Teaching proofs without words using dynamic geometry
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A Proof Without Words (PWW) contains data, the claim that is to be proved, and one or more diagrams, sometimes without anything else and in other cases with a few mathematical expressions, without any verbal justifications [1]. It is assumed that students and researchers who possess the related appropriate mathematical knowledge will view the drawings and the expressions, will be able to follow and justify each step in the proof and develop their own visual proof abilities. PWW is very much like a cartoon which contains a drawing with sometimes only a few words or sometimes no words at all and the observers are expected to understand the context or the projected message.
[1] William G. Faris. Philosophy of Mathematics : An Introduction to the World of Proofs and Pictures , 2000 .
[2] Roger B. Nelsen. Proofs Without Words III: Further Exercises in Visual Thinking , 2015 .
[3] Michael de Villiers,et al. An alternative approach to proof in dynamic geometry , 1998 .
[4] R. B. Manfrino,et al. Inequalities: A Mathematical Olympiad Approach , 2009 .
[5] Howard Eves. Great Moments in Mathematics Before 1650 , 1980 .