AN APPROXIMATION OF A CATENOID CONSTRUCTED FROM PIECEWISE TRUNCATED CONICAL MINIMAL SURFACES

Abstract

In the second author's previous work, we considered an approximation of a catenoid constructed from even truncated cones that maintains minimality in a certain sense. In this paper, we consider such an approximation consisting of odd truncated cones that maintains minimality in the same sense. Through 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 hypergeometric functions plays an important role.