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Klein-Beltrami Model. Part II Cover
By: Roland Coghetto  
Open Access
|Jul 2018

References

  1. [1] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.10.1007/978-3-319-20615-8_17
  2. [2] Eugenio Beltrami. Saggio di interpetrazione della geometria non-euclidea. Giornale di Matematiche, 6:284–322, 1868.
  3. [3] Eugenio Beltrami. Essai d’interprétation de la géométrie non-euclidéenne. In Annales scientifiques de l’École Normale Supérieure. Trad. par J. Hoüel, volume 6, pages 251–288. Elsevier, 1869.10.24033/asens.60
  4. [4] Karol Borsuk and Wanda Szmielew. Podstawy geometrii. Państwowe Wydawnictwo Naukowe, Warszawa, 1955 (in Polish).
  5. [5] Roland Coghetto. Homography in ℝℙ2. Formalized Mathematics, 24(4):239–251, 2016. doi:10.1515/forma-2016-0020.10.1515/forma-2016-0020
  6. [6] Roland Coghetto. Group of homography in real projective plane. Formalized Mathematics, 25(1):55–62, 2017. doi:10.1515/forma-2017-0005.10.1515/forma-2017-0005
  7. [7] Roland Coghetto. Klein-Beltrami model. Part I. Formalized Mathematics, 26(1):21–32, 2018. doi:10.2478/forma-2018-0003.10.2478/forma-2018-0003
  8. [8] Roland Coghetto. Pascal’s theorem in real projective plane. Formalized Mathematics, 25 (2):107–119, 2017. doi:10.1515/forma-2017-0011.10.1515/forma-2017-0011
  9. [9] Adam Grabowski. Tarski’s geometry modelled in Mizar computerized proof assistant. In Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, FedCSIS 2016, Gdańsk, Poland, September 11–14, 2016, pages 373–381, 2016. doi:10.15439/2016F290.10.15439/2016F290
  10. [10] Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.10.1007/s10817-015-9345-1
  11. [11] Kanchun, Hiroshi Yamazaki, and Yatsuka Nakamura. Cross products and tripple vector products in 3-dimensional Euclidean space. Formalized Mathematics, 11(4):381–383, 2003.
  12. [12] Timothy James McKenzie Makarios. A mechanical verification of the independence of Tarski’s Euclidean Axiom. Victoria University of Wellington, New Zealand, 2012. Master’s thesis.
  13. [13] Yatsuka Nakamura. Graph theoretical properties of arcs in the plane and Fashoda Meet Theorem. Formalized Mathematics, 7(2):193–201, 1998.
  14. [14] Karol Pąk and Andrzej Trybulec. Laplace expansion. Formalized Mathematics, 15(3): 143–150, 2007. doi:10.2478/v10037-007-0016-5.10.2478/v10037-007-0016-5
  15. [15] Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4): 535–545, 1991.
DOI: https://doi.org/10.2478/forma-2018-0004 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 33 - 48
Submitted on: Mar 27, 2018
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Published on: Jul 28, 2018
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2018 Roland Coghetto, published by University of Białystok
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.