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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.
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.
Mathematics of symmetries and tesselation
Explained in detail with numerous colour illustrations
For mathematicians and all other interested parties with a mathematical background
| Erscheinungsjahr: | 2022 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| 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 |
| Einband: | Kartoniert / Broschiert |
| Autor: | Behrends, Ehrhard |
| Auflage: | 1st edition 2022 |
| Hersteller: |
Springer Fachmedien Wiesbaden
Springer Fachmedien Wiesbaden GmbH |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 17 mm |
| Von/Mit: | Ehrhard Behrends |
| Erscheinungsdatum: | 13.11.2022 |
| Gewicht: | 0,452 kg |
Mathematics of symmetries and tesselation
Explained in detail with numerous colour illustrations
For mathematicians and all other interested parties with a mathematical background
| Erscheinungsjahr: | 2022 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| 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 |
| Einband: | Kartoniert / Broschiert |
| Autor: | Behrends, Ehrhard |
| Auflage: | 1st edition 2022 |
| Hersteller: |
Springer Fachmedien Wiesbaden
Springer Fachmedien Wiesbaden GmbH |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 17 mm |
| Von/Mit: | Ehrhard Behrends |
| Erscheinungsdatum: | 13.11.2022 |
| Gewicht: | 0,452 kg |
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