Open AccessJournal Article
Geometric analysis of shell coiling; general problems
TL;DR: In this article, the spectrum of possible shell forms is shown by a block diagram, where functional and evolutionary groups are confined to discrete regions of the spectrum and three parameters are considered at a time.
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Abstract: Among the shells of invertebrates that exhibit spiral growth, differences in form can be expressed by differences in geometric parameters. If three parameters are considered at a time, the spectrum of possible shell forms may be shown by a block diagram. Analog and digital computer constructions make it possible to visualize shell forms that are theoretically possible but do not occur in nature. Actual species are not randomly distributed in the total spectrum of theoretically possible forms. Functional and evolutionary groups are confined to discrete regions of the spectrum. For example, a bivalve must have non-overlapping whorls in order to have a functional hinge. This fact restricts the geometric range of both brachiopods and bivalved molluscs. Ontogenetic change in coiling geometry may be interpreted as compensation for effects of increase in absolute size during growth.
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References
•Book
On Growth and Form
D'Arcy Wentworth Thompson
- 01 Jan 1917
TL;DR: This book is an application of some of the concepts of physical science and sundry mathematical methods to the study of organic form and is like one of Darwin's books, well-considered, patiently wrought-out, learned, and cautious.
4.9K
The geometry of coiling in gastropods.
TL;DR: A chronology of key events leading to and after the publication of the Biological Problems of Grafting, edited by F. Albert and P. B. Medawar:.
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On the Geometrical Forms of Turbinated and Discoid Shells
TL;DR: The surface of any turbinated or discoid shell may be imagined to be generated by the revolution about a fixed axis (the axis of the shell) of the perimeter of a geometrical figure, which, remaining always geometrically similar to itself, increases continually its dimensions.
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The growth and form of brachiopod shells
TL;DR: In this paper, the authors analyse the shell form of brachiopod shells in terms of the rates of growth, the rate at each point being resolved into component rates, and two major varieties of external hinge structure are defined: strophic shells have a true hinge line and may also have interareas; non-strophic shells have no true hinge lines but may have palintropes.
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