## JMI2012A-4 Piecewise truncated conical minimal surfaces and the Gauss hypergeometric functions (pp.25-33)

Author(s)： Yosiroh Machigashira

J. Math-for-Ind. **4A** (2012) 25-33.

- File： JMI2012A-4.pdf (137KB)

Abstract

The catenary is the curve which a hanging chain forms, that is, mathematically, the graph of the function $t \mapsto c \cosh\frac{t}{c}$ for a constant $c > 0$. The study of catenaries is applied to the design of arches and suspension bridges. The surface of revolution generated by a catenary is called a catenoid. It is well-known that a catenoid is a minimal surface and the shape which a soap film between two parallel circles forms. In this article, we consider the approximation of a catenoid by combinations of some truncated cones keeping the minimality in a certain sense. In investigating the *minimal* combinations, the theory of the Gauss hypergeometric functions plays an important role.

Keyword(s). catenoid, hypergeometric function, truncated cone