Mathematics in Ancient Egypt: A Contextual History

388 Pages·2016·5.24 MB·English

by  Annette Imhausen

Mathematics in Ancient Egypt
Mathematics in Ancient Egypt
A Contextual History
Annette Imhausen
Princeton University Press
Princeton and Oxford
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Jacket image: Model granary from tomb of Meketre. Middle Kingdom, ca. 1981–1975 B.C.
Wood, plaster, paint, linen, grain, H. 36.5 (14 3/8 in.); l. 74 (29 1/8 in.); w. 58 cm (22 13/16
in.).
Egyptian; Thebes, Meketre. Rogers Fund and Edward S. Harkness Gift, 1920 (20.3.11).
© The Metropolitan Museum of Art. Image source: Art Resource, NY
All Rights Reserved
Library of Congress Cataloging-in-Publication Data Imhausen, Annette.
Mathematics in ancient Egypt : a contextual history / Annette Imhausen.
pages cm
Includes bibliographical references and index.
ISBN 978-0-691-11713-3 (hardcover : alk. paper) 1. Mathematics, Egyptian. 2. Mathematics—
History. I. Title.
QA27.E3I43 2015
510.932—dc23
2015009708
British Library Cataloging-in-Publication Data is available This book has been composed in
Minion Pro.
Printed on acid-free paper. ∞
Printed on acid-free paper. ∞
Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
Contents
Preface ix
0. Introduction 1
0.1 Past Historiography 2
0.2 Aims of This Study 7
PREHISTORIC AND EARLY DYNASTIC PERIOD 11
1. The Invention of Writing and Number Notation 15
2. The Egyptian Number System 18
3. Uses of Numbers and Their Contexts in Predynastic and Early Dynastic Times 22
4. Summary 29
OLD KINGDOM 31
5. The Cultural Context of Egyptian Mathematics in the Old Kingdom 35
6. Metrological Systems 41
6.1 Length Units 41
6.2 Area Units 46
6.3 Capacity Units 48
6.4 Weights 49
7. Notation of Fractions 52
8. Summary 55
MIDDLE KINGDOM 57
9. Mathematical Texts (I): The Mathematical Training of Scribes 63
9.1 Extant Hieratic Mathematical Texts 63
 9.1.1 Rhind Mathematical Papyrus 65
 9.1.2 Lahun Mathematical Fragments 67
 9.1.3 Papyrus Berlin 6619 68
 9.1.4 Cairo Wooden Boards 68
 9.1.5 Mathematical Leather Roll 68
 9.1.6 Moscow Mathematical Papyrus 69
9.2 Teaching Mathematics: Mathematical Procedure Texts 70
 9.2.1 The Formal Elements of a Procedure Text 76
 9.2.2 Collections of Procedure Texts 79
9.3 Types of Mathematical Problems 81
10. Foundation of Mathematics 84
10.1 Arithmetic Techniques 84
 10.1.1 Multiplication of Integers 86
 10.1.2 Division of Integers 88
10.2 Fraction Reckoning 89
 10.2.1 Multiplications and Divisions Involving Fractions 90
 10.2.2 Using Auxiliary Numbers 91
10.3 Tables for Fraction Reckoning 92
 10.3.1 2 ÷ n Table 93
 10.3.2 Mathematical Leather Roll 96
10.4 Metrological Tables 99
10.5 Summary 101
11. Mathematics in Practice and Beyond 102
11.1 Distribution of Rations 104
 11.1.1 Ration Problems within the Mathematical Texts 105
 11.1.2 Calculation of Rations in Papyrus Berlin 10005 108
 11.1.3 Further Evidence 110
11.2 Architectural Calculations 112
 11.2.1 Architectural Problems within the Mathematical Texts 112
 11.2.2 Mathematics of Papyrus Reisner I 116
11.3 Land Measurement 117
 11.3.1 Area Calculations within the Mathematical Texts 118
 11.3.2 Evidence of Land Surveying 123
11.4 Summary 125
NEW KINGDOM 127
12. New Kingdom Mathematical Texts: Ostraca Senmut 153 and Turin 57170 131
13. Two Examples of Administrative Texts 133
13.1 Papyrus Harris I 134
13.2 Papyrus Wilbour 139
14. Mathematics in Literature 143
14.1 Mathematical Education 143
14.2 Mathematics in the Scribe’s Daily Work 146
14.3 Mathematics in Papyrus Anastasi I 148
 14.3.1 Digging a Lake (Papyrus Anastasi I, 13,6–13,7) 150
 14.3.2 Constructing a Brick Ramp (Papyrus Anastasi I, 13,8–14,8) 151
14.3.3 Transport of an Obelisk (Papyrus Anastasi I, 14,8–16,5) 152
 14.3.4 Erection of a Colossal Monument (Papyrus Anastasi I, 16,8–17,2) 154
 14.3.5 Rations for an Expedition (Papyrus Anastasi I, 17,2–18,2) 155
15. Further Aspects of Mathematics from New Kingdom Sources 157
15.1 Mathematics and Wisdom Literature: Metrology in the Teaching of Amenemope 158
15.2 Mathematics in the Duties of the Vizier 161
15.3 Mathematics and Death 165
15.4 Mathematics in Architecture and Art 170
16. Summary 177
GRECO-ROMAN PERIODS 179
17. Mathematical Texts (II): Tradition, Transmission, Development 183
17.1 Overview of Extant Demotic Mathematical Papyri 183
 17.1.1 Papyrus Cairo JE 89127-30, 89137-43 184
 17.1.2 Papyrus BM 10399 184
 17.1.3 Papyrus BM 10520 185
 17.1.4 Papyrus BM 10794 185
 17.1.5 Papyrus Carlsberg 30 185
 17.1.6 Papyrus Griffith I E7 185
 17.1.7 Papyrus Heidelberg 663 186
17.2 Demotic Arithmetic 186
 17.2.1 Multiplication 186
 17.2.2 Division (and a Note on Types of Fractions) 189
17.3 Selected Examples of Demotic Mathematical Problems 192
 17.3.1 Calculation of Areas 192