Ehrhard Behrends: Tilings of the Plane

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Cover: 9783658388096 | Tilings of the Plane | From Escher via Möbius to Penrose | Behrends

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Sprache: Englisch

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Beschreibung

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 Möbius 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.

Über den Autor

Prof. Dr. Ehrhard Behrends, Free University of Berlin, Department of Mathematics and Computer Science

Zusammenfassung

Mathematics of symmetries and tesselation

Explained in detail with numerous colour illustrations

For mathematicians and all other interested parties with a mathematical background

Inhaltsverzeichnis

Part I: Escher seen over his shoulders.- Part II: Furniture transformations.- Part III: Penrose tesselation.

Details

Erscheinungsjahr:	2022
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	296
Reihe:	Mathematics Study Resources
Inhalt:	xi 283 S. 10 s/w Illustr. 303 farbige Illustr. 283 p. 313 illus. 303 illus. in color.
ISBN-13:	9783658388096
ISBN-10:	3658388099
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Behrends, Ehrhard
Auflage:	1st ed. 2022
Hersteller:	Springer Fachmedien Wiesbaden Springer Fachmedien Wiesbaden GmbH Mathematics Study Resources
Maße:	235 x 155 x 17 mm
Von/Mit:	Ehrhard Behrends
Erscheinungsdatum:	13.11.2022
Gewicht:	0,452 kg

preigu-id: 122089341