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The Penrose triangle, also known as the Penrose tribar, is an impossible object. It was first created by the Swedish artist Oscar Reutersvärd in 1934. The psychologist Lionel Penrose and his mathematician son Roger Penrose independently devised and popularised it in the 1950s, describing it as "impossibility in its purest form". It is featured prominently in the works of artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it. ==Impossible object== The tribar appears to be a solid object, made of three straight beams of square cross-section which meet pairwise at right angles at the vertices of the triangle they form. The beams may be broken, forming cubes or cuboids; the logo of National Westminster Bank, comprising three chevrons that form a broken hexagon, has sometimes been depicted with the chevrons as two sides of cubes forming the corners of a Penrose triangle. This combination of properties cannot be realized by any 3-dimensional object in ordinary Euclidean space. Such an object can exist in certain Euclidean 3-manifolds.〔 In the chapter on the Penrose tribar, Francis attributes this observation to John Stillwell.〕 There also exist 3-dimensional solid shapes each of which, when viewed from a certain angle, appears the same as the 2-dimensional depiction of the Penrose triangle on this page (such as - for example - the image to the left depicting a sculpture in Perth, Australia). The term "Penrose triangle" can refer to the 2-dimensional depiction or the impossible object itself. M.C. Escher's lithograph ''Waterfall'' (1961) depicts a watercourse that flows in a zigzag along the long sides of two elongated Penrose triangles, so that it ends up two stories higher than it began. The resulting waterfall, forming the short sides of both triangles, drives a water wheel. Escher helpfully points out that in order to keep the wheel turning some water must occasionally be added to compensate for evaporation. If a line is traced around the Penrose triangle, a 3-loop Möbius strip is formed. 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「Penrose triangle」の詳細全文を読む スポンサード リンク
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