Archimedes' balance and Bianchi's Backlund transformation for quadrics

Abstract

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 Bäcklund transformation for quadrics.

arXiv comment11 pages, 1 figure; fourth improved version to be resubmitted for publication. arXiv admin note: substantial text overlap with arXiv:math/0612375