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Chaos - A Geometry of Nature

Chaos - A Geometry of Nature

          
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About the Book

Studienarbeit aus dem Jahr 2005 im Fachbereich Mathematik - Geometrie, Note: 1,3, Universität Osnabrück, Veranstaltung: Seminar: Chaos - Making a new science, 17 Quellen im Literaturverzeichnis, Sprache: Deutsch, Abstract: Es liegt in der Natur des Menschen, komplizierte Sachverhalte zu hinterfragen und zu verstehen. So beschäftigen sich Wissenschaftler seit Jahrhunderten damit, ihre Umwelt und vor allem dort auftauchende, scheinbar chaotische Systeme in eine geordnete und verständliche Struktur zu bringen. Ein Beispiel hierfür ist die über zweitausend Jahre gültige Euklidische Geometrie, die als Standardgeometrie ein Bestandteil der klassischen Mathematik ist und unter anderem unsere Umwelt in ein ganzzahlig dimensionales System einordnet. Sie ermöglicht z. B. Daten mittels grafischer Instrumente aufzuarbeiten, zu veranschaulichen und daraus folgend besser analysieren bzw. verstehen zu können. Der Wissenschaftler Benoit Mandelbrot hat seit den sechziger Jahren mit seinen wissenschaftlichen Forschungen und seiner Gabe, Muster und Formen intuitiv zu erfassen, ein neues Gebiet der Geometrie erschlossen, das sich auf Grenzen der euklidischen Dimension bezieht. Ausgangspunkt hierfür waren Überlegungen über eine bis dahin vollkommen neue Ansicht der geometrischen Welt. Diese zeigt sich in Gebilden mathematischer Monster wie der Koch Kurve, deren Dimensionen nach Mandelbrot den "fraktalen Dimensionen" zugeordnet werden. Inwiefern Mandelbrots Erkenntnisse die bis dahin gültige Wissenschaft revolutionierte und der Wissenschaft bis zum heutigen Zeitpunkt neue, leistungsfähige Methoden bereitstellt, wird in den folgenden Kapiteln betrachtet. Zunächst wird in Kapitel 2 auf die Geschichte, die Euklidische Geometrie und ihre Grenzen eingegangen. In Kapitel 3 wird die fraktale Geometrie bzw. die gebrochenzahlige Dimension sowie die Koch Kurve dargestellt, wobei insbesondere das Wesen einer Küstenlinie näher analysiert wird. Zudem wird auf den Begriff der Selbstähnlichkeit eingega


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Product Details
  • ISBN-13: 9783640864195
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Height: 216 mm
  • No of Pages: 40
  • Series Title: German
  • Weight: 59 gr
  • ISBN-10: 3640864190
  • Publisher Date: 19 Mar 2011
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 3 mm
  • Width: 140 mm


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