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goldene Schnitt im Sekantenverfahren. Definition und Beweis

goldene Schnitt im Sekantenverfahren. Definition und Beweis


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About the Book

Bachelorarbeit aus dem Jahr 2019 im Fachbereich Didaktik - Mathematik, Note: 2, Universität Wien, Sprache: Deutsch, Abstract: Das konkrete Thema in meiner Arbeit ist ein Beweis, dass die Konvergenzordnung des Sekantenverfahren der goldene Schnitt ist. Der goldene Schnitt faszinierte die MathematikerInnen schon seit je her, und er taucht in vielen Bereich des Alltags auf, wie in der Musik, in der Natur oder in der Kunst. Was allerdings die Wenigsten wissen ist, dass der goldene Schnitt auch in einem numerischen Verfahren auftaucht, in dem es darum geht, durch ein geeignetes Intervall und in weiterer Folge durch geeignete Sekanten die Nullstellen von Funktionen zu ermitteln. Bevor ich allerdings diesen Beweis führe, gebe ich in Kapitel 1 einige allgemeine Informationen zum goldenen Schnitt bzw. gebe einen Überblick, was die goldene Zahl 1+√52 geometrisch überhaupt bedeutet. Das Kapitel 1 orientiert sich an dem Buch "Der goldene Schnitt" von Albrecht Beutelspacher und Bernhard Petri. Außerdem führe ich einen Beweis von Euler in diesem Kapitel, um den LeserInnen zu zeigen, wie man von einem gewissen Verhältnis zu dieser besonderen Zahl überhaupt gelangt. Der Beweis in Kapitel 2, der sich an den Beweis von Bourgeois aus dem Buch "Grundlagen der Numerischen Mathematik und des Wissenschaftlichen Rechnens" orientiert, wurde in drei Schritte aufgeteilt. Bevor allerdings dieser Beweis geführt wird, werde ich zunächst mal ganz allgemein einige Begriffe wie das Sekantenverfahren oder die Konvergenzordnung erklären. Weiters möchte ich ausführen, wofür das Sekantenverfahren angewendet wird.


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Product Details
  • ISBN-13: 9783346883193
  • Publisher: Bod Third Party Titles
  • Publisher Imprint: Grin Verlag
  • Height: 210 mm
  • No of Pages: 22
  • Spine Width: 1 mm
  • Width: 148 mm
  • ISBN-10: 3346883191
  • Publisher Date: 26 May 2023
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Weight: 95 gr


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goldene Schnitt im Sekantenverfahren. Definition und Beweis
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