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Symmetrien Von Ornamenten Und Kristallen

Symmetrien Von Ornamenten Und Kristallen

          
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About the Book

Dieses Buchbehandelt zwei miteinander verwandte Themenkreise: 1) Die Theorie der diskreten Bewegungsgruppen in Euklidischen Raumen beliebiger Dimension. Diese Theorie wurde von Bieberbach und Frobenius entwickelt. Ihr In- halt sind verschiedene Beschreibungen der sogenannten Raumgruppen, sowie der Satz, daB es bei vorgegebener Dimension des Raumes bis auf quivalenz nur endlich viele Raumgruppen gibt. Daneben sind Abschat- zungen fUr die Ordnung einer endlichen Matrizengruppe von Interesse. 2) Die Aufzahlung der Ornament- und Kristallgruppen, also der Raum- gruppen fUr die Dimensionen.2 und 3. Diese Aufzahlung erfolgt hier im Gegensatz zu den geometrischen Ab- leitungen von Fedorow und Schoenflies mit Hilfe einer algebraischen Methode, die Burckhardt das Losen der Frobeniusschen Kongruenzen ge- nannt hat. Diese Methode wurde von Zassenhaus prazisiert und als Algorithmus formuliert, spater dann fUr den Einsatz von Computern aus- gearbeitet. Es sei erwahnt, daB Brown, BUlow, NeubUser, Wondratschek und Zassenhaus auf diesem Wege nicht nur die 230 Kristallgruppen nach- gerechnet, sondern auch 4895 vierdimensionale Raumgruppen aufgefunden haben. Das Buch wendet sich an Studenten und Dozenten der Mathematik, denen es als Proseminartext oder Begleitbuch zur Vorlesung dienen soll. Die Darstellung setzt Grundkenntnisse in linearer Algebra und einige Definitionen aus der Gruppentheorie voraus, Ubungsaufgaben dienen der Vertiefung des Stoffs. Auf die Bedeutung der dreidimensionalen Raum- VI und Punktgruppen fUr die Kristallgeometrie und die Kristallphysik der Kontinua wird eingegangen, andere Gebiete der Kristallographie bleiben dagegen unberUcksichtigt. FUr den Schulunterricht habe ich eine Liste der diskreten Bewegungsgruppen der Ebene mit jeweils einer Illustration und der zugehorigen Symmetriekarte angefertigt.


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Product Details
  • ISBN-13: 9783540116448
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Height: 244 mm
  • No of Pages: 214
  • Series Title: Hochschultext
  • Weight: 368 gr
  • ISBN-10: 3540116443
  • Publisher Date: 01 May 1982
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Spine Width: 12 mm
  • Width: 170 mm


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