Random uniform triangles and the alignment problem

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Abstract
Let n points be drawn independently and uniformly from a compact convex set K. The distribution of the shape of the resulting n–ad is determined and studied in the region corresponding to near alignment. Special attention is given to the case n ≥ 4 and a table provided to help in the assessment of practical data (e.g. megalithic ‘alignments’). The Broadbent factor, representing the effect of stretching the parent distribution, is computed explicitly.

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