Expansion formulae for Bessel functions in series of Bessel functions
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This article explores the use of the euclidian algorithm as a most useful way of handling ratios, especially when good rational approximations are required. Illustrations are taken from a discussion of the analysis of greek architecture by J.J Coulton. Although this is intended as a practical account, some discussions of theoretical aspects are included, and also of the relationship of this procedure to a new interpretation of early greek mathematics.