Mathematical determination of coiled shell volumes and surface areas

Lethaia

Volumn 30, Issue 3, 1997, Pages 213-219

  Stone, Jon R ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Allometry; Fossil; Gastropod; Isometry; Mathematical model; Theorem of Pappus; Whorl

Indexed keywords

GASTROPODA;

ALLOMETRY; COILED SHELL; GASTROPOD; ISOMETRY; MATHEMATICAL MODEL; WHORL;

EID: 0031461572     PISSN: 00241164     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1502-3931.1997.tb00463.x     Document Type: Article

References (16)

1. Cain, A.J. 1981: Possible ecological significance of variation in shape of Cerion shells with age. Journal of Conchology 30, 305-315.
2. Gould, S.J. 1989: A developmental constraint in Cerion with comments on the definition and interpretation of constraint in evolution. Evolution 43, 516-539.
3. Heath, D.J. 1985: Whorl overlap and the economical construction of the gastropod shell. Biological Journal of the Linnean Society 24, 165-174.
4. Johnston, M.R., Tobachnick, R.E., & Bookstein, F.L. 1991: Landmark-based morphometrics of spiral accretionary growth. Paleobiology 17, 19-36.
5. Moseley, H. 1838: On the geometrical forms of turbinate and discoid shells. Philosophical Transactions of the Royal Society of London, 351-370.
6. Moseley, H. 1842: On conchyliometry. Philosophical Magazine, Series 3, 21, 300-305.
7. Raup, D.M. 1966: Geometric analysis of shell coiling: general problems. Journal of Paleontology 40, 1178-1190.
8. Raup, D.M., & Chamberlain Jr, J.A. 1967: Equations for volume and center of gravity in ammonoid shells. Journal of Paleontology 41, 566-574.
9. Raup, D.M. & Graus, R.R. 1972: General equations for volume and surface area of a logarithmically coiled shell. Mathematical Geology 4, 307-316.
10. Salas, S.L. & Hille, E. 1982. Calculus of One and Several Variables. 1136 pp. Wiley, Toronto.
11. Stone, J.R. 1995: CerioShell: a computer program designed to simulate variation in shell form. Paleobiology 21, 501-519.
12. Stone, J.R. 1996: Computer simulated shell shape variation in the Caribbean land snail genus Cerion: a test of geometric constraint. Evolution 50, 341-347.
13. Swokowski, E.W. 1984. Calculus. 720 pp. Wadsworth, Toronto.
14. Thompson, D.W. 1961: On Growth and Form. Cambridge University Press, London.
15. Trueman, A.E. 1941: The ammonite body chamber, with special reference to the buoyancy and mode of life of the living ammonite. Quarterly Journal of the Geological Society of London 96, 339-383.
16. Woodruff, D.S. 1978: Evolution and adaptive radiation of Cerion: a remarkably diverse group of West Indian land snails. Malacologia 17, 223-239.