English

An approximation of a catenoid constructed from piecewise truncated conical minimal surfaces

Differential Geometry 2012-07-26 v1 Classical Analysis and ODEs

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