When Two Circles Determine a Triangle. Discovering and Proving a Geometrical Condition in a Computer Environment |
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Authors: | Nikolaos Metaxas and Andromachi Karagiannidou |
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Institution: | (1) Department of Mathematics, University of Athens, Athens, Greece |
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Abstract: | Visualization of mathematical relationships enables students to formulate conjectures as well as to search for mathematical
arguments to support these conjectures. In this project students are asked to discover the sufficient and necessary condition
so that two circles form the circumscribed and inscribed circle of a triangle and investigate how this condition effects the
type of triangle in general and its perimeter in particular. Its open-ended form of the task is a departure from the usual
phrasing of textbook’s exercises “show that…”. |
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Keywords: | |
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