Mathematics in the Time of the Pharaohs

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In this carefully researched study, the author examines Egyptian mathematics, demonstrating that although operations were limited in number, they were remarkably adaptable to a great many applications: solution of problems in direct and inverse proportion, linear equations of the first degree, and arithmetical and geometrical progressions.

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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

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