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An illustration of the explanatory and discovery functions of proof

Michael de Villiers

Pythagoras; Vol 33, No 3 (2012), 8 pages. doi: 10.4102/pythagoras.v33i3.193

Submitted: 02 September 2012
Published:  30 November 2012


This article provides an illustration of the explanatory and discovery functions of proof with an original geometric conjecture made by a Grade 11 student. After logically explaining (proving) the result geometrically and algebraically, the result is generalised to other polygons by further reflection on the proof(s). Different proofs are given, each giving different insights that lead to further generalisations. The underlying heuristic reasoning is carefully described in order to provide an exemplar for designing learning trajectories to engage students with these functions of proof.

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Author affiliations

Michael de Villiers, Mathematics Education, University of KwaZulu-Natal, Edgewood Campus, South Africa


discovery; explanation; generalisation; proof; Viviani’s theorem


Total abstract views: 6125
Total article views: 18513  


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ISSN: 1012-2346 (print) | ISSN: 2223-7895 (online)

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