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The Shape of the Great Pyramid

By Roger Herz-Fischler
Subjects History, Mathematics
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Paperback : 9780889203242, 305 pages, October 2000
Ebook (EPUB) : 9781554587032, 305 pages, October 2009
Ebook (PDF) : 9780889207769, 305 pages, January 2006

Table of contents

Table of Contents for The Shape of the Great Pyramid by Roger Herz-Fischler
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
Chapter 4. A Summary of Theories
Definitions of the Symbols—Observered 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
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)
Becektt (1876)
Howards, Wells (1912)
Chapter 7. Side : Apothem = 5 : 4
The Mathematical Description of the Theory
Plutarch’s Isis and Osiris
Jomard (1809)
Perring (1842)
Ramée (1860)
Chapter 8. Side : Height = 8 : 5
The Mathematical Description of the Theory
Jomard (1809)
Agnew (1838)
Perring (1840?)
Röber (1855)
Ramée (1860)
Viollet-le-Duc (1863)
Garbett, (1866)
A.X., (1866)
Brunés (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
Röber (1855)
Drach, Garbett (1866)
Jarolimek (1890)
Neikes (1907)
Chapter 12. Height = Golden Number
The Mathematical Description of the Theory
Röber (1855)
Zeising (1855)
Misinterpretations of Röber
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 Britian
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?
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


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.


Apart from the special subject of this very readable book, the last chapters will be a most valuable base for any study of a related kind. One can only look forward to the next volume by the author about the secrets of the `golden section'.

- Benno Artmann, British Journal of the History of Science, Volume 37, Number 3, September 2004, 2005 February