• Allometry;
  • fossil;
  • gastropod;
  • isometry;
  • mathematical model;
  • Theorem of Pappus;
  • whorl

Mathematical models of shells enable researchers to estimate the maximum possible sizes of organisms that once occupied fossil shells. In this study, a whorl-by-whorl method of determining coiled shell volumes and surface areas is introduced. The whorl-by-whorl analysis yielded results that were more accurate than those obtained from a model that assumes isometric growth, when both were used to calculate volumes of gastropod shells. The whorl-by-whorl method is more laborious, but it is better suited for the analysis of shells exhibiting allometric variation than are methods that use models of isometric growth.