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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

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

``It is readable, enjoyable and generates a sense of curiosity concerning the technical expertise and mathematical know-how of those who constructed the pyramids. ...Roger Herz-Fischler has written a work of great scholarship, which may very well succeed in recruiting adherents to the field of pyramidology. ''

- P.N. Ruane, The Mathematical Gazette, July 2002