Original Research

An illustration of the explanatory and discovery functions of proof

Michael de Villiers
Pythagoras | Vol 33, No 3 | a193 | DOI: https://doi.org/10.4102/pythagoras.v33i3.193 | © 2012 Michael de Villiers | This work is licensed under CC Attribution 4.0
Submitted: 02 September 2012 | Published: 30 November 2012

About the author(s)

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


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.


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


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