From ‘proofs without words’ to ‘proofs that explain’ in secondary mathematics
نویسندگان
چکیده
منابع مشابه
On Proofs Without Words
Most mathematicians will be familiar with the above picture. This diagram, credited to the Ancient Chinese mathematical text Zhou Bi Suan Jing, is a charmingly simple visual proof of the Pythagorean Theorem, one of mathematics’ most fundamental results. It would be hard to argue that this proof is not convincing. In fact, most standard proofs of the Pythagorean Theorem still use this picture, o...
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Plummer, David I. Beaver, Johan van Benthem, and Patrick Scotto di Luzio published by CSLI Publications. ©2002 by CSLI Publications. All rights reserved. This text may be used and shared in accordance with the fair-use provisions of U.S. copyright law, and it may be archived and redistributed in electronic form, provided that this entire notice, including copyright information, is carried and p...
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Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional calculus (propositional logic) in which proofs are combinatorial (graph-theoretic), rather than syntactic. It defines a combinatorial proof of a proposition φ as a graph homomorphism h : C → G(φ), where G(φ) is a graph associated with φ and C is a coloured...
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ژورنال
عنوان ژورنال: Pythagoras
سال: 2007
ISSN: 2223-7895,1012-2346
DOI: 10.4102/pythagoras.v0i65.92