Original Research

Generalizing the Nagel line to circumscribed polygons by analogy and constructive defining

Michael de Villiers
Pythagoras | Issue 68 | a65 | DOI: https://doi.org/10.4102/pythagoras.v0i68.65 | © 2008 Michael de Villiers | This work is licensed under CC Attribution 4.0
Submitted: 10 October 2008 | Published: 10 October 2008

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Michael de Villiers, School of Science, Mathematics & Technology Education, University of KwaZulu-Natal, South Africa

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This paper first discusses the genetic approach and the relevance of the history of mathematics for teaching, reasoning by analogy, and the role of constructive defining in the creation of new mathematical content. It then uses constructive defining to generate a new generalization of the Nagel line of a triangle to polygons circumscribed around a circle, based on an analogy between the Nagel line and the Euler line of a triangle.


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