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The moving sofa problem was formulated by the Austrian-Canadian mathematician Leo Moser in 1966. The problem is a two-dimensional idealisation of real-life furniture moving problems, and asks for the rigid two-dimensional shape of largest area ''A'' that can be maneuvered through an L-shaped planar region with legs of unit width. The area ''A'' thus obtained is referred to as the ''sofa constant''. The exact value of the sofa constant is an open problem. ==Lower and upper bounds== As a semicircular disk of unit radius can pass through the corner, a lower bound for the sofa constant is readily obtained. John Hammersley derived a considerably higher lower bound based on a handset-type shape consisting of two quarter-circles of radius 1 on either side of a 1 by 4/π rectangle from which a semicircle of radius has been removed.〔(Moving Sofa Constant ) by Steven Finch at MathSoft, includes a diagram of Gerver's sofa〕 Joseph Gerver found a sofa that further increased the lower bound for the sofa constant to 2.219531669. In a different direction, an easy argument by Hammersley shows that the sofa constant is at most . 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「Moving sofa problem」の詳細全文を読む スポンサード リンク
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