Divine proportion

The following two passages tell of geometry s Divine Proportion, 1.618. 

Inscribe the pentacle star inside a pentagon and you have the pentagram, symbol of the ancient Greek School of Mathematics founded by Pythagoras—solid evidence that the ancient Mystery Schools knew about PHI and appreciated the Divine Proportion s multitude of uses to form our physical and biological worlds. 

PHI s ubiquity in nature clearly exceeds coincidence, and so the ancients assumed the number PHI must have been preordained by the creator of the universe. Early scientists heralded 1.618 as the Divine Proportion. ... 

Stettner, the math major, raised his hand. Because if you draw a (50) pentagram, the lines automatically divide themselves into segments according to the Divine Proportion. ... 

Landgon gave the kid a proud nod. Nice job. Yes, the ratios of line segments in a pentacle all equal PHI, making the symbol the ultimate expression of the Divine Proportion. ... 

Passage 2, line 46) signify what about the divine proportion ... 

H.E. Huntley, The Divine Proportion, Dover Publications, New York, 1970. 

Certain structures, when examined on different scales from small to large, always appear exactly the same. Such structures are said to be self-similar or to be endowed with the symmetry of self-similarity. Self-similar structures are found to be invariably associated with the geometrical relationship known as the golden ratio, or what Johannes Kepler (1571 - 1630) referred to as the "divine proportion", adding ... 

This tradition was finally broken by Kepler who developed the contention of Pythagoras and Plato that a proportional relationship exists between polyhedron and circle. In time, this approach led to modern astronomy and, in the hands of Robert Boyle (1661) and Antoine Lavoisier (1789), to chemistry. However, the victory of science over magic has by no means been final . Modern big-bang cosmology, like the chain of assumptions in computational quantum chemistry (Rouvray, 2009), are rapidly reverting to the occult approach. An alternative model, emerging in chemistry, is based on the golden ratio, which both Kepler and Leonardo da Vinci referred to as the Divine Proportion. 

FIGURE 1.4 The golden ratio and da Vinci s Mona Lisa. The frame of the picture, as well as the rectangle outlining her face, has divine proportions. 

The positive root,

golden ratio. According to the ancient Greeks, this was supposed to represent the most aesthetically pleasing proportions for a rectangle, as shown in Fig. 1.4. Leonardo da Vinci also referred to it as the divine proportion. ... 

Golden Ratio Represented as (p or a seemingly ubiquitous naturally occurring ratio or proportion having the approximate value 1.618018513 also known as the golden mean, the golden section, and the divine proportion. 

One of the most mysterious observations in Nature is the appearance of a single parameter that determines the macroscopic structure of a large variety of apparently unrelated objects, such as the distribution of florets in a composite seed head [1], the periodic table of the elements [2], the flight path of a predator bird in pursuit of its prey, the curvature of a kudu horn [1] and the surface features of a nanoparticle [3], This ubiquitous parameter, known as the golden ratio, has also been called the divine proportion and for millennia has been used in architectural design, as a measure of human anatomical features, in works of art and in musical composition [1],... 

The simplest and most beautiful illustration of golden-ratio self-similarity must surely be the quantization of bond order, shown in Figs. 3 and 4. It is so intimately entangled with golden symmetry and gives such a precise definition of the otherwise elusive bond-order concept that the possibility of this being mere coincidence is zero. Small wonder that the great Johannes Kepler referred to the divine proportion which served as idea to the Creator when He introduced the creation of likeness out of likeness, which also continues indefinitely . 

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