Mathematics in the Time of the Pharaohs - Brossura

Gillings, Richard J.

Brossura

ISBN 10: 048624315X ISBN 13: 9780486243153

Casa editrice: Dover Pubns, 1982

Riassunto

In the past, scholars have tended to dismiss the mathematics of the ancient Egyptians as "child's play," compared with the achievements of the Greeks and other later civilizations. Nevertheless, in a society that achieved the marvelous accuracy of construction revealed in the Pyramids, extensive systems of irrigation canals, the erection of large granaries, levying and collecting of taxes, and other evidences of a well-organized and highly developed culture, mathematics must have played a major role.
In this remarkably erudite work, the first book-length study of ancient Egyptian mathematics, Professor Gillings examines the development of Egyptian mathematics from its origins in commercial and practical computations to such accomplishments as the solution of problems in direct and inverse proportion; the solution of linear equations of the first degree; determining the sum of arithmetical and geometrical progressions, and the use of rudimentary trigonometric functions in describing the slopes of pyramids. Drawing on all the extant sources — Egyptian Mathematical Leather Roll, the Reisner Papyri, the Moscow Mathematical Papyrus, and, most extensively, the Rhind Mathematical Papyrus, a training manual for scribes- the author shows that although the mathematical operations of the ancient Egyptians were limited in number, they were adaptable to a great many applications. Professor Gillings is also at pains to debunk such myths as the numerical mysticism that arose in connection with the construction of the great Pyramids, and the oft-repeated assertion that the Egyptians were conversant with the Pythagorean Theorem.
Enhanced with photographs of age-old papyri and other artifacts, as well as the author's own calligraphic renderings of hieroglyphic and hieratic words and numerals, this carefully researched and well-presented study will fascinate Egyptologists, mathematicians, engineers, archaeologists, and any student or admirer of the remarkable civilization that flourished on the shores of the Nile so many centuries ago.

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Contenuti

PREFACE Introduction Hieroglyphic and Hieratic Writing and Numbers The Four Arithmetic Operations ADDITION AND SUBTRACTION MULTIPLICATION DIVISION FRACTIONS The Two-Thirds Table for Fractions PROBLEMS 61 AND 61B OF THE RHIND MATHEMATICAL PAPYRUS TWO-THIRDS OF AN EVEN FRACTION AN EXTENSION OF RMP 61B AS THE SCRIBE MAY HAVE DONE IT EXAMPLES FROM THE RHIND MATHEMATICAL PAPYRUS OF THE TWO-THIRDS TABLE The G Rule in Egyptian Arithmetic FURTHER EXTENSIONS OF THE G RULE The Recto of the Rhind Mathematical Papyrus THE DIVISION OF 2 BY THE ODD NUMBERS 3 TO 101 CONCERNING PRIMES FURTHER COMPARISONS OF THE SCRIBE'S AND THE COMPUTERS DECOMPOSITIONS The Recto Continued EVEN NUMBERS IN THE RECTO: 2 ÷ 13 MULTIPLES OF DIVISORS IN THE RECTO TWO DIVIDED BY THIRTY-FIVE: THE SCRIBE DISCLOSES HIS METHOD Problems in Completion and the Red Auxiliaries USE OF THE RED AUXILIARIES OR REFERENCE NUMBERS AN INTERESTING OSTRACON The Egyptian Mathematical Leather Roll THE FIRST GROUP THE SECOND GROUP THE THIRD GROUP THE FOURTH GROUP THE NUMBER SEVEN LINE 10 OF THE FOURTH GROUP THE FIFTH GROUP Unit-Fraction Tables UNIT-FRACTION TABLES OF THE RHIND MATHEMATICAL PAPYRUS PROBLEMS 7 TO 20 OF THE RHIND MATHEMATICAL PAPYRUS Problems of Equitable Distribution and Accurate Measurement DIVISION OF THE NUMBERS 1 TO 9 BY 10 CUTTING UP OF LOAVES SALARY DISTRIBUTION FOR THE PERSONNEL OF THE TEMPLE OF ILLAHUN Pesu Problems EXCHANGE OF LOAVES OF DIFFERENT PESUS Area and Volumes THE AREA OF A RECTANGLE THE AREA OF A TRIANGLE THE AREA OF A CIRCLE THE VOLUME OF A CYLINDRICAL GRANARY THE DETAILS OF KAHUN IV Equations of the First and Second Degree THE FIRST GROUP SIMILAR PROBLEMS FROM OTHER PAPYRI THE SECOND AND THIRD GROUPS EQUATIONS OF THE SECOND DEGREE KAHUN LV "SUGGESTED RESTORATION OF MISSING LINES OF KAHUN LV 4, AND MODERNIZATION OF OTHERS" Geometric and Arithmetic Progressions GEOMETRIC PROGRESSIONS: PROBLEM 79 OF THE RHIND MATHEMATICAL PAPYRUS ARITHMETIC PROGRESSIONS: PROBLEM 40 OF THE RHIND MATHEMATICAL PAPYRUS KAHUN IV "Think of a Number" Problems" PROBLEM 28 OF THE RHIND MATHEMATICAL PAPYRUS PROBLEM 29 OF THE RHIND MATHEMATICAL PAPYRUS Pyramids and Truncated Pyramids THE SEKED OF A PYRAMID THE VOLUME OF A TRUNCATED PYRAMID The Area of a Semicylinder and the Area of a Hemisphere Fractions of a Hekat Egyptian Weights and Measures Squares and Square Roots The Reisner Papyri: The Superficial Cubit and Scales of Notation APPENDIX 1 The Nature of Proof APPENDIX 2 The Egyptian Calendar APPENDIX 3 Great Pyramid Mysticism APPENDIX 4 "Regarding Morris Kline's Views in Mathematics, A Cultural Approach" APPENDIX 5 The Pythagorean Theorem in Ancient Egypt APPENDIX 6 The Contents of the Rhind Mathematical Papyrus APPENDIX 7 The Contents of the Moscow Mathematical Papyrus APPENDIX 8 A Papyritic Memo Pad APPENDIX 9 "Horus-Eye Fractions in Terms of Hinu: Problems 80, 81 of the Rhind Mathematical Papyrus" APPENDIX 10 The Egyptian Equivalent of the Least Common Denominator APPENDIX 11 A Table of Two-Term Equalities for Egyptian Unit Fractions APPENDIX 12 "Tables of Hieratic Integers and Fractions, Showing Variations" APPENDIX 13 Chronology APPENDIX 14 A Map of Egypt APPENDIX 15 The Egyptian Mathematical Leather Roll BIBLIOGRAPHY INDEX

Product Description

Used book

Dettagli dell'edizione

• Editore: Dover Pubns
• Data di pubblicazione: 1982
• Lingua: Inglese
• ISBN 10: 048624315X
• ISBN 13: 9780486243153
• Rilegatura: Copertina flessibile
• Numero di pagine: 286
• Contatto del produttore: non disponibile
• Persona responsabile: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italia