Cylinders Through Five Points: Computational Algebra and Geometry

Daniel Lichtblau

Abstract


We address the following question: Given five points in \(\mathbb{R}^3\), determine a right circular cylinder containing
those points. We obtain algebraic equations for the axial line and radius parameters and show that these give six solutions in the generic case. An even number (0, 2, 4, or 6) will be real valued and hence correspond to actual cylinders in \(\mathbb{R}^3\). We will investigate computational and theoretical matters related to this problem. In particular we will show how exact and numeric Gr{\" o}bner bases, equation solving, and related symbolic-numeric methods may be used to advantage. We will also discuss some applications.

Full Text: PDF DOI: 10.5539/jmr.v4n6p65

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This work is licensed under a Creative Commons Attribution 3.0 License.

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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