315
Views
2
CrossRef citations to date
0
Altmetric
Classroom Notes

Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model

, &
Pages 594-612 | Received 04 Jun 2017, Published online: 05 Jan 2018

References

  • Heath TL. The thirteen books of Euclid's elements. New York: Dover Publications; 1956.
  • Greenberg M. Euclidean and non-Euclidean geometry: development and history. San Francisco (CA): W.H. Freeman and Company; 1980.
  • Gray J. Worlds out of nothing. London: Springer; 2007.
  • Efimov NV. Higher geometry. Moscow: Mir Publishers; 1980.
  • Bonola R. Non Euclidean geometry: a critical and historical study of its development. New York: Dover; 1955.
  • Lambert M. Mémoire surQuelques Propriétés Remarquables des Quantités Transcendentes Circulaires etLogarithmiques. In: Pi: a source book. New York (NY): Springer; 2004.
  • Lambert JH. Theorie der parallellinien. In: Stäckel P and Engel F, editors. Die Theorie der Parallellinien von Euklid bis auf Gauss, eine Urkundensammlung zur Vorgeschichte der nicht-euklidischen Geometrie. Leipzig: Teubner; 1786.
  • Beltrami E. Saggio di interpretazione della geometria non-euclidea. Naples: Grande stabilimento tipografico di Franc. e Gennaro de Angelis; 1868.
  • Hilbert D. Über Flächen von konstanter Krümmung. Trans Amer Math Soc. 1901;2:87–99.
  • O'Neill B. Elementary differential geometry. revised 2nd ed. New York: Academic Press; 2006.
  • Poincaré H. Science and hypothesis. New York: Walter Scott Publishing; 1905.
  • Wartofsky M. Models: representation and the scientific understanding. Boston studies in the philosophy of science, vol. XLVIII. Boston (MA): Reidel Publishing Company; 1979.
  • Wittgenstein L. Philosophical investigations. Oxford: Blackwell; 1958.
  • Hohenwarter M. GeoGebra: ein softwaresystem fur dynamische geometrie und algebra der ebene. Salzburg: Paris Lodron University; 2002.
  • Arzarello F, Olivero F, Paola D, et al. A cognitive analysis of dragging practices in Cabri environments. Zentralblatt für Didaktik der Mathematik. 2002;34(3):66–72.
  • Lopez-Real F, Leung A. Dragging as a conceptual tool in dynamic geometry environments. Int J Math Educ Sci Technol. 2006;37(6):665–679.
  • Jones K. Providing a foundation for deductive reasoning: students' interpretations when using dynamic geometry software and their evolving mathematical explanations. Educ Stud Math. 2000;44(1–2):55–85.
  • Guven B, Karatas I. Students discovering spherical geometry using dynamic geometry software. Int J Math Educ Sci Technol. 2009;40(3):331–340.
  • Junius P. A case example of insect gymnastics: how is non-Euclidean geometry learned? Int J Math Educ Sci Technol. 2008;39(8):987.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.