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1965 — Alexander arrangement of elements: Designed to complement the point at which education on the arrangement of atoms into a chart begins, much as the world globe establishes the reality, and to emphasise the vital and convenient nature of flat printed projections or maps [81] 1999 — Moran's spiral periodic table: In hexagonal form [82]
The form with the f-block included in the main body is sometimes called the 32-column [6] or long form; [33] the form with the f-block cut out the 18-column [6] or medium-long form. [33] The 32-column form has the advantage of showing all elements in their correct sequence, but it has the disadvantage of requiring more space. [34]
where n is the index number of the floret and c is a constant scaling factor, and is a form of Fermat's spiral. The angle 137.5° is the golden angle which is related to the golden ratio and gives a close packing of florets. [14] Spirals in plants and animals are frequently described as whorls. This is also the name given to spiral shaped ...
Many biological structures including the shells of mollusks. [14] In these cases, the reason may be construction from expanding similar shapes, as is the case for polygonal figures. Logarithmic spiral beaches can form as the result of wave refraction and diffraction by the coast. Half Moon Bay (California) is an example of such a type of beach ...
The shape of the spirals depends on the growth of the elements generated sequentially. In mature-disc phyllotaxis, when all the elements are the same size, the shape of the spirals is that of Fermat spirals—ideally. That is because Fermat's spiral traverses equal annuli in equal turns. The full model proposed by H. Vogel in 1979 [5] is
For <, spiral-ring pattern; =, regular spiral; >, loose spiral. R is the distance of spiral starting point (0, R) to the center. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by ( − θ {\displaystyle -\theta } ) for plotting.
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I give references to some spiral-shaped periodic systems of elements. The French geologist , Alexandre-Émile Béguyer de Chancourtois was the first person to make use of atomic weights to produce a classification of periodicity. He drew the elements as a continuous spiral around a metal cylinder divided into 16 parts.