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Parkettierungen Der Ebene: Von Escher Über Möbius Zu Penrose
Paperback
ISBN13: 9783658232696
Publisher: Springer Spektrum
Published: Jan 24 2019
Pages: 285
Weight: 1.06
Height: 0.63 Width: 6.69 Depth: 9.61
Language: German
Ziel des Buches ist das Studium von Symmetrien und Parkettierungen, die Künstler und Mathematiker schon seit langer Zeit interessieren. Berühmte Beispiele sind die von den Arabern in der Alhambra geschaffenen Werke und die Bilder des holländischen Malers Maurits Escher. Die Mathematiker haben sich erst im 19. Jahrhundert des Themas intensiv angenommen. Dabei führt die Visualisierung der mathematischen Zusammenhänge zu sehr ansprechenden Bildern. Drei Ansätze werden in diesem Buch beschrieben.
Bei den entsprechenden Untersuchungen für die komplexe Ebene in Teil II werden Bewegungen durch bijektive holomorphe Abbildungen ersetzt. Das führt in die Theorie der Gruppen von Möbiustransformationen: Kleinsche Gruppen, Schottkygruppen usw. Dort gibt es auch interessante Verbindungen zur hyperbolischen Geometrie.
Schlie lich wird in Teil III noch ein dritter Aspekt des Themas behandelt, die Penroseparkettierungen. Dabei geht es um Ergebnisse aus den siebziger Jahren, als erstmals einfach zu beschreibende und beweisbar nichtperiodische Parkettierungen der Ebene angegeben wurden.
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