Geogebra and problems of tangent circles

• Autorzy: Billich M.

Identyfikatory

DOI

10.16926/m.2017.22.02

• Języki publikacji: EN

Abstrakty

EN

There are many mathematical programmes for teaching and learning geometry from middle school to the university level. Dynamic software package Geogebra can help students to explore and understand more concepts in geometry on their own. In this paper we are concentrating in one of the most interesting and less known two-dimensional transformations like inversion with respect to a circle supported by GeoGebra. The use of this transformation through GeoGebra makes possible a number of elegant solutions to classical construction problems in geometry. Contribution of this paper is presentation of some problems which require the construction of the circle tangent to given circles.

Słowa kluczowe

EN

GeoGebra; tangent circles; geometry software

PL

GeoGebra; kręgi styczne; oprogramowanie geometrii

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2017
• Tom: Vol. 22
• Strony: 23--29
• Opis fizyczny: Bibliogr. 6 poz., rys.

Twórcy

autor

Billich M.

• Catholic University in Ružomberok, Department of Mathematics, Faculty of Education, Place A. Hlinka 56/1, 034 01 Ružomberok, Slovakia

Bibliografia

• [1] I. Ya. Bakel’man, Inversions, Chicago, IL: University of Chicago Press, 1974.
• [2] M. Billich, Circle inversion and problems on tangent circles, In: Proceedings of International Congress IMEM 2009, Catholic University in Ružomberok, 2009, 492- 496.
• [3] H. S. M. Coxeter, Introduction to geometry, John Wiley & Sons., 1961.
• [4] D. Gisch; J. M. Ribando, Apollonius’ Problem: A Study of Solutions and Their Connections, American Journal of Undergraduate Research 3, 2004, 15–25.
• [5] Z. Sklenáriková, K metódam riešenia Apolloniovej úlohy, In: Matematika v proměnách veku III, Edícia Dějiny matematiky, Praha, 2004, 45-55.
• [6] Z. Sklenáriková, J. Čižmár, Elementárna geometria euklidovskej roviny, FMFI UK Bratislava, 2002.