Nexus Network Journal

, Volume 17, Issue 1, pp 287–309 | Cite as

Geometry and Proportions in the Funeral Chapel of Sarenput II

  • Juan Antonio Martínez Hermoso
  • Fernando Martínez Hermoso
  • Francisco de Paula Montes Tubío
  • Alejandro Jiménez Serrano
Research

Abstract

This paper analyzes the geometry and proportions of the funeral chapel of Sarenput II, built some 4,000 years ago in the necropolis of Qubbet el-Hawa in Egypt. The analysis is done with the utmost respect for ancient sources, and in particular for Egyptian mathematical knowledge. In a first general analysis, the different parts that make up the chapel are analysed in terms of both volume and surface. Later, the most representative elements, the hypostyle hall and sanctuary are studied in greater detail. Here, we encounter geometric shapes that are very close to the ratios √2, 2/√3 and √2/√3, which are derived from simple geometric shapes such as squares, rectangles √2 and equilateral triangles. Ancient Egyptians could achieve their approximations by unit fractions in accordance with the Egyptian system of numerical notation. Finally, with the data obtained, the study proposes a hypothesis about the possible design method of the funeral chapel.

Keywords

Ancient Egypt Design analysis Commensurables Diagonal Equilateral triangle Equilibrium Funerary architecture Geometry Hypostyle hall Incommensurables Irrational numbers Measurement Middle Kingdom Modules Necropolis of Qubbet El-Hawa Proportion Ratio Rational numbers Square Symmetry Trigonometry 12th Dynasty 

References

  1. Arnold, Dieter. 1991. Building in Egypt. Pharaonic Stone Masonry. New York: Oxford University Press.Google Scholar
  2. Arnold, Dieter. 1996. Hypostile Halls of the Old and Middle Kingdoms. Studies in Honour of Wiliam Kelly Simpson, vol I: 39–54. Boston: Museum of Fine Arts.Google Scholar
  3. Arnold, Dieter. 2003. The encyclopaedia of ancient Egyptian architecture. London: I.B. Tauris & Co Ltd.Google Scholar
  4. Badawy, Alexander. 1965. Ancient Egyptian Architectural Design. A Study of the Harmonic System. Berkeley: University of California Pres.Google Scholar
  5. Badawy, Alexander. 1966. A history of Egyptian architecture. Los Angeles: University of California Press.Google Scholar
  6. Breasted, J.H. 1906. Ancient Record of Egypt, vol. I. Chicago: The University of Chicago Press.Google Scholar
  7. Budge, Wallis. 1888. Excavations made at Aswan by Major-General Sir F. Grenfell during the years 1885 and 1886. Proceedings of the Society of Biblical Archaeology, vol X: 4–40. London.Google Scholar
  8. Ching, Francis D. K. 1982. Architecture, Form, Space and Order. (Spanish ed., Arquitectura. Forma, espacio y orden, trans. Santiago Castán. Barcelona: Gustavo Gili, 2012 (3rd ed.).Google Scholar
  9. Choisy, Auguste. 1899. Histoire de l´Architecture. Tome I. Paris: Gauthier-Villars.Google Scholar
  10. Clagett, Marshall. 1999. Ancient Egyptian Science A Source Book. Philadelphia: American Philosophical Society Independence Square.MATHGoogle Scholar
  11. Clarke, Somers, and Reginald. Engelbach. 1930. Ancien egyptian construction and architecture. New York: Courier Dover Publications.Google Scholar
  12. De Morgan, Jacques. 1894. Catalogue des monuments et inscriptions de l´Ègypte Antique. Haute Égypte. Tome Premier: de la frontière de Nubie a Kom Ombos. Vienne: Adolphe Holzhausen.Google Scholar
  13. De morgan, Jacques. 1903. Fouilles à Dahchour en 1894–1895. Vienne: Adolphe Holzhausen.Google Scholar
  14. Edel, Elmar. 2008. Die Felsgräbernekropole der Qubbet el-Hawa bei Assuan. I. Abteilung. Architekture, Darstellungen, Texte, archäologischer Befund und Funde. 4 vols. München: Ferdinand Schöningh.Google Scholar
  15. Engelbach, Reginald. 1927. An architect’s project from Thebes. Annales du Service des Antiquités de l’ Égypte 27: 72–76.Google Scholar
  16. Franke, Detlef. 1984. Personendaten aus dem Mittleren Reich (20.-16. Jahrhundert v. Chr.). Wiesbaden: Otto Harrassowitz.Google Scholar
  17. Glanville, Stephen R.K. 1927. The Mathematical leather roll in the British museum. Journal of Egyptian Archaeology 13: 232–238.CrossRefGoogle Scholar
  18. Glanville, Stephen R.K. 1930. Working plan for a shrine. Journal of Egyptian Archaeology 16: 237–239.CrossRefGoogle Scholar
  19. Garcia Valdes, Manuela. 1996. Plutarco. Istituti Editoriali e Poligrafici Internazionali: De iside et Osiride. Pisa-Roma.Google Scholar
  20. Gardiner, Alan H. 1908. Inscriptions from the tomb of Si-renpowet I, prince of Elephantine. Zeitschrift für ägyptische Sprache und Altertumskunde 45: 123–140.Google Scholar
  21. Gardiner, Alan H. 1957. Egyptian Grammar. Ashmolean Museum: Oxford. Griffith Institute.Google Scholar
  22. Gillings, Richard J. 1972. Mathematics at the Time of the Pharaohs. Cambridge, Mass.: Massachusettes Institute of Technology Press.Google Scholar
  23. Griffith, Francis L. 1881–2. Notes on Egyptian Weights and Measures. Proceedings of the Society of Biblical Archaeology, vol XIV: 403–450. London.Google Scholar
  24. Griffith, Francis L. 1897. The Petrie Papyri: Hieratic papyri from Kahun and Gurob. London: University College.Google Scholar
  25. Habachi, Labid. 1985. Elephantine IV. Verlang Philip Von Zabern: The Santuary of Heqaib. Berlín.Google Scholar
  26. Hayes, William. C. 1942. Ostraca and Name Stones from the Tomb of Sen-mut (nº71) at Thebes. Metropolitan Museum of Art, Publication 15. New York.Google Scholar
  27. Hournung, Erik, Rolf Krauss, and David A. Warbuton. 2006. Ancient Egyptian chronology. Boston: Brill.Google Scholar
  28. Jiménez Serrano, Alejandro. 2013. Los nobles de la VI Dinastía enterrados en Qubbet el-Hawa. Estudios Filológicos 337: 29-37. Salamanca.Google Scholar
  29. Jiménez Serrano, Alejandro, Botella López, Miguel, Martínez de Dios, Juan L., Piquette, Kathryn E., Chapon, Linda, Torallas Tovar, Sofia, and Valenti Costales, Marta. 2014. The monumental courtyard of tomb nº 33 in Qubbet el-Hawa: preliminary report of four years of archaeological works in a middle Kingdom funerary complex. Mitteilungen des Deutsches Archäologisches Institut abtailung Kairo 70: in press.Google Scholar
  30. Kostof, Spiro. 1977. The practice of architecture in the Ancient World: Egypt and Greece. The Architect. Chapters in the History of the Profession. 3–27. New York: Oxford University Press.Google Scholar
  31. Lauer, Jean-Philippe. 1960. Observations sur les pyramides. Bibliothèque d’ Étude, 30. Cairo: Institut Français d´Archéologie Orientale.Google Scholar
  32. Lepsius, Richard. 1865. Die alt-aegyptische Elle und ihre Eintheilung. Berlín: Druckerei der Königlichen Akademie der Wissenschaften.Google Scholar
  33. Müller, Hans W. 1940. Die Felsengräber der Fürsten von Elephantine aus der Zeit des Mittleren Reiches. Glückstadt-Hamburg-New York: Verlag J. J. Augustin.Google Scholar
  34. Newberry, Percy E. 1893. Beni Hassan. Part I. London: Kegan Paul, Trench, Trübner & Co., Ltd.Google Scholar
  35. Peet, Thomas E. 1923. The Rhind Mathematical Papyrus. Liverpool: University Press/London: Hodder amd Stoughton.Google Scholar
  36. Reeves, Nicholas C. 1986. Two architectural drawings from the Valley of the Kings. Chronique d’ Égypte 61: 43–49.Google Scholar
  37. Rossi, Corina, and Christopher Tout. 2002. Were the fibonacci series and the golden section known in Ancient Egypt. Historia Mathematica 29: 101–113.CrossRefMATHMathSciNetGoogle Scholar
  38. Rossi, Corina. 2003. Architecture and mathematics in ancient Egypt. New York: Cambridge University Press.Google Scholar
  39. Schiaparelli, Ernesto. 1927. La Tomba intatta dell’architetto Cha: relazione sui lavori Della missione italiana in Egitto, anni 1903—1920. Torino: R. Museo di Antichità.Google Scholar
  40. Schulz, Regine, and Matthias Seidel. 2005. Egipto. Könemann: Arte y Arquitectura. Barcelona.Google Scholar
  41. Sethe, Kurt. 1935. Historisch-Biographische Urkunden des Mittleren Reiches. Leipzig: J. C. Hinrichssche Buchhandlund.Google Scholar
  42. Struve, Wassili W. 1930. Mathematischer Papyrus des Staatlichen Museums der Schönen Künste in Moskau. Quellen und Studien zur Geschichte der Mathematik 1.Google Scholar
  43. Siclen, Van, and C. Charles. 1986. Ostracon BM41228: a sketch plan of a shrine reconsidered. Góttinger Miszellen 90: 71–77.Google Scholar
  44. Viollet-le-duc, Eugène. 1877. Lectures on Architecture (Entretiens sur l`architecture. Paris. 1863), Eby Benjamin Bucknall, New York: Dover Publications.Google Scholar
  45. Wilkinson, Richard H. 2000. The complete temples of Ancient Egypt. London: Thames and Hudson Ltd.Google Scholar

Copyright information

© Kim Williams Books, Turin 2014

Authors and Affiliations

  • Juan Antonio Martínez Hermoso
    • 1
  • Fernando Martínez Hermoso
    • 1
  • Francisco de Paula Montes Tubío
    • 2
  • Alejandro Jiménez Serrano
    • 3
  1. 1.JaénSpain
  2. 2.Departamento de Ingeniería Gráfica y GeomáticaUniversidad de CórdobaCórdobaSpain
  3. 3.Area de Historia Antigua, Facultad de HumanidadesUniversidad de JaénJaénSpain

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