| 書目名稱 | Tilings of the Plane | | 副標題 | From Escher via M?bi | | 編輯 | Ehrhard Behrends | | 視頻video | http://file.papertrans.cn/926/925389/925389.mp4 | | 概述 | Mathematics of symmetries and tesselation.Explained in detail with numerous colour illustrations.For mathematicians and all other interested parties with a mathematical background | | 叢書名稱 | Mathematics Study Resources | | 圖書封面 |  | | 描述 | .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 M?bius transformations: Kleinian groups, Schottky groups, etc. There are also interesting connections to hyperbolic geometry.. | | 出版日期 | Textbook 2022 | | 關鍵詞 | Symmetry; Parqueting; Mathematics and art; Escher; M?bius; M?bius transformations; hyperbolic geometry; Pen | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-658-38810-2 | | isbn_softcover | 978-3-658-38809-6 | | isbn_ebook | 978-3-658-38810-2Series ISSN 2731-3824 Series E-ISSN 2731-3832 | | issn_series | 2731-3824 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wies |
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