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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 geometry ： ウィキペディア英語版 Egyptian geometry ''Egyptian geometry'', as that term is used in this article, refers to geometry as it was developed and used in Ancient Egypt. Ancient Egyptian mathematics as discussed here spans a time period ranging from ca. 3000 BC to ca 300 BC. We only have a limited number of problems from ancient Egypt that concern geometry. Geometric problems appear in both the Moscow Mathematical Papyrus (MMP) and in the Rhind Mathematical Papyrus (RMP). The examples demonstrate that the Ancient Egyptians knew how to compute areas of several geometric shapes and the volumes of cylinders and pyramids. Also the Egyptians used many sacred geometric shapes such as squares and triangles on temples and obelisks. ==Area== The Ancient Egyptians wrote out their problems in multiple parts. They gave the title and the data for the given problem, in some of the texts they would show how to solve the problem, and as the last step they verified that the problem was correct. The scribes did not use any variables and the problems were written in prose form. The solutions were written out in steps, outlining the process. b h b = base, h = height |- | rectangles|| Problem 49 in RMP and problems 6 in MMP and Lahun LV.4. problem 1 || $A\; =\; b\; h$ b = base, h = height |- | circle || Problems 51 in RMP and problems 4, 7 and 17 in MMP|| $A\; =\; \backslash frac\; (\backslash frac)\; d^2$ d= diameter. This uses the value 256/81 = 3.16049... for $\backslash pi\; =\; 3.14159...$ |- | hemisphere || Problem 10 in MMP || |} Triangles: The Ancient Egyptians knew that the area of a triangle is $A\; =\; \backslash frac\; b\; h$ where ''b'' = base and ''h'' = height. Calculations of the area of a triangle appear in both the RMP and the MMP.〔Clagett, Marshall Ancient Egyptian Science, A Source Book. Volume Three: Ancient Egyptian Mathematics (Memoirs of the American Philosophical Society) American Philosophical Society. 1999 ISBN 978-0-87169-232-0〕 Rectangles: Problem 49 from the RMP finds the area of a rectangular plot of land〔 Problem 6 of MMP finds the lengths of the sides of a rectangular area given the ratio of the lengths of the sides. This problem seems to be identical to one of the Lahun Mathematical Papyri in London. The problem is also interesting because it is clear that the Egyptians were familiar with square roots. They even had a special hieroglyph for finding a square root. It looks like a corner and appears in the fifth line of the problem. We suspect that they had tables giving the square roots of some often used numbers. No such tables have been found however.〔R.C. Archibald Mathematics before the Greeks Science, New Series, Vol.71, No. 1831, (Jan. 31, 1930), pp.109-121〕 Problem 18 of the MMP computes the area of a length of garment-cloth.〔 The Lahun PapyrusProblem 1 in LV.4 is given as: ''An area of 40 "mH" by 3 "mH" shall be divided in 10 areas, each of which shall have a width that is 1/2 1/4 of their length.''〔Anette Imhausen Digitalegypt website: Lahun Papyrus (IV.3 )〕 A translation of the problem and its solution as it appears on the fragment is given on the website maintained by University College London.〔Anette Imhausen Digitalegypt website: Lahun Papyrus (LV.4 )〕 Circles: Problem 48 of the RMP compares the area of a circle (approximated by an octagon) and its circumscribing square. This problem's result is used in problem 50. ''Trisect each side. Remove the corner triangles. The resulting octagonal figure approximates the circle. The area of the octagonal figure is: '' $9^2\; -4\; \backslash frac\; (3)\; (3)\; =\; 63$ Next we approximate 63 to be 64 and note that $64=8^2$ ''Thus the number $4(\backslash frac)^2\; =\; 3.16049...$ plays the role of π = 3.14159.... That this octagonal figure, whose area is easily calculated, so accurately approximates the area of the circle is just plain good luck. Obtaining a better approximation to the area using finer divisions of a square and a similar argument is not simple.'' 〔 Problem 50 of the RMP finds the area of a round field of diameter 9 khet.〔 This is solved by using the approximation that circular field of diameter 9 has the same area as a square of side 8. Problem 52 finds the area of a trapezium with (apparently) equally slanting sides. The lengths of the parallel sides and the distance between them being the given numbers.〔 Hemisphere: Problem 10 of the MMP computes the area of a hemisphere.〔 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 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.