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• W2325911077 abstract "S piral forms abound in organic nature, and the beautiful Nautilus pompilius is frequently cited as an exquisite example of mathematical laws governing growth (Fig. 1). Cook [2] speaks of the Curves of Life to epitomize the geometric diversity in nature. In contrast to Cook, Colman's [3] Nature's Harmonic Unity follows Zeising's [4] thesis that the Golden Section [5] is the central principle in art and nature. Colman draws a maze of traces regulateurs [6] over natural and human-made objects to support his argument that the complicated forces in life and art conform to the law of the extreme and mean proportional [7]. Colman's method is open to the criticism that there is no objective way of determining whether a proposed analysis is the one intended and not simply another way of explaining the shape and proportions of an artifact by an entirely different procedure. It is a well-known fact that absolute uniformity of growth forces leads to straight lines and circles; however, growth is not uniform-it is this feature that signals the production of curves. Stevens explains the process: lesson of curvature is quite general and has nothing to do with what tissue or material is involved. Forms curl so that the faster growing or longer surface lies outside and the slower growing or shorter surface lies inside, there being more room outside than inside [8]. Huxley is more precise: If the length-width growth-ratio remains constant, but the absolute magnitudes of both components are greatest at one margin [and] least at the opposite margin, and are intermediately graded around the two sides of the mantel, [the form] will be distorted, and, so long as the growth-ratios concerned remain constant, will grow into a true logarithmic spiral in a single plane [9]. Since all growth in organic nature that follows this rule yields a logarithmic spiral, there is nothing mysterious about spirals. Clearly, it is the growth-ratios that control the shape of a spiral, and, as is soon apparent from a study of shells, there is no one particular spiral that fits all shells-some have tighter curves than others [10]. Every planar logarithmic spiral has an acute angle P3, termed the angle of the spiral, which controls its shape. This angle, between a tangent to any point on the curve and its polar radius vector, is constant for a particular spiral. The idea that phenomena in organic nature and art exhibit unity in obedience to some quintessential force in Nature, particularly the Golden Section ratio (), is a mystic belief that pervades the literature on proportion [11,12]. A recent example is that of Fletcher, who states that the Golden Section describes the shape of the Nautilus pompilius [13]. Fletcher arrives at this conclusion by examining the proportions of a rectangle enclosing a cross-section of the shell, and careful measurement confirms that her rectangle ABCD has its sides AB and BC in a ratio 1:(/)4), where =( (5+1)1/2. However, an examination of an accurate reconstruction of Fletcher's diagram (Fig. 2) reveals that whereas AB, BC and AD (the left, bottom and top edges of the enclosing rectangle) are tangential to the shell's boundary curve, the position of the right edge is dictated by the arbitrary position of point X, the terminal point of the curve. In other words, the shell should be rotated about its" @default.
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• W2325911077 date "1993-01-01" @default.
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• W2325911077 title "Shape and Order in Organic Nature: The Nautilus Pompilius" @default.
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• W2325911077 doi "https://doi.org/10.2307/1575811" @default.
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