Relational understanding and paths of reasoning through a Boolean lattice classification of quadrilaterals

• Autores: J. Karakonstantis, T. Patronis
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 41, Nº. 3, 2010, págs. 341-349
• Idioma: inglés
• DOI: 10.1080/00207390903477434
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• Resumen

  • In this article we study a specific lattice classification of converse quadrilaterals, based on the relations between diagonals. This lattice contains 16 = 24 elements, which form a hypercube, and therefore it is a Boolean lattice. 'Complementary' species of quadrilaterals thus appear and may be related in the lattice diagram. We also introduce and study the idea of paths of reasoning, which may connect distinct species of quadrilaterals in various ways, thus leading to a relational understanding of these concepts.