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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 Egyptian Mathematical Leather Roll ： ウィキペディア英語版 Egyptian Mathematical Leather Roll The Egyptian Mathematical Leather Roll (EMLR) was a 10 × 17 in (25 × 43 cm) leather roll purchased by Alexander Henry Rhind in 1858. It was sent to the British Museum in 1864, along with the Rhind Mathematical Papyrus, but the former was not chemically softened and unrolled until 1927 (Scott, Hall 1927). The writing consists of Middle Kingdom hieratic characters written right to left. Scholars date the EMLR to the 17th century BCE.〔Clagett, Marshall. Ancient Egyptian Science: A Source Book. Volume 3: Ancient Egyptian Mathematics. Memoirs of the American Philosophical Society 232. Philadelphia: American Philosophical Society, 1999, pp. 17–18, 25, 37–38, 255–257〕 ==Mathematical content== This leather roll is an aid for computing Egyptian fractions. It contains 26 sums of unit fractions which equal another unit fraction. The sums appear in two columns, and are followed by two more columns which contain exactly the same sums.〔Annette Imhausen, in The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Edited by Victor J. Katz, 2007, pp. 21–22〕 + \frac = \frac || $\backslash frac\; +\; \backslash frac\; +\; \backslash frac=\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ |- | $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ |- | $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ |- | $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ |- | $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ |- | $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ |- | $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ |- | $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |- | $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |- | $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || || $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |- | $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |- | $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || || $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |- | $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |- | $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || || $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |- | $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || || $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |- | $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || || $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |- | $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || || $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |- | || || $\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |- | || || $\backslash frac\; +\; \backslash frac\; =\; \backslash frac$ || |} Of the 26 rational numbers listed, ten are Eye of Horus numbers: 1/2, 1/4 (twice), 1/8 (thrice), 1/16 (twice), 1/32, 1/64 converted to Egyptian fractions. There are seven other even rational numbers converted to Egyptian fractions: 1/6 (listed twice–but wrong once), 1/10, 1/12, 1/14, 1/20 and 1/30. Finally, there were nine odd rational numbers converted to Egyptian fractions: 2/3, 1/3 (twice), 1/5, 1/7, 1/9, 1/11, 1/13 and 1/15, training patterns for scribal students to learn the RMP 2/n table method. The British Museum examiners found no introduction or description to how or why the equivalent unit fraction series were computed.〔Gillings, Richard J. “The Egyptian Mathematical Leather Role–Line 8. How Did the Scribe Do it?” (Historia Mathematica 1981), 456–457.〕 Equivalent unit fraction series are associated with fractions 1/3, 1/4, 1/8 and 1/16. There was a trivial error associated with the final 1/15 unit fraction series. The 1/15 series was listed as equal to 1/6. Another serious error was associated with 1/13, an issue that the 1927 examiners did not attempt to resolve. 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「Egyptian Mathematical Leather Roll」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.