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Contemporary interpretation of a historical locus problem with the use of computer algebra. (English) Zbl 1395.51004
Kotsireas, Ilias S. (ed.) et al., Applications of computer algebra, Kalamata, Greece, July 20–23, 2015. Cham: Springer (ISBN 978-3-319-56930-7/hbk; 978-3-319-56932-1/ebook). Springer Proceedings in Mathematics & Statistics 198, 191-205 (2017).
Summary: This paper deals with the joint use of computer algebra and the dynamic geometry features of the mathematics software GeoGebra to solve a locus problem. Through a generally unknown problem from an eighteenth century Latin book of geometry exercises the use of the computer algebra features of GeoGebra will be presented on the one hand as a means of automatic computation of the locus equation and on the other hand as an environment to realize the symbolic step-by-step derivation of the equation. The core principles of the effective implementation of computer algebra functions within the dynamic geometry system will be presented. An enhanced approach to solving the problem, inspired by the findings from the use of the computer to investigate the locus, will cause the appearance of an unexpected and until now not described curve.
For the entire collection see [Zbl 1379.13001].

51-04 Software, source code, etc. for problems pertaining to geometry
68W30 Symbolic computation and algebraic computation
01A05 General histories, source books
51-03 History of geometry
GeoGebra; Giac; SINGULAR; Xcas
Full Text: DOI
[1] 1. Botana, F., Kovács, Z.: Teaching loci and envelopes in GeoGebra, GeoGebraBook.
[2] 2. Botana, F., Kovács, Z.: A singular web service for geometric computations. Ann. Math. Artif. Intell. 74 (3), 359-370 (2015) · Zbl 1330.68336
[3] 3. Botana, F., Hohenwarter, M., Janičić, P., Kovács, Z., Petrović, I., Recio, T., Weitzhofer, S.: Automated theorem proving in GeoGebra: current achievements. J. Autom. Reason. 55 (1), 39-59 (2015) · Zbl 1356.68181
[4] 4. Clark, K.M.: History of mathematics: illuminating understanding of school mathematics concepts for prospective mathematics teachers. Educ. Stud. Math. 81 (1), 67-84 (2012)
[5] 5. Courant, R., Robbins, H.: What is Mathematics? An Elementary Approach to Ideas and Methods, 2nd edn. Oxford University Pre, Oxford (1996) · Zbl 0865.00001
[6] 6. Cundy, H.M.: Mathematical Models, 2nd edn. Oxford University Press, Oxford (1961) · Zbl 0095.38001
[7] 7. Czédli, G., Szendrei, Á.: Geometriai szerkeszthetőség (in Hungarian). Polygon, Szeged (1997)
[8] 8. Decker, W., Greuel, G.-M., Pfister, G., Schönemann, H.:
[9] 9. Dennis, D.: The role of historical studies in mathematics and science educational research. In: Kelly, R., Lesh, A. (eds.) Research Design in Mathematics and Science Education. Lawrence Erlbaum, Mahwah (2000)
[10] 10. Furinghetti, F.: Teacher education through the history of mathematics. Educ. Stud. Math. 66 (2), 131-143 (2007)
[11] 11. Hašek , R., Kovács, Z.: The pretzel curve in Ioannis Holfeld’s 35th problem, GeoGebra worksheet.
[12] 12. Hašek, R., Zahradník, J.: Study of historical geometric problems by means of CAS and DGS. The International Journal for Technology in Mathematics Education, pp. 53-58. Research Information Ltd., Burnham (2015)
[13] 13. Hašek, R., Zahradník, J.: Současná interpretace vybraných historických úloh na množiny bodů dané vlastnosti (in Czech). In \( Sborník příspěvků 33. konference o geometrii a grafice. Horní Lomná, 9. - 12. září 2013\) . Ostrava: Vysoká škola báňská - Technická univerzita Ostrava, pp. 115-120 (2013)
[14] 14. Hohenwarter, M., Borcherds, M., Ancsin, G., Bencze, B., Blossier, M., Bogner, S., Denizet, C., Éliás, J., Gál, L., Konečný, Z., Kovács, Z., Krismayer, T., Küllinger, W., Lizelfelner, S., Parisse, B., Rathgeb, P., Sólyom-Gecse, C.S., Stadlbauer, C., Tomaschko, M.: GeoGebra, free mathematics software for learning and teaching.
[15] 15. Holfeld, I.: Exercitationes Geometricae. Charactere Collegii Clementini Societas Jesu, Praha (1773)
[16] 16. Katz, V.J.: A History of Mathematics: An Introduction, 2nd edn. Adison-Wesley, Reading (1998) · Zbl 1066.01500
[17] 17. Kovács, Z., Parisse, B.: Giac and GeoGebra—improved Gröbner basis computations. In: Gutierrez, J., Schicho, J., Weimann, M. (eds.) Computer Algebra and Polynomials. Lecture Notes in Computer Science 8942, pp. 126-138. Springer, Heidelberg (2015) · Zbl 1434.68708
[18] 18. Kovács, Z.: \( Holfeld’s 35th Problem as An Implicit Locus\) .
[19] 19. Moise, E.: Elementary Geometry from An Advanced Standpoint, 2nd edn. Addison-Wesley Publishing Company, New York (1990) · Zbl 0797.51002
[20] 20. Montes, A., Wibmer, M.: Groebner bases for polynomial systems with parameters. J. Symb. Comput. 45 , 1391-1425 (2010) · Zbl 1207.13018
[21] 21. Parisse, B.: Giac/Xcas, a free computer algebra system.
[22] 22. Struik, D.J.: A Concise History of Mathematics, 4th edn. Dover Publications, New York (1987) · Zbl 0645.01003
[23] 23. Weisstein, E.W.: Knot curve. From MathWorld-a wolfram web resource.
[24] 24. Zahradník, J.: Problémy z geometrie ve sbírce Ioannise Holfelda Exercitationes geometricae (in Czech). In \( Sborník 34. mezinárodní konference Historie matematiky, Poděbrady, 23. - 27. srpna 2013\) , Matfyzpress, Praha, p. 191 (2013)
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