Abstract

The mathematical technique of R-mode factor analysis was applied to the long, intermediate and short axes of one synthetic random data set and three sets of natural pebbles to extract the three fundamental factors related to these parameters. One factor corresponds to size, which is best described by the mean of the axes. Two further factors correspond to shape: sphericity and disc-rodness. These factors are revealed whether synthetic data or natural pebble samples are analyzed. Extending the factor analysis to include shape indices revealed which indices are equivalent, which are most useful, and which should be discarded. Sphericity is best described with the Corey shape index, S/(IL) (super 1/2) , and disc-rodness is best described with the disc-rod index, (L - I)/(L - S). Accordingly, the most effective shape diagram is a triangular plot of these two shape indices; the three end-members of shape are spheres, discs and rods. Shape is best investigated using this shape diagram; a 2-D technique such as contouring point density on this diagram should be used to determine the mean and standard deviation of shape. "While others ask themselves 'What is there to do?', I ask myself 'What is there that I can avoid doing?'" Masanobu Fukuoka, One Straw Revolution

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