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Teaching Mathematics and its Applications Advance Access originally published online on May 31, 2009
Teaching Mathematics and its Applications 2009 28(3):113-116; doi:10.1093/teamat/hrp012
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© The Author 2009. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

A proof of the converse of the Pythagorean proposition

Aldo Scimone{dagger}

via C. Nigra 30 – 90141 Palermo (Sicily)

{dagger}Email: aldo.scimone{at}libero.it

Submitted March 2009; accepted April 2009

The article presents a demonstration of the converse of the Pythagorean Theorem based on the reductio ad absurdum. This is necessary to overcome the discrepancy, noticed by pupils, between the Euclidean purpose to demonstrate that the given triangle is right-angled and the auxiliary figure by which the given triangle is drawn as if it were already a right-angled one. To the eyes of students this does not make the Euclidean reasoning clear.

Aldo Scimone, PhD (Mathematics Didactics) is a secondary school teacher of mathematics and supervisor for mathematics teachers at SISSIS (University of Palermo). His current research interests centre on elementary number theory, geometry, the history of mathematics and the mathematics didactics. His last book is: ‘Talete, chi era costui? Vita e opera dei matematici incontrati a scuola (Thales, who was he? The life and works of mathematicians met at school), 2006, Palumbo.’


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