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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Mylar balloon (geometry) ： ウィキペディア英語版 Mylar balloon (geometry) In geometry, a mylar balloon is a surface of revolution. While a sphere is the surface that encloses a maximal volume for a given surface area, the mylar balloon instead maximizes volume for a given generatrix arc length. It resembles a slightly flattened sphere. The shape is approximately realized by inflating a physical balloon made of two circular sheets of flexible, inelastic material; for example, a popular type of toy balloon made of aluminized plastic. Perhaps counterintuitively, the surface area of the inflated balloon is less than the surface area of the circular sheets. This is due to physical crimping of the surface, which increases near the rim. "Mylar balloon" is the name for the figure given by W. Paulson, who first investigated the shape. The term was subsequently adopted by other writers. "Mylar" is a trademark of DuPont. == Definition == The positive portion of the generatrix of the balloon is the function ''z''(''x'') where for a given generatrix length ''a'': :$z(r)=0$ :$\backslash int\_0^r\; \backslash !\backslash sqrt\backslash ,dx\; \backslash ,\; =\; a$ (i.e.: the generatrix length is given) :$\backslash int\_0^r\; \backslash !\; 4\backslash pi\; x\; z(x)\; \backslash ,\; dx$ is a maximum (i.e.: the volume is maximum) Here, the radius ''r'' is determined from the constraints. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Mylar balloon (geometry)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.