Computer proofs in plane geometry

• Autorzy: Billich M.
• Języki publikacji: EN

Abstrakty

EN

Over the past 25 years highly successful methods for geometry theorem proving have been developed. We will use elementary and understandable examples to show the nature of the techniques for verification of geometric constructions made with interactive geometry environment and for proving geometric statements. In addition to some informations about the WinGCLC software with specific language, we look at the system GeoThms that integrates Automatic Theorem Provers, Dynamic Geometry Tools and a database. The abovementioned system provides an environment suitable for new ways of studying and teaching geometry at different levels.

Słowa kluczowe

EN

plane geometry; teaching geometry; studying geometry; geometry theorem proving

PL

geometria płaska; nauczanie geometrii; studiowanie geometrii; dowodzenie twierdzeń geometrii

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2011
• Tom: Vol. 16
• Strony: 197--204
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Billich M.

• Faculty of Education, Catholic University in Ružomberok Hrabovská cesta 1, 034 01 Ružomberok, Slovak Republic

Bibliografia

• [1] Shang-Ching Chou, Xiao-Shan Gao, Jing-Zhong Zhang. Automated generation of readable proofs with geometric invariants: Multiple and shortest proof generation. Journal of Automated Reasoning, 17, 325-347, 1996.
• [2] J. Escibrano, F. Botana, M.A. Abandés. Adding remote computational capabilities to dynamic geometry systems. Mathematics and Computers in Simulation, 80, 1177-1184, 2010.
• [3] P. Janičić, P. Quaresma. System Description: GCLCprover + GeoThms. In: International Joint Conference on Automated Reasoning. Lecture Notes in Artificial Intelligence, pp. 145-150, Springer, Berlin 2006.
• [4] N. Matsuda, K. Vanlehn. GRAMY: A geometry theorem prover capable of construction. Journal of Automated Reasoning, 32, 3-33, 2004.
• [5] J. Narboux. A graphical user interface for formal proofs in geometry. Journal of Automated Reasoning, 39, 161-180, 2007.
• [6] P. Quaresma, P. Janičić. GeoThms - a Web system for Euclidean constructive geometry. Electronic Notes in Theoretical Computer Science, 174(2), 35-48, 2007.
• [7] P. Quaresma, P. Janičić. Integrating dynamic geometry software, deduction systems, and theorem repositories. In: Mathematical Knowledge Management. Lecture Notes in Artificial Intelligence, pp. 280-294, Springer, Berlin 2006.
• [8] P. Quaresma, P. Janičić. The Area Method, Rigorous Proofs of Lemmas in Hilbert's Style Axioms Systems. Technical Report TR2006/001, Center for Informatics and Systems of the University of Coimbra, 2009.
• [9] V. Santos, P. Quaresma. Adaptative learning environment for geometry. In: Advances in Learning Processes, M.B. Rosson (Ed.), pp. 71-91, InTech, 2010.