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An illustration of the explanatory and discovery functions of proof

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Author(s): Michael de Villiers

Journal: Pythagoras
ISSN 1012-2346

Volume: 33;
Issue: 3;
Start page: 1;
Date: 2012;
Original page

Keywords: discovery | explanation | generalisation | proof | Viviani’s theorem

ABSTRACT
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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