Archimedes' balance and Bianchi's Backlund transformation for quadrics
Ion Dinca
TL;DR
This paper connects Archimedes' classical geometric integration methods with Bianchi's Backlund transformation for quadrics, revealing a novel link between ancient geometry and modern integrable systems.
Contribution
It introduces a new relationship between Archimedes' geometric approach and Bianchi's Backlund transformation, bridging classical and modern mathematical techniques.
Findings
Established a link between Archimedes' method and Bianchi's transformation
Demonstrated factorization via moments of a balance for quadrics
Connected ancient geometry with integrable systems theory
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.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Mathematics and Applications · Nonlinear Waves and Solitons