Table of Contents
Geometry
Volume 2014 (2014), Article ID 276108, 7 pages
http://dx.doi.org/10.1155/2014/276108
Research Article

Proving and Generalizing Desargues’ Two-Triangle Theorem in 3-Dimensional Projective Space

Department of Applied Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece

Received 22 August 2014; Accepted 15 November 2014; Published 18 December 2014

Academic Editor: Isaac Pesenson

Copyright © 2014 Dimitrios Kodokostas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Dörrie, 100 Great Problems of Elementary Mathematics: Their History and Solution, Dover, 1965.
  2. W. R. Knorr, The Ancient Tradition of Geometric Problems, Dover Publications, New York, NY, USA, 1993. View at MathSciNet
  3. M. Kline, Mathematics in Western Culture, Oxford University Press, 1967. View at MathSciNet
  4. W. V. Hodge and D. Pedoe, Methods of Algebraic Geometry, vol. 1, Cambridge University Press, Cambridge, UK, 1953. View at MathSciNet
  5. A. Pogorelov, Geometry, Mir Publishers, Moscow, Russia, 1987.
  6. D. Hilbert, Grundlagen der Geometrie, 1899, (translated as The Foundations of Geometry and first published in English by The Open Court Publishing Company, Chicago, 1992 and offered as an ebook by Project Gutenberg, 2005, https://www.gutenberg.org/).
  7. I. Bachmann, Aufbau der Geometrie aus dem Spiegelungsbegriff, Grundlehren der Mathematischen Wissenschaften 96, Springer, Berlin, Germany, 2nd edition, 1973.
  8. H. S. M. Coxeter, Introduction to Geometry, John Wiley & Sons, Inc, New York, NY, USA, 2nd edition, 1989.
  9. K. Levenberg, “A class of non-desarguesian plane geometries,” The American Mathematical Monthly, vol. 57, pp. 381–387, 1950. View at Publisher · View at Google Scholar · View at MathSciNet
  10. F. Moulton, “A simple non-Desarguesian plane geometry,” Transactions of the American Mathematical Society, vol. 3, pp. 102–195, 1901. View at Google Scholar
  11. K. Sitaram, “A real non-desarguesian plane,” The American Mathematical Monthly, vol. 70, pp. 522–525, 1963. View at Publisher · View at Google Scholar · View at MathSciNet
  12. O. Veblen and J. H. Maclagan-Wedderburn, “Non-Desarguesian and non-Pascalian geometries,” Transactions of the American Mathematical Society, vol. 8, no. 3, pp. 379–388, 1907. View at Publisher · View at Google Scholar · View at MathSciNet
  13. M. Hall, “Projective planes,” Transactions of the American Mathematical Society, vol. 54, pp. 229–277, 1943. View at Publisher · View at Google Scholar · View at MathSciNet