The Shape of the Great Pyramid

Roger Herz-Fischler

Description

Who has not seen a picture of the Great Pyramid of Egypt, massive in size but deceptively simple in shape, and not wondered how that shape was determined?

Starting in the late eighteenth century, eleven main theories were proposed to explain the shape of the Great Pyramid. Even though some of these theories are well known, there has never been a detailed examination of their origins and dissemination. Twenty years of research using original and difficult-to-obtain source material has allowed Roger Herz-Fischler to piece together the intriguing story of these theories. Archaeological evidence and ancient Egyptian mathematical texts are discussed in order to place the theories in their proper historical context. The theories themselves are examined, not as abstract mathematical discourses, but as writings by individual authors, both well known and obscure, who were influenced by the intellectual and social climate of their time.

Among results discussed are the close links of some of the pyramid theories with other theories, such as the theory of evolution, as well as the relationship between the pyramid theories and the struggle against the introduction of the metric system. Of special note is the chapter examining how some theories spread whereas others were rejected.

This book has been written to be accessible to a wide audience, yet four appendixes, detailed endnotes and an exhaustive bibliography provide specialists with the references expected in a scholarly work.

Sujets

• Mathematics
• History

Informations

• Publié par: Wilfrid Laurier University Press
• Date de parution: 21 octobre 2009
• Nombre de lectures: 0
• EAN13: 9781554587032
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

The Shape of the Great Pyramid
The three large pyramids at Giza. From L. Borchardt, Egypt: Architecture, Landscape, Life of the People (New York: Westermann, 1929[?]).
The Shape of the Great Pyramid
Roger Herz-Fischler
O you Great Ennead which is in n, make the King s endure, make this pyramid of this King and this construction of his endure for ever, just as the name of Atum who presides over the Great Ennead endures. As the name of Shu, Lord of the Upper Mnst in n, endures, so may the King s name endure, and so may this pyramid of his and this construction of his endure likewise for ever.
- Utterance 601 [Fifth Dynasty] , The Ancient Egyptian Pyramid Texts , [Faulkner, 1969, 247]
This book has been published with the help of a grant from the Humanities and Social Sciences Federation of Canada, using funds provided by the Social Sciences and Humanities Research Council of Canada. We acknowledge the financial support of the Government of Canada through the Book Publishing Industry Development Program for our publishing activities.
Canadian Cataloguing in Publication Data
Herz-Fischler, Roger, 1940-
The shape of the Great Pyramid
Includes bibliographical references and index.
ISBN 0-88920-324-5
1. Great Pyramid (Egypt) - Miscellanea. 2. Weights and measures - Egypt - Miscellanea. I. Title.
DT63.H47 2000
932
C99-930688-X
2000 Wilfrid Laurier University Press Waterloo, Ontario N2L 3C5
Cover design by Leslie Macredie, using a photograph of the Great Pyramid from L. Borchardt, Egypt: Architecture, Landscape , Life of the People (New York: Westermann, 1929[?]). Back cover visual: the Star Cheops.

Printed in Canada
The Shape of the Great Pyramid has been produced from a manuscript supplied in camera-ready form by the author.
All rights reserved. No part of this work covered by the copyrights hereon may be reproduced or used in any form or by any means-graphic, electronic or mechanical-without the prior written permission of the publisher. Any request for photocopying, recording, taping or reproducing in information storage and retrieval systems of any part of this book shall be directed in writing to the Canadian Reprography Collective, 214 King Street West, Suite 312, Toronto, Ontario M5H 3S6.
Pour Eliane, Mych le, Seline et Rachel
F r Issak, Teddy und Morris Fischleiber Julie Sommer Joseph und Artur H llander die uns zu fr h verliessen
I o pas mie sons fie, ni roso sons espino, ni nouse sons crubil-Proven al proverb
TABLE OF CONTENTS
Acknowledgements
Introduction
PART I. THE CONTEXT
Chapter 1. Historical and Architectural Context
Chapter 2. External Dimensions and Construction
Surveyed Dimensions
Angle of Inclination of the Faces
Egyptian Units of Measurement
Building and Measuring Techniques
Chapter 3. Historiography
Early Writings on the Dimensions
Modern Historiographers
PART II. ONE PYRAMID, MANY THEORIES
Diagrams
Chapter 4. A Summary of the Theories
Terminology, Notation, Observed Dimensions
Definitions of the Symbols - Observed Values
A Comparison of the Theories
Chapter 5. Seked Theory
The Mathematical Description of the Theory
Seked Problems in the Rhind Papyrus
Archaeological Evidence
Early Interpretations of the Rhind Papyrus
Petrie
Borchardt
Philosophical and Practical Considerations
Chapter 6. Arris = Side
The Mathematical Description of the Theory
Herodotus (vth century)
Greaves (1641)
Paucton (1781)
Jomard (1809)
Agnew (1838)
Fergusson (1849)
Beckett (1876)
Howard, Wells (1912)
Chapter 7. Side: Apothem = 5:4
The Mathematical Description of the Theory
Plutarch s Isis and Osiris
Jomard (1809)
Perring (1842)
Ram e (1860)
Chapter 8. Side: Height = 8:5
The Mathematical Description of the Theory
Jomard (1809)
Agnew (1838)
Perring (1840?)
R ber (1855)
Ram e (1860)
Viollet-le-Duc (1863)
Garbett, (1866)
A. X., (1866)
Brun s (1967)
Chapter 9. Pi-theory
The Mathematical Description of the Theory
Egyptian Circle Calculations
Agnew (1838)
Vyse (1840)
Chantrell (1847)
Taylor (1859)
Herschel (1860)
Smyth (1864)
Petrie (1874)
Beckett (1876)
Proctor (1877)
Twentieth-Century Authors
Chapter 10. Heptagon Theory
The Mathematical Description of the Theory
Fergusson (1849)
Texier (1934)
Chapter 11. Kepler Triangle Theory
The Mathematical Description of the Theory
Kepler Triangle and Equal Area Theories
Kepler Triangle, Golden Number, Equal Area
R ber (1855)
Drach, Garbett (1866)
Jarolimek (1890)
Neikes (1907)
Chapter 12. Side: Height = Golden Number
The Mathematical Description of the Theory
R ber (1855)
Zeising (1855)
Misinterpretations of R ber
Choisy (1899)
Chapter 13. Equal Area Theory
The Mathematical Description of the Theory
The Passage from Herodotus
Agnew (1838)
Taylor (1859)
Herschel (1860)
Thurnell (1866)
Garbett (1866)
Smyth (1874)
Hankel (1874)
Beckett and Friend (1876)
Proctor (1880)
Ballard (1882)
Petrie (1883)
Twentieth-Century Authors
Chapter 14. Slope of the Arris = 9/10
The Mathematical Description of the Theory
William Petrie (1867)
James and O Farrell (1867)
Smyth (1874)
Beckett (1876), Bonwick (1877), Ballard (1882)
Flinders Petrie (1883)
Texier (1939)
Lauer (1944)
Chapter 15. Height: Arris = 2:3
The Mathematical Description of the Theory
Unknown (before 1883)
Chapter 16. Additional Theories
PART III. CONCLUSIONS
Chapter 17. Philosophical Considerations
Chapter 18. Sociology of the Theories - A Case Study: The Pi-theory
The Social and Intellectual Background in Victorian Britain
Relationship of the Pi-theory to Other Topics
A Profile of the Authors
Chapter 19. Conclusions
The Sociology of the Theories
What Was the Design Principle?
APPENDICES
Appendix 1. An Annotated Bibliography
Appendix 2. Tombal Superstructures: References and Dimensions
Appendix 3. Egyptian Measures
Appendix 4. Egyptian Mathematics
Appendix 5. Greek and Greek-Egyptian Measures
NOTES
BIBLIOGRAPHY/INDEX
Symbols
The symbols for the quantities directly related to a pyramid are shown on the diagrams at the beginning of Chapter 4 .

Cover
The aerial photograph of the Great Pyramid on the cover is taken from a wonderful 1929 work by the Egyptologist Ludwig Borchardt entitled Egypt: Architecture, Landscape, Life of the People. This book of text and photographs shows not only the monuments of Egypt, but also the people, their dwellings and their habitat.
Acknowledgements
Il fait bon ne rien savoir: l on apprend toujours.
-French Proverb [Dournon, 1993, 296]
One often finds authors thanking their spouses either for their support or direct help. While I have to thank my wife Eliane in both these categories there is much more to her influence upon me. The reader should keep in mind that my studies were in engineering and very abstract mathematics. While I had taken a few general courses in English literature, the universe of the humanities was completely foreign to me. After our marriage in 1964, I began to look over her shoulder as she pursued her studies in French literature. Her ability to work from many sources and to analyze texts amazed me and I have always considered her to be the intellectual in the family. My true apprenticeship in the humanities started out in a way consistent with my abilities; I typed her papers, sought out books and references for her and worked on mastering the language of Moli re, Racine and Thomas Corneille. The next step came in the summer of 1970 when she worked on her doctoral thesis 1 at the Biblioth que Nationale in Paris and under her guidance I became an expert on the bibliography of Thomas Corneille. I believe that it was because of all this that when I started doing my research on the pyramid theories and golden numberism in 1975-76, I did not feel that I was in a strange world.
I would like to take this opportunity to publicly thank the unsung heroes of the academic world: the librarians and especially the interlibrary loan librarians. My particular thanks go to two particularly wonderful interlibrary loans librarians, Terry Sulymko and Callista Kelly.
Many other people have been of assistance to me and I have mentioned some of them in the notes. Two of the referees of the manuscript made some very pertinent criticisms and their comments have resulted in a major revision of the original manuscript. I wish to thank these referees for the time and effort that they devoted to my work.
I am especially appreciative of the support of Sandra Woolfrey, former director of Wilfrid Laurier University Press, and in particular her willingness to publish my books, which are not only different from those usually published by the Press, but which do not easily fit into precise categories.
Caroline Gowdy-Williams, Eliane Herz-Fischler and Andrew Williams read the text before it was sent to Wilfrid Laurier University Press. David Millman provided important editorial assistance and Jeff Coughlin drew the diagrams.
Many improvements were suggested-and errors eliminated-by the fine staff at Wilfrid Lau