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Piecewise truncated conical minimal surfaces and the Gauss hypergeometric functions

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概要 The catenary is the curve which a hanging chain forms, that is, mathematically, the graph of the function t ↦ c cosh t/c for a constant c > 0. The study of catenaries is applied to the design of arche...s 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.続きを見る

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登録日 2012.05.25
更新日 2019.09.26

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