Phi in the human body 1.- Introduction Marcus Vitruvius Pollio, Roman architect (c. 25 B.C.), remarked a similarity between the human body and a perfect building: Nature has designed the human body so that its members are duly proportioned to the frame as a whole. He inscribed the human body into a circle and a square, the two figures considered images of perfection. It is widely accepted that the proportions in the human body follow the Golden Ratio. In this article we will review some studies on the subject. We will show the nineteenth century findings of the Golden Ratio in the human body by Adolf Seizing, actually approximated by a Fibonacci sequence of measures. Then we will examine the Golden proportions of the human body proposed by architects Erns Neufert and Le Corbusier in the twentieth century. Finally we will show how a common study with a german and an indian population samples confirmed the presence of the Golden Ratio in some proportions of the human body. 2.- Golden proportions in the human body found by Adolf Zeising Adolf Zeisings main interests, back in the nineteenth century, were mathematics and philosophy. But after having retired he began his researches on proportions in nature and art. In the field of botany, he discovered the Golden Ratio in the arrangement of branches along the stem of plants, and of veins in leaves. From this starting point he extended his researches to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, etc., and finally to human and artistic proportions. The title of his first publication in 1854 declares his program: New theory of the proportions of the human body, developed from a basic morphological law which stayed hiherto unknown, and which permeates the whole nature and art, accompanied by a complete summary of the prevailing systems. That universal law was, in efect, the Golden Ratio. There he presents his own proportional analyses of the human body (Figure 1). Zeising divides the total height of a mans body into four principal zones: top of head to shoulder, shoulder to navel, navel to knee, and knee to base of foot. Each zone is further subdivided into five segments, which are arranged symmetrically within each zone: either following the pattern ABBBA or the pattern ABABA, but always summing up 2A+3B. By the way, the 3/2 proportion in each zone is a Perfect Fifth in the equal temperament musical scale. Is music involved in the design of our own body? On the right of Figure 1 you can see the Golden proportions present in each of the segments, and between them, at different scales. Zeisings proportions of the human body are a beautiful example of how Nature closely approximates the Golden Ratio by means of a Fibonacci sequence of measures. Zeising erroneusly substitutes 90 for 89 in his measures, but we have used the exact value in the following calculations. The Fibonacci numbers present in his scheme, explicitly (green) or implicitly as grand totals (magenta), are the following: (^_^)>sacred-geometry.es/en/content/phi-human-body Sacred geometry: (^_^)>en.wikipedia.org/wiki/Sacred_geometry KGB
Posted on: Thu, 09 Oct 2014 23:36:38 +0000
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