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The Lahun Mathematical Papyri (also known as the Kahun Mathematical Papyri) are part of a collection of Kahun Papyri discovered at El-Lahun (also known as Lahun, Kahun or Il-Lahun) by Flinders Petrie during excavations of a worker's town near the pyramid of Sesostris II. The Kahun Papyrus are a collection of texts including administrative texts, medical texts, veterinarian texts and six fragments devoted to mathematics.〔(The Lahun Papyri ) at University College London〕 The mathematical texts most commented on are usually named: * Lahun IV.2 (or Kahun IV.2) ((UC 32159 )): This fragment contains a table of Egyptian fraction representations of numbers of the form 2/''n''. A more complete version of this table of fractions is given in the Rhind Mathematical Papyrus.〔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; Annette Imhausen, Jim Ritter: ''Mathematical Fragments'', In: Marc Collier, Stephen Quirke: ''The UCL Lahun Papyri: Religious, Literary, Legal, Mathematical and Medical'', Oxford 2004, ISBN 1-84171-572-7, 92-93〕 * Lahun IV.3 (or Kahun IV.3) ((UC 32160 )) contains numbers in arithmetical progression and a problem very much like problem 40 of the Rhind Mathematical Papyrus.〔〔Annette Imhausen, Jim Ritter: ''Mathematical Fragments'', In: Marc Collier, Stephen Quirke: ''The UCL Lahun Papyri: Religious, Literary, Legal, Mathematical and Medical'', Oxford 2004, ISBN 1-84171-572-7, 84-85〕〔Legon, J., A Kahun mathematical fragment, retrieved from (), based on Discussions in Egyptology 24 (1992), p.21-24〕 Another problem on this fragment computes the volume of a cylindrical granary.〔Gay Robins and Charles Shute, "The Rhind Mathematical Papyrus", British Museum Press, Dover Reprint, 1987.〕 In this problem the scribe uses a formula which takes measurements in ''cubits'' and computes the volume and expresses it in terms of the unit ''khar''. Given the diameter (d) and height (h) of the cylindrical granary: :. : In modern mathematical notation this is equal to : (measured in khar). : This problem resembles problem 42 of the Rhind Mathematical Papyrus. The formula is equivalent to measured in cubic-cubits as used in the other problems.〔Katz, Victor J. (editor),Imhausen, Annette et al. The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton University Press. 2007 ISBN 978-0-691-11485-9〕 * Lahun XLV.1 (or Kahun XLV.1) ((UC 32161 )) contains a group of very large numbers (hundreds of thousands).〔〔Annette Imhausen, Jim Ritter: ''Mathematical Fragments'', In: Marc Collier, Stephen Quirke: ''The UCL Lahun Papyri: Religious, Literary, Legal, Mathematical and Medical'', Oxford 2004, ISBN 1-84171-572-7, 94-95〕 * Lahun LV.3 (or Kahun LV.3) ((UC 32134A ) and (UC 32134B )) contains a so-called aha problem which asks one to solve for a certain quantity. The problem resembles ones from the Rhind Mathematical Papyrus (problems 24-29).〔〔Annette Imhausen, Jim Ritter: ''Mathematical Fragments'', In: Marc Collier, Stephen Quirke: ''The UCL Lahun Papyri: Religious, Literary, Legal, Mathematical and Medical'', Oxford 2004, ISBN 1-84171-572-7, 74-77〕 * Lahun LV.4 (or Kahun LV.4) ((UC 32162 )) contains what seems to be an area computation and a problem concerning the value of ducks, geese and cranes.〔〔Annette Imhausen, Jim Ritter: ''Mathematical Fragments'', In: Marc Collier, Stephen Quirke: ''The UCL Lahun Papyri: Religious, Literary, Legal, Mathematical and Medical'', Oxford 2004, ISBN 1-84171-572-7, 78-79〕 The problem concerning fowl is a baku problem and most closely resembles problem 69 in the Rhind Mathematical Papyrus and problems 11 and 21 in the Moscow Mathematical Papyrus.〔(UC 32162 Lahun LV.4 )〕 * Unnamed fragment ((UC 32118B )). This is a fragmentary piece.〔Annette Imhausen, Jim Ritter: ''Mathematical Fragments'', In: Marc Collier, Stephen Quirke: ''The UCL Lahun Papyri: Religious, Literary, Legal, Mathematical and Medical'', Oxford 2004, ISBN 1-84171-572-7, 90-91〕 ==The 2/''n'' tables== The Lahun papyrus IV.2 reports a 2/''n'' table for odd ''n'', ''n'' = 1, , 21. The Rhind Mathematical Papyrus reports an odd ''n'' table up to 101.〔Imhausen, Annette, Ancient Egyptian Mathematics: New Perspectives on Old Sources, The Mathematical Intelligencer, Vol 28, Nr 1, 2006, pp. 19–27〕 These fraction tables were related to multiplication problems and the use of unit fractions, namely n/p scaled by LCM m to mn/mp. With the exception of 2/3, all fractions were represented as sums of unit fractions (i.e. of the form 1/n), first in red numbers. Multiplication algorithms and scaling factors involved repeated doubling of numbers, and other operations. Doubling a unit fraction with an even denominator was simple, divided the denominator by 2. Doubling a fraction with an odd denominator however results in a fraction of the form 2/n. The RMP 2/n table and RMP 36 rules allowed scribes to find decompositions of 2/n into unit fractions for specific needs, most often to solve otherwise un-scalable rational numbers (i.e. 28/97 in RMP 31,and 30/53 n RMP 36 by substituting 26/97 + 2/97 and 28/53 + 2/53) and generally n/p by (n - 2) /p + 2/p. Decompositions were unique. Red auxiliary numbers selected divisors of denominators mp that best summed to numerator mn. 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「Lahun Mathematical Papyri」の詳細全文を読む スポンサード リンク
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