Archimedes' balance and Bianchi's Backlund transformation for quadrics
Differential Geometry
2012-05-30 v4
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 B\"{a}cklund transformation for quadrics.
Keywords
Cite
@article{arxiv.0709.4222,
title = {Archimedes' balance and Bianchi's Backlund transformation for quadrics},
author = {Ion Dinca},
journal= {arXiv preprint arXiv:0709.4222},
year = {2012}
}
Comments
11 pages, 1 figure; fourth improved version to be resubmitted for publication. arXiv admin note: substantial text overlap with arXiv:math/0612375