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Polareuklidische Geometrie: Unendlichferne Peripherie Und Absoluter Mittelpunkt: Eine Duale Erweiterung Der Klassischen Geometrie

Polareuklidische Geometrie: Unendlichferne Peripherie Und Absoluter Mittelpunkt: Eine Duale Erweiterung Der Klassischen Geometrie

          
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About the Book

Dieses Buch bietet eine spannende Einführung in die polareuklidische Geometrie, eine noch kaum bekannte Erweiterung der klassischen Geometrie.

Die polareuklidische Geometrie setzt der Perspektive der unendlichfernen Peripherie bei der gewohnten euklidischen Betrachtung eine zweite entgegen, die sich auf einen Bezugspunkt, ein absolutes Zentrum stützt. Die beiden komplementären Raumbeschreibungen erweisen sich als dual zueinander im Sinne des Dualitätsprinzips der projektiven Geometrie, das auch in der polareuklidischen Geometrie gilt.

Beim Dualisieren der Begriffe und Sätze der euklidischen Geometrie lernen die Leserinnen und Leser überraschende neue Sachverhalte und bisher unbeachtete Verbindungen zwischen geometrischen Tatsachen kennen. Sie erwerben dabei ein erweitertes Raumverständnis und entdecken die Geometrie ganz neu. Ganz nebenher schulen sie ihr geometrisches Vorstellungsvermögen und ein bewegliches, konstruktives geometrisches Denken.

Die Darstellung setzt keine speziellen Fachkenntnisse voraus, alles wird auch für Laien verständlich erklärt und anhand von vielen Abbildungen und Anwendungsbeispielen erläutert. An die Stelle strenger mathematischer Beweise treten anschauliche Begründungen. Koordinaten, Formalismus und Abstraktion werden vermieden. Fachmathematiker finden im Text weiterführende Hinweise und im Anhang eine kurze Zusammenfassung der mathematischen Konstruktion.


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Product Details
  • ISBN-13: 9783662633007
  • Publisher: Springer
  • Publisher Imprint: Springer Spektrum
  • Height: 244 mm
  • No of Pages: 319
  • Spine Width: 18 mm
  • Weight: 530 gr
  • ISBN-10: 3662633000
  • Publisher Date: 22 Jul 2021
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Sub Title: Unendlichferne Peripherie Und Absoluter Mittelpunkt: Eine Duale Erweiterung Der Klassischen Geometrie
  • Width: 170 mm


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Polareuklidische Geometrie: Unendlichferne Peripherie Und Absoluter Mittelpunkt: Eine Duale Erweiterung Der Klassischen Geometrie
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