Abstract
It is impossible to construct circles and squares of equal areas or perimeters precisely, for circles are measured by the incommensurable value pi (π) and squares by rational whole numbers. But from early times, geometers have attempted to reconcile these two orders of geometry. “Squaring the circle” can represent the union of opposing eternal and finite qualities, symbolizing the fusion of matter and spirit and the marriage of heaven and earth. In this column, we consider various methods for squaring the circle and related geometric constructions.
Preview
Unable to display preview. Download preview PDF.
References
BECKMANN, Petr. A History of π (PI). New York: St. Martin’s Press.
BRUNÉS, Tons. 1967. The Secrets of Ancient Geometry — and Its Use. 2 vols. Copenhagen: Rhodos.
BOND, Frederick Bligh and Thomas Simcock Lea. 1977. Gematria: A Preliminary Investigation of the Cabala. London: Research Into Lost Knowledge Organization.
CRITCHLOW, KEITH. 1982. Time Stands Still: New light on Megalithic Science. New York: St. Martin’s Press.
FLETCHER, Rachel. 2004. Musings on the Vesica Piscis. Nexus Network Journal 6,2 (Autumn 2004): 95–110.
-. 2005a. SIX + ONE. Nexus Network Journal 7,1 (Spring 2005): 141–160.
-. 2005b. The Square. Nexus Network Journal 7,2 (Autumn 2005): 35–70.
-. 2006. The Golden Section. Nexus Network Journal 8,1 (Spring 2006): 67–89.
HARPER, Douglas, ed. 2001. Online Etymological Dictionary. http://www.etymonline.com/
HOBSON, E. W. 1913. “Squaring the Circle”: A History of the Problem. Cambridge: Cambridge University Press. Reprint. Michigan Historical Reprint Series. University of Michigan University Library. No date.
LAWLOR, Robert. 1982. Sacred Geometry: Philosophy and Practice. New York: Thames and Hudson.
LEWIS, Charlton T. and Charles Short, eds. 1879. A Latin Dictionary. Oxford: Clarendon Press.
Perseus Digital Library Project. Gregory R. Crane, ed. Medford, MA: Tufts University. 2005. http://www.perseus.tufts.edu
LIDDELL, Henry George and Robert Scott, eds. 1889. An Intermediate Greek-English Lexicon. Oxford. Clarendon Press. Perseus Digital Library Project. Gregory R. Crane, ed. Medford, MA: Tufts University. 2005. http://www.perseus.tufts.edu
LIDDELL, Henry George and Robert Scott, eds. 1940. A Greek-English Lexicon. Henry Stuart Jones, rev. Oxford: Clarendon Press. Perseus Digital Library Project. Gregory R. Crane, ed. Medford, MA: Tufts University. 2005. http://www.perseus.tufts.edu
MARCH, Lionel. 1998. Architectonics of Humanism: Essays on Number in Architecture. London: Academy Editions.
MENDELSSOHN, Kurt. The Riddle of the Pyramids. New York: Praeger.
MICHELL, John. 1969. The View Over Atlantis. New York: Ballantine.
-. 1983. The New View Over Atlantis. London: Thames and Hudson.
-. 1988. The Dimensions of Paradise: The Proportions and Symbolic Numbers of Ancient Cosmology. San Francisco: Harper and Row.
O’CONNOR, J. J. and E. F. Robertson. 1999. Squaring the Circle. School of Mathematics and Statistics, University of St. Andrews: St. Andrews, Fife, Scotland. http://www-history.mcs.standrews.ac.uk/HistTopics/Squaring_the_circle.html
PADOVAN, Richard. 1999. Proportion: Science, Philosophy, Architecture. London: E & FN Spon.
PETRIE, W. M. Flinders. 1990. The Pyramids and Temples of Gizeh. 1885. Reprint. London: Histories & Mysteries of Man Ltd.
PLATO 1961. The Collected Dialogues of Plato Including the Letters. Edith Hamilton and Huntington Cairns, eds. Princeton: Bollingen Series LXXI of Princeton University Press.
RICHTER, Jean Paul, ed., 1970 The Notebooks Works of Leonardo da Vinci. 2 vols. 1883. Reprint. New York: Dover Publications.
SIMPSON, John and Edmund Weiner, eds. 1989. The Oxford English Dictionary. 2nd ed. OED Online. Oxford: Oxford University Press. 2004. http://www.oed.com/
SMITH, David Eugene. 1958. History of Mathematics. Vol. II. 1925. Reprint. New York: Dover Publications.
VAN DER WAERDEN, B. L. 1983. Geometry and Algebra in Ancient Civilizations. Berlin: Springer-Verlag.
VITRUVIUS. 1999. Ten Books on Architecture. Trans. Ingrid D. Rowland, Ed. Ingrid D. Rowland and Thomas Noble Howe. Cambridge: Cambridge University Press.
WATTS, Carol Martin and Donald J. Watts. 1987. Geometrical Orderings of the Garden Houses at Ostia. Journal of the Society of Architectural Historians 46,3 (1987): 265–276.
WATTS, Carol Martin and Donald J. Watts. 1992. The Role of Monuments in the Geometrical Ordering of the Roman Master Plan of Gerasa. Journal of the Society of Architectural Historians 51,3 (1992): 306–314.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2007 Kim Williams Books, Turin
About this chapter
Cite this chapter
Fletcher, R. (2007). Squaring the Circle: Marriage of Heaven and Earth. In: Nexus Network Journal. Nexus Network Journal, vol 9,1. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8519-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8519-4_8
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8443-2
Online ISBN: 978-3-7643-8519-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)