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Parallel Projected Sphere on a Plane: A New Plane–Geometric Investigation

Year 2017, Volume: 10 Issue: 1, 58 - 80, 30.04.2017

Thomas L. Toulias George E. Lefkaditis

https://doi.org/10.36890/iejg.584443

Abstract

Keywords

Pohlke’s Theorem conjugate semi–diameters of an ellipse affine transformations orthogonal decomposition of a symmetric matrix

References

  • [1] Emch, A., Proof of Pohlke’s theorem and its generalizations by affinity. American Journal of Mathematics 40(2) (1918), 366-374.
  • [2] Fishburn, P.C. and Trotter, W.T., Containment orders for similar ellipses with a common center. Discrete Mathematics 256 (2002), 129–136.
  • [3] Lefkaditis, G.E., Thomas, T.L. and Markatis, S., The four ellipses problem. International Journal of Geometry 5(2) (2016), 77–92.
  • [4] Müller, E. and Kruppa, E., Lehrbuch der Darstellenden Geometrie. Springer–Verlag, Wien, 1961.
  • [5] Peschka, G. A., Elementarer beweis des Pohlke’schen fundamentalsatzes der Axonometrie. Stzgsb. Math. Nat., Akad. Wien LXXVIII II Abth. (1879), 1043-1054.
  • [6] Sklenáriková, Z. and Pémová, M., The Pohlke-Schwarz theorem and its relevancy in the didactics of mathematics. Quaderni di Ricerca in Didattica. http://math.unipa.it/~grim/quad17_sklenarikova-pemova_07.pdf 7).

Year 2017, Volume: 10 Issue: 1, 58 - 80, 30.04.2017

Thomas L. Toulias George E. Lefkaditis

https://doi.org/10.36890/iejg.584443

Abstract

References

  • [1] Emch, A., Proof of Pohlke’s theorem and its generalizations by affinity. American Journal of Mathematics 40(2) (1918), 366-374.
  • [2] Fishburn, P.C. and Trotter, W.T., Containment orders for similar ellipses with a common center. Discrete Mathematics 256 (2002), 129–136.
  • [3] Lefkaditis, G.E., Thomas, T.L. and Markatis, S., The four ellipses problem. International Journal of Geometry 5(2) (2016), 77–92.
  • [4] Müller, E. and Kruppa, E., Lehrbuch der Darstellenden Geometrie. Springer–Verlag, Wien, 1961.
  • [5] Peschka, G. A., Elementarer beweis des Pohlke’schen fundamentalsatzes der Axonometrie. Stzgsb. Math. Nat., Akad. Wien LXXVIII II Abth. (1879), 1043-1054.
  • [6] Sklenáriková, Z. and Pémová, M., The Pohlke-Schwarz theorem and its relevancy in the didactics of mathematics. Quaderni di Ricerca in Didattica. http://math.unipa.it/~grim/quad17_sklenarikova-pemova_07.pdf 7).
There are 6 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Thomas L. Toulias This is me

George E. Lefkaditis This is me

Publication Date April 30, 2017
Published in Issue Year 2017 Volume: 10 Issue: 1

Cite

APA Toulias, T. L., & Lefkaditis, G. E. (2017). Parallel Projected Sphere on a Plane: A New Plane–Geometric Investigation. International Electronic Journal of Geometry, 10(1), 58-80. https://doi.org/10.36890/iejg.584443
AMA Toulias TL, Lefkaditis GE. Parallel Projected Sphere on a Plane: A New Plane–Geometric Investigation. Int. Electron. J. Geom. April 2017;10(1):58-80. doi:10.36890/iejg.584443
Chicago Toulias, Thomas L., and George E. Lefkaditis. “Parallel Projected Sphere on a Plane: A New Plane–Geometric Investigation”. International Electronic Journal of Geometry 10, no. 1 (April 2017): 58-80. https://doi.org/10.36890/iejg.584443.
EndNote Toulias TL, Lefkaditis GE (April 1, 2017) Parallel Projected Sphere on a Plane: A New Plane–Geometric Investigation. International Electronic Journal of Geometry 10 1 58–80.
IEEE T. L. Toulias and G. E. Lefkaditis, “Parallel Projected Sphere on a Plane: A New Plane–Geometric Investigation”, Int. Electron. J. Geom., vol. 10, no. 1, pp. 58–80, 2017, doi: 10.36890/iejg.584443.
ISNAD Toulias, Thomas L. - Lefkaditis, George E. “Parallel Projected Sphere on a Plane: A New Plane–Geometric Investigation”. International Electronic Journal of Geometry 10/1 (April 2017), 58-80. https://doi.org/10.36890/iejg.584443.
JAMA Toulias TL, Lefkaditis GE. Parallel Projected Sphere on a Plane: A New Plane–Geometric Investigation. Int. Electron. J. Geom. 2017;10:58–80.
MLA Toulias, Thomas L. and George E. Lefkaditis. “Parallel Projected Sphere on a Plane: A New Plane–Geometric Investigation”. International Electronic Journal of Geometry, vol. 10, no. 1, 2017, pp. 58-80, doi:10.36890/iejg.584443.
Vancouver Toulias TL, Lefkaditis GE. Parallel Projected Sphere on a Plane: A New Plane–Geometric Investigation. Int. Electron. J. Geom. 2017;10(1):58-80.