
Stephen M. Barr
Thousands of years ago the ancients had an advanced mathematical understanding of universe that is revealed in many sources. There is a consistent link to knowledge of the golden mean, but the way in which the ancients were able to formulate and use this information speaks of a technical grasp of the subject that exceeds what we know about it in the present day.
Alison Charlotte Primrose
You too can make the golden cut, relating the two poles of your being in perfect golden proportion, thus enabling the lower to resonate in tune with the higher, and the inner with the outer. In doing so, you will bring yourself to a point of total integration of all the separate parts of your being, and at the same time, you will bring yourself into resonance with the entire universe....Nonetheless the universe is divided on exactly these principles as proven by literally thousands of points of circumstantial evidence, including the size, orbital distances, orbital frequencies and other characteristics of planets in our solar system, many characteristics of the sub-atomic dimension such as the fine structure constant, the forms of many plants and the golden mean proportions of the human body, to mention just a few well known examples. However the circumstantial evidence is not that on which we rely, for we have the proof in front of us in the pure mathematical principles of the golden mean.
Alison Charlotte Primrose
Thus nature provides a system for proportioning the growth of plants that satisfies the three canons of architecture. All modules are isotropic and they are related to the whole structure of the plant through self-similar spirals proportioned by the golden mean.
Jay Kappraff
The Golden Mean is for the weakling, it was not meant for the likes of Alexander the Great, Cyrus, Pharaohs, or Hitlers of the world
Bangambiki Habyarimana
When Coleridge tried to define beauty, he returned always to one deep thought; beauty, he said, is unity in variety! Science is nothing else than the search to discover unity in the wild variety of nature,—or, more exactly, in the variety of our experience. Poetry, painting, the arts are the same search, in Coleridge’s phrase, for unity in variety.
Bronowski
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