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Aufbau Der Geometrie Aus Dem Spiegelungsbegriff

Aufbau Der Geometrie Aus Dem Spiegelungsbegriff

          
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About the Book

torischen Gruppenelemente sind und in den en wir geometrische Bezie- hungen wie Inzidenz undOrthogonalitat durch gruppentheoretische Rela- tionen erklaren. Die rein gruppentheoretisch formulierten Axiome, die wir wahlen, stellen einfache geometrische Aussagen flir die Punkte und Geraden der metrischen Ebenen dar. Dementsprechend kann man beim Beweisen aus den Axiomen die Vorteile des gruppentheoretischen Kalktils ausnutzen, ohne den Leitfaden der Anschauung aus der Hand zu geben. Bemerkenswert ist, wie wenige Axiome notig sind. Die metrischen Ebenen, die mit den axiomatisch gegebenen Gruppen definiert sind, sind daher von recht allgemeiner Natur. Eine metrische Ebene braucht nicht anordenbar (erst recht nicht stetig) zu sein. In einer metrischen Ebene braucht nicht freie Beweglichkeit zu bestehen. Es gibt auch metrische Ebenen mit nur endlich vielen Punkten und Geraden. Der Begriff der metrischen Ebene enthalt keine Entscheidung tiber die Parallelenfrage, d.h. tiber die Frage nach dem Schneiden oder Nicht- schneiden der Geraden. Die ebene metrische Geometrie, die wir ent- wickeln, enthalt ebene euklidische, hyperbolische und elliptische Geo- metrie als Spezialfalle, und wird daher, mit einem Ausdruck von J. BOLYAI, auch ebene absolute Geometrie genannt.


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Product Details
  • ISBN-13: 9783642655388
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: Softcover reprint of the original 2nd ed. 1973
  • Language: German
  • Returnable: Y
  • Spine Width: 21 mm
  • Width: 152 mm
  • ISBN-10: 3642655386
  • Publisher Date: 25 Feb 2012
  • Binding: Paperback
  • Height: 229 mm
  • No of Pages: 376
  • Series Title: Grundlehren Der Mathematischen Wissenschaften
  • Weight: 530 gr


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