[First experience with using a series of generalized golden proportions for studying the shell of brachiopod and mollusks].
Symmetry of shells of clams (Veneridae: Katelysia, Venus, Periglypta; Fimbriidae: Corbis fimbriata) and brachioipods (Cancrinella undata, Echinoconhus punctatus, Reticulatia inflatiformis and Neophricodothyris waageni) was studied geometrically with spiral symmetry and connected mathematical methods (complex proportions and Fibonacci numbers). Location regularity of the elements of concentrical sculpture connected with shell growth is interpreted as unrolling of logarithmic spiral in the process of growth. Correlations of radius of sculpture circles were studied with the raw of generalized golden sections of V.I. Korobko and G.N. Primak. The discovered regularities of circles location being similar to some peculiarities of phyllotaxis are governed by the rules of the raw of generalized golden sections. Two spiral folds could keep correspondence between the increase in mass of growing animal and the increase in intensity of water drawing by ciliate apparatus.
Lukash
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Dept. of Invertebrate Zoology, Biological Faculty, M.V. Lomonosov Moscow State University, Vorob'evy Gory, Moscow 119899, Russia.
D000818:Animals; D007448:Invertebrates / Q000033:anatomy & histology*; D008974:Mollusca / Q000033:anatomy & histology*; D013045:Species Specificity
Pervyĭ opyt primeneniia riada obobshchennykh zolotykh proportsiĭ k izucheniiu rakovin dvustvorchatykh molliuskov i brakhiopod.