An approximation of a catenoid constructed from piecewise truncated conical minimal surfaces
Abstract
We consider an appoximation of a catenoid constructed from "odd" truncated cones that maintains minimality in a certain sense. Thorough this procedure, we obtain a discrete curve approximating a catenary by exploiting the fact that it is the function that generates a catenoid. In this investigation, the theory of the Gauss hypergeomtric functions plays an important role. This work is a sequel to [Y.Machigashira, Piecewise truncated conical minimal surfaces and the Gauss hypergeometric functions, Journal of Math-for-Industry 4(2012), pp. 25-33 ]. The paper covers an appoximation of a catenoid constructed from "even" truncated cones that maintains minimality in the same sense. Keywords: catenary, catenoid, truncated cone, hypergeomtric function, Chebyshev polynomial of the third kind.
Keywords
Cite
@article{arxiv.1207.5920,
title = {An approximation of a catenoid constructed from piecewise truncated conical minimal surfaces},
author = {Akihito Ebisu and Yoshiroh Machigashira},
journal= {arXiv preprint arXiv:1207.5920},
year = {2012}
}
Comments
17 pages, 2 figures