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Lead and slant on the geometry of coiling in gastropods
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Authors
Ido Filin 
Abstract
Molluscan shells have been studied with various geometric models. Here I show that lead angle, the defining slope of a conical helix, emerges as a more useful parameter in morphometric analyses and (adaptationist) interpretation of covariation in coiling parameters. The widely used apical semiangle becomes redundant and uninformative, a passive consequence of taxon-specific lead angles and plasticity in growth (expansion rate). Treating coiled shells as conical helices, and extending to logarithmic slant helices (curves of precession), provides insights into ontogenetic allometry, irregular coiling, previously formulated shell models, and unifying fixed- and moving-frame approaches.
DOI
https://doi.org/10.32942/X28Q23
Subjects
Ecology and Evolutionary Biology, Evolution, Life Sciences, Other Ecology and Evolutionary Biology, Physical Sciences and Mathematics
Keywords
allometry, Developmental plasticity, Theoretical morphology, morphometrics, Mollusc, Molluscan shell, ontogeny, conical helix, slant helix, Conchology, Logarithmic spiral, Differential geometry
Dates
Published: 2026-05-01 14:15
Last Updated: 2026-05-01 14:15
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License
CC-By Attribution-NonCommercial-NoDerivatives 4.0 International
Additional Metadata
Data and Code Availability Statement:
Dataset: https://doi.org/10.5281/zenodo.19763621 , Webapp: https://doi.org/10.5281/zenodo.19762139
Language:
English
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