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Stereological Implications of the Geometry of Cones
Author(s) -
GualArnau X.
Publication year - 1997
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710390509
Subject(s) - curvature , cone (formal languages) , geometry , stereology , tortuosity , mathematics , surface (topology) , mathematical analysis , geology , medicine , geotechnical engineering , algorithm , porosity
Given a cone around a curve β in IR 3 it is shown that there is no relation between the curvature of β and the volume of the cone but, in contrast to the volume, the surface area of the cone depends, albeit rather weakly, on the curvature of β. The geometric meaning of the stereological formulae when applied to cones is considered and it is noted that stereological methods to estimate the surface area of a cone need to be extremely precise to provide information concerning curvature or tortuosity.