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Geometrie Und Billard by Serge Tabachnikov, Micaela Krieger-Hauwede

Geometrie Und Billard

by Serge Tabachnikov , Micaela Krieger-Hauwede
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Book cover type: Paperback
  • ISBN13: 9783642319242
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer Spektrum
  • Publisher Imprint: Springer Spektrum
  • Publication Date:
  • Pages: 165
  • Original Price: EUR 28.03
  • Language: German
  • Edition: 2013
  • Item Weight: 295 grams
  • BISAC Subject(s): Geometry / Differential

Wie bewegt sich ein Massenpunkt in einem Gebiet, an dessen Rand er elastisch zurückprallt? Welchen Weg nimmt ein Lichtstrahl in einem Gebiet mit ideal reflektierenden Rändern? Anhand dieser und ähnlicher Fragen stellt das vorliegende Buch Zusammenhänge zwischen Billard und Differentialgeometrie, klassischer Mechanik sowie geometrischer Optik her. Dabei beschäftigt sich das Buch unter anderem mit dem Variationsprinzip beim mathematischen Billard, der symplektischen Geometrie von Lichtstrahlen, der Existenz oder Nichtexistenz von Kaustiken, periodischen Billardtrajektorien und dem Mechanismus für Chaos bei der Billarddynamik. Ergänzend wartet dieses Buch mit einer beachtlichen Anzahl von Exkursen auf, die sich verwandten Themen widmen, darunter der Vierfarbensatz, die mathematisch-physikalische Beschreibung von Regenbögen, der poincaresche Wiederkehrsatz, Hilberts viertes Problem oder der Schlie ungssatz von Poncelet.​

Prof. Serge Tabachnikov, Pennsylvania State University, Mathematical Institute, USA

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