Tilings of the Plane

Name: Tilings of the Plane
Brand: Springer Fachmedien Wiesbaden
SKU: 2049099

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2092639Tilings of the Planehttps://www.gandhi.com.mx/tilings-of-the-plane/phttps://gandhi.vtexassets.com/arquivos/ids/417026/3c881ada-9c03-4f6d-9836-9c894783346d.jpg?v=63833473033137000011551283MXNSpringer Fachmedien WiesbadenInStock/Ebooks/The aim of the book is to study symmetries and tesselation, which have long interested artists and mathematicians. Famous examples are the works created by the Arabs in the Alhambra and the paintings of the Dutch painter Maurits Escher. Mathematicians did not take up the subject intensively until the 19th century. In the process, the visualisation of mathematical relationships leads to very appealing images. Three approaches are described in this book.In Part I, it is shown that there are 17 principally different possibilities of tesselation of the plane, the so-called plane crystal groups. Complementary to this, ideas of Harald Heesch are described, who showed how these theoretical results can be put into practice: He gave a catalogue of 28 procedures that one can use creatively oneself following in the footsteps of Escher, so to speak to create artistically sophisticated tesselation.In the corresponding investigations forthe complex plane in Part II, movements are replaced by bijective holomorphic mappings. This leads into the theory of groups of Mbius transformations: Kleinian groups, Schottky groups, etc. There are also interesting connections to hyperbolic geometry.Finally, in Part III, a third aspect of the subject is treated, the Penrose tesselation. This concerns results from the seventies, when easily describable and provably non-periodic parquetisations of the plane were given for the first time....2049099Tilings of the Plane11551283https://www.gandhi.com.mx/tilings-of-the-plane/phttps://gandhi.vtexassets.com/arquivos/ids/417026/3c881ada-9c03-4f6d-9836-9c894783346d.jpg?v=638334730331370000InStockMXN99999DIEbook20229783658388102_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_The aim of the book is to study symmetries and tesselation, which have long interested artists and mathematicians. Famous examples are the works created by the Arabs in the Alhambra and the paintings of the Dutch painter Maurits Escher. Mathematicians did not take up the subject intensively until the 19th century. In the process, the visualisation of mathematical relationships leads to very appealing images. Three approaches are described in this book.In Part I, it is shown that there are 17 principally different possibilities of tesselation of the plane, the so-called plane crystal groups. Complementary to this, ideas of Harald Heesch are described, who showed how these theoretical results can be put into practice: He gave a catalogue of 28 procedures that one can use creatively oneself - following in the footsteps of Escher, so to speak - to create artistically sophisticated tesselation.In the corresponding investigations for the complex plane in Part II, movements are replaced by bijective holomorphic mappings. This leads into the theory of groups of Mbius transformations: Kleinian groups, Schottky groups, etc. There are also interesting connections to hyperbolic geometry.Finally, in Part III, a third aspect of the subject is treated, the Penrose tesselation. This concerns results from the seventies, when easily describable and provably non-periodic parquetisations of the plane were given for the first time....(*_*)9783658388102_The aim of the book is to study symmetries and tesselation, which have long interested artists and mathematicians. Famous examples are the works created by the Arabs in the Alhambra and the paintings of the Dutch painter Maurits Escher. Mathematicians did not take up the subject intensively until the 19th century. In the process, the visualisation of mathematical relationships leads to very appealing images. Three approaches are described in this book.In Part I, it is shown that there are 17 principally different possibilities of tesselation of the plane, the so-called plane crystal groups. Complementary to this, ideas of Harald Heesch are described, who showed how these theoretical results can be put into practice: He gave a catalogue of 28 procedures that one can use creatively oneself following in the footsteps of Escher, so to speak to create artistically sophisticated tesselation.In the corresponding investigations forthe complex plane in Part II, movements are replaced by bijective holomorphic mappings. This leads into the theory of groups of Mbius transformations: Kleinian groups, Schottky groups, etc. There are also interesting connections to hyperbolic geometry.Finally, in Part III, a third aspect of the subject is treated, the Penrose tesselation. This concerns results from the seventies, when easily describable and provably non-periodic parquetisations of the plane were given for the first time....9783658388102_Springer Fachmedien Wiesbadenlibro_electonico_274dd16d-b110-3709-8e7e-0880bdecd7ab_9783658388102;9783658388102_9783658388102Ehrhard BehrendsInglésMéxico2022-11-12T00:00:00+00:00Springer Fachmedien Wiesbaden