Nowe cechy równobocznych trójkątów

Michał Biesiada; Jan Górowski; Adam Łomnicki

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2014)

  • Volume: 6, page 5-18
  • ISSN: 2080-9751

Abstract

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In this paper the authors formulate and prove several conditions fortriangle to be equilateral. These conditions are associated with Gergonne,Nagel and Torricelli points and were obtained by composing and solvingthe so-called ‘enforcement tasks’. Both, the method and the results, can beused to trigger some mathematical student activities at different levels ofeducation or even some teacher activities.

How to cite

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Michał Biesiada, Jan Górowski, and Adam Łomnicki. "Nowe cechy równobocznych trójkątów." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 6 (2014): 5-18. <http://eudml.org/doc/296333>.

@article{MichałBiesiada2014,
abstract = {In this paper the authors formulate and prove several conditions fortriangle to be equilateral. These conditions are associated with Gergonne,Nagel and Torricelli points and were obtained by composing and solvingthe so-called ‘enforcement tasks’. Both, the method and the results, can beused to trigger some mathematical student activities at different levels ofeducation or even some teacher activities.},
author = {Michał Biesiada, Jan Górowski, Adam Łomnicki},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
keywords = {equilateral triangle; Georgonne point; Nagel point; Torricelli point},
language = {pol},
pages = {5-18},
title = {Nowe cechy równobocznych trójkątów},
url = {http://eudml.org/doc/296333},
volume = {6},
year = {2014},
}

TY - JOUR
AU - Michał Biesiada
AU - Jan Górowski
AU - Adam Łomnicki
TI - Nowe cechy równobocznych trójkątów
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2014
VL - 6
SP - 5
EP - 18
AB - In this paper the authors formulate and prove several conditions fortriangle to be equilateral. These conditions are associated with Gergonne,Nagel and Torricelli points and were obtained by composing and solvingthe so-called ‘enforcement tasks’. Both, the method and the results, can beused to trigger some mathematical student activities at different levels ofeducation or even some teacher activities.
LA - pol
KW - equilateral triangle; Georgonne point; Nagel point; Torricelli point
UR - http://eudml.org/doc/296333
ER -

References

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  1. Coxeter, H.: 1967, Wstęp do geometrii dawnej i nowej, PWN, Warszawa. 
  2. Górowski, J., Klakla, M., Łomnicki, A.: 2004, Zadania „na wymuszanie” jako środekmatematycznej aktywizacji uczących się, Roczniki Polskiego Towarzystwa Matematycznego, Seria V, Dydaktyka Matematyki 26, 61-80. 
  3. Górowski, J., Klakla, M., Łomnicki, A.: 2011, Projekt materiałów dydaktycznych wyzwalających odkrywanie twierdzeń, w: J. Żabowski (red.), O nauczaniu matematyki (wybrane materiały do studiowania dydaktyki matematyki), Wyd. Nauk. NOVUM, Płock, 385-417. 
  4. Górowski, J., Łomnicki, A.: 2012, Cechy równoboczności trójkątów, Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia IV, 83-92. 
  5. Górowski, J., Łomnicki, A., Żabowski, J.: 2013, Karakterizaj punktoj de triangulo, Litera scripta manet, Serta in honorem Helmar Frank, Wyd. KAVA-PECH, Dobřichovice, 295-306. 

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