Archimedes' balance and Bianchi's Backlund transformation for quadrics

Details Archimedes' balance and Bianchi's Backlund transformation for quadrics Archimedes' balance and Bianchi's Backlund transformation for quadrics

2007-09-26

arxiv.org/abs/0709.4222v3

Mathematics

Differential Geometry

11 pages, 1 figure; third improved version to be resubmitted for publication

Scientific paper

We establish a link between Archimedes' method of integration for calculating
areas, volumes and centers of mass of segments of parabolas and quadrics of
revolution by factorization via the moments of a balance and an integration
technique for a particular integrable system, namely Bianchi's B\"{a}cklund
transformation for quadrics.

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