A mathematical modeling applied to the study of two forms of artistic representation

• Autores: Henrique Marins de Carvalho, Rodney C. Bassanezi, Geraldo Pompeu Junior
• Localización: Modelling in Science Education and Learning, ISSN-e 1988-3145, Vol. 8, Nº. 1, 2015, págs. 5-21
• Idioma: inglés
• DOI: 10.4995/msel.2015.2336
• Títulos paralelos:
  • Un modelo matemático aplicado al estudio de dos formas artísticas de representación
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• Resumen
  • español

    La manifestacion cultural de los pueblos indgenas Arican de Chile es analizada a traves de los diseños que se encuentran en sus prendas. Comparando sus tecnicas de formacion de mosaicos (usando transformaciones geometricas), se investigo si, matematicamente, era posible explicar su evolucion. Los mosaicos, as como las obras mas conocidas de Escher, se construyen a partir de la aplicacion de las traslaciones, rotaciones, re exiones o traslaciones/re exiones (\slip re ection") de un motivo inicial (una roseta). Con nes similares |entender la relacion entre la musica y la evolucion y la complejidad de una posible representacion matematica| se analizaron las transformaciones geometricas y extractos de tres obras de Johann Sebastian Bach. De esta manera se concluye la existencia de una posible lnea entre la evolucion artstica (la cultura artstica de un pueblo o de la obra de un musico) y la representacion matematica/geometra de tales manifestaciones.

  • English

    The cultural manifestation of the Arican indigenous people from Chile, through the designs found in their garments was analyzed. Comparing their techniques of mosaic formation, using geometric transformations (bijection plans in itself), it was investigated whether, mathematically, its evolution could be explained.The mosaics, as well as the known works of Escher, are constructed from the application of translations, rotations, reflections or slip reflections of an initial motif (a rosette). The archaeological clothing pieces of the Arican people were then analyzed in the same evolutionary perspective of such applications.With similar purpose - understanding the relationship between music and the evolution and complexity of a possible mathematical representation - were analyzed the geometric transformations and excerpts from three works of Johann Sebastian Bach, exponent German composer of the Baroque period.It was possible to see the link between the improvement and refinement of musical composition mathematics, particularly in the geometry necessary to translate the musical representation into a graphic symbol.It is concluded, then, the existence of a possible line between artistic evolution (the artistic culture of a people or the work of a musician) and mathematical representation / geometry of such manifestations. In other words, it was possible to formulate conjectures in a search to find a possible relationship between the development degree of a given culture or musical piece and the development of a science, if mathematics, able to explain it.

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