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''Circle Limit III'' is a woodcut made in 1959 by Dutch artist M. C. Escher, in which "strings of fish shoot up like rockets from infinitely far away" and then "fall back again whence they came".〔Escher, as quoted by .〕 It is one of a series of four woodcuts by Escher depicting ideas from hyperbolic geometry. Dutch physicist and mathematician Bruno Ernst called it "the best of the four".〔.〕 ==Inspiration== Escher became interested in tesselations of the plane after a 1936 visit to the Alhambra in Granada, Spain,〔.〕〔.〕 and from the time of his 1937 artwork ''Metamorphosis I'' he had begun incorporating tessellated human and animal figures into his artworks.〔 In a 1958 letter from Escher to H. S. M. Coxeter, Escher wrote that he was inspired to make his ''Circle Limit'' series by a figure in Coxeter's article "Crystal Symmetry and its Generalizations".〔〔 Coxeter's figure depicts a tessellation of the hyperbolic plane by right triangles with angles of 30°, 45°, and 90°; triangles with these angles are possible in hyperbolic geometry but not in Euclidean geometry. This tessellation may be interpreted as depicting the lines of reflection and fundamental domains of the (6,4,2) triangle group.〔Coxeter expanded on the mathematics of triangle group tessellations, including this one in .〕 An elementary analysis of Coxeter's figure, as Escher might have understood it, is given by .〔.〕 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「Circle Limit III」の詳細全文を読む スポンサード リンク
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