2012/07/25 by Akihito Ebisu, Ebisu, Akihito, Yoshiroh Machigashira +1
Computer Science · Mathematics · #33C05 #33C45 #53A04 #53A05 #53A10 #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Rough Sets and Fuzzy Logic #math.CA #math.DG #msc:33C05 #msc:33C45 #msc:53A04 #msc:53A05 #msc:53A10
paper · pdf · doi:10.48550/arxiv.1207.5920
17 pages, 2 figures
arxiv created 2012/07/25 · openalex publication_date 2012/07/25 · arxiv updated 2012/07/26 · openalex created_date 2022/10/07 · openalex updated_date 2026/08/04
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.