摘要：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.
其他摘要：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.
