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Lagerungen in Der Ebene Auf Der Kugel Und Im Raum by L. Fejes Toth

Lagerungen in Der Ebene Auf Der Kugel Und Im Raum

by L. Fejes Toth
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Book cover type: Paperback
  • ISBN13: 9783642652356
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 240
  • Original Price: EUR 51.39
  • Language: German
  • Edition: 2. Aufl. 1972.
  • Item Weight: 363 grams
  • BISAC Subject(s): Geometry / General

IX Werk Lagerungsproblemen gewidmet, bei denen aueh beliebige irre- guliire Anordnungen in Betraeht gezogen werden. Die reguliire Gestalt der Extremalfigur ist hier oft eine Folgerung dey Extremalforderung. Wir erwahnen zwei typisehe Probleme. 1. In welcher Anordnung haben die meisten Hellerstiieke auf einem "groBen" Tisch Platz? Die Antwort ist, daB jeder Heller sechs andere beriihren muB. Die beste Anordnung wird daher von selbst gitterformig. 2. Betraehten wir zwolf Punkte einer fest en Kugel. In welcher Lagerung wird das Volumen der konvexen Hiille der Punkte maximal? Diese Aufgabe fiihrt uns zum reguHiren Ikosaeder. Das erste Problem, d. h. das Problem der dichtesten ebenen Kreis- lagerung, wurde von dem groBen norwegisehen Zahlentheoretiker A. TRUE in einer Jugendarbeit (1892) gelOst. Dann kam eine groBere Pause in der EntwiekIung in dieser Riehtung, so daB die meisten Er- gebnisse, die wir hier behandeln wollen, Friiehte etwa der letzten 10 his 12 Jahre sind. In einem Lehrbueh wurde dieser Problemkreis noeh nieht bearbeitet.

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