On a problem that was not interesting for Erdős

Authors

DOI:

https://doi.org/10.23925/2237-9657.2021.v10i1p005-018

Keywords:

Automated Reasoning Tools, inscribed angle theorem, Pythagorean theorem

Abstract

We study a problem in elementary Euclidean geometry by using multiple approaches. We conclude that today's computer assisted study can introduce new methods to understand relationships and concepts better. Namely, using GeoGebra's Automated Reasoning Tools, several details of the original problem can be put into an algebraic context, and therefore, its automated investigation is possible, in some sense, mechanically. Still, creative thinking and reformulation of the problem in a different setting remains useful.

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Author Biography

Zoltán Kovács, The Private University College of Education of the Diocese of Linz

Assistant Professor

References

CHOU, S.C. Mechanical Geometry Theorem Proving. Springer Science + Business Media. 1987

COX, D.; LITTLE, J.; O'SHEA, D. Ideals, Variaties and Algorithms. Third Edition. Springer. 2007

ERDŐS, P. Problem 3740. American Mathematical Monthly, v. 42, p. 396, 1935.

HOHENWARTER, M.; KOVÁCS, Z.; RECIO, T. Using Automated Reasoning Tools to Explore Geometric Statements and Conjectures. In: HANNA, G.; REID, D.A.; DeVILLIERS, M. Proof Technology in Mathematics Research and Teaching. Springer, 2019, p. 215 – 236.

KOVÁCS, Z.; PARISSE, B. Giac and GeoGebra – Improved Gröbner Basis Computations. In: GUTIERREZ, J.; SCHICHO, J.; WEIMANN, M. Computer Algebra and Polynomials. Lecture Notes in Computer Science. Springer, 2015, p. 126 – 138.

KOVÁCS, Z.; RECIO, T.; VÉLEZ, M.P. Using Automated Reasoning Tools in GeoGebra in the Teaching and Learning of Proving in Geometry. International Journal for Technology in Mathematics Education, v. 25, no 2, p. 33-50, 2018.

LOSADA, R. El color dinámico de GeoGebra. La Gaceta de la RSME, v. 17, no 3, p. 525-547, 2014.

REIMAN, I. Fejezetek az elemi geometriából. Budapest: Tankönyvkiadó Vállalat. 1987 (in Hungarian)

UNDERWOOD, D. Elementary Number Theory. Second Edition. Mineola, New York: Dover Publications. 1978

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Published

2021-06-05

How to Cite

Kovács, Z. (2021). On a problem that was not interesting for Erdős. Revista Do Instituto GeoGebra Internacional De São Paulo, 10(1), 5–18. https://doi.org/10.23925/2237-9657.2021.v10i1p005-018

Issue

Vol. 10 No. 1 (2021)

Section

Artigos

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