Niekoľko dôkazov Mongeho vety o troch kružniciach
Several Proofs of Monge’s Three-Circle Theorem
Abstract
In this article, several distinct proofs of Monge's theorem on three circles are presented. The objective is to demonstrate the integration of separate geometric findings into a coherent framework and to direct the reader towards specific geometric interrelations. The paper is primarily addressed to students of mathematics education taking foundational geometry courses as a part of their university studies.
- Keywords
- Monge’s Circle Theorem, Desargues Theorem, Menelaus’ Theorem, stereometry
- Classification
- 97G40
References
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Šedivý O. a kol. (1987). Geometria 2. Pre študentov matematiky učiteľského štúdia na univerzitách a pedagogických fakultách. SPN Bratislava
Šedivý O, Vallo, D. (2013). Geometria III. FPV UKF v Nitre, Nitra
Vallo D. (2026). Úvod do afinnej geometrie. Afinné zobrazenia. FPVaI UKF v Nitre. Nitra
Weisstein, Eric W. "Menelaus' Theorem." From MathWorld--A Wolfram Resource. Dostupné online [5. október 2026]: https://mathworld.wolfram.com/MenelausTheorem.html
Weisstein, Eric W. "Desargues' Theorem." From MathWorld--A Wolfram Resource. Dostupné online [3.október 2026] https://mathworld.wolfram.com/DesarguesTheorem.html
Šedivý O. a kol. (1987). Geometria 2. Pre študentov matematiky učiteľského štúdia na univerzitách a pedagogických fakultách. SPN Bratislava
Šedivý O, Vallo, D. (2013). Geometria III. FPV UKF v Nitre, Nitra
Vallo D. (2026). Úvod do afinnej geometrie. Afinné zobrazenia. FPVaI UKF v Nitre. Nitra
Weisstein, Eric W. "Menelaus' Theorem." From MathWorld--A Wolfram Resource. Dostupné online [5. október 2026]: https://mathworld.wolfram.com/MenelausTheorem.html
Weisstein, Eric W. "Desargues' Theorem." From MathWorld--A Wolfram Resource. Dostupné online [3.október 2026] https://mathworld.wolfram.com/DesarguesTheorem.html