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When Two Circles Determine a Triangle. Discovering and Proving a Geometrical Condition in a Computer Environment

  • Nikolaos Metaxas
  • Andromachi Karagiannidou
Computer Math Snapshots - Column Editor: Uri Wilensky* Computational Diversions

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…”.

Keywords

Open ended task Proving Power of a point 

References

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AthensAthensGreece

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