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When One Form Is between Two Others: An Application of Biorthogonal Analysis

Fred L. Bookstein
American Zoologist
Vol. 20, No. 4, Analysis of Form (1980), pp. 627-641
Published by: Oxford University Press
Stable URL: http://www.jstor.org/stable/3882695
Page Count: 15
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When One Form Is between Two Others: An Application of Biorthogonal Analysis
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Abstract

This essay presents a method for measuring the degree to which one biological outline form lies in between two others. The procedure does not measure forms separately, but rather compares pairs of tensors expressing D'Arcy Thompson's "Cartesian transformations" according to the biorthogonal formalism of Bookstein. In analogy with conventional methods, betweenness is computed as a similarity score, the cosine of a non-Euclidean angle between the tensors. The new quantities, size-betweenness and shape-betweenness, enable comparisons of form series against a priori orderings intra- and interspecifically.

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