The Golden Ratio or Divine Proportion

The golden ratio, also known as the golden proportion, golden mean, golden section, golden number, divine proportion or sectio divina, is an irrational number, approximately 1.618 033 988 749 894 848, that possesses many interesting properties.           Shapes proportioned according to the golden ratio have long been considered aesthetically pleasing in Western cultures, and the golden ratio is still used frequently in art and design, suggesting a natural balance between symmetry and asymmetry. The ancient Pythagoreans, who defined numbers as expressions of ratios (and not as units as is common today), believed that reality is numerical and that the golden ratio expressed an underlying truth about existence.           The golden ratio was first studied by ancient mathematicians because of its frequent appearance in geometry and may have even been understood and used as far back in history as the Egyptians.

The white line is the body's height. The blue line, a golden section of the white line, defines the distance from the head to the finger tips.The yellow line, a golden section of the blue line, defines the distance from the head to the navel and the elbows. The green line, a golden section of the yellow line, defines the distance from the head to the pectorals and inside top of the arms, the width of the shoulders, the length of the forearm and the shin bone. The magenta line, a golden section of the green line, defines the distance from the head to the base of the skull and the width of the abdomen. The sectioned portions of the magenta line determine the position of the nose and the hairline.

Illustrations from goldennumber.net

Like the illustrations above, the golden ratio can be found in many aspects of nature. However, because natural forms and patterns offer such wildly random shapes, the ratios are approximate and will not sometimes fit each and every case, and even when they do, the results are open to interpretation and adjustments. This is because, like fractals, the pure mathematical form can exist as the ideal linear form, but when manifested in nature is influenced by the non-linear aspect of spirit, such as with art and aesthetics, which also cannot be governed by just the linear, mathematical form of phi. They are also greatly affected by the golden rule, the spiritual form of the golden ratio. The essence of true art is the inspiration, and inspiration is spiritual. In art, as with life,  it is not so much the mathematically quantifiable precision of the numbers that matters as much as the quality; the relationship of the part to the group and to the whole--beauty.  (See Chapter Four)

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