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Ein zahlentheoretischer Exkurs: geometrische Zahlen und das pythagoräische Zahlenfeld by Knuth, Jennifer

Ein zahlentheoretischer Exkurs: geometrische Zahlen und das pythagoräische Zahlenfeld

by Jennifer Knuth
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Book cover type: Paperback
  • ISBN13: 9783638704533
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 228
  • Original Price: USD 67.5
  • Language: German
  • Edition: N/A
  • Item Weight: 304 grams
  • BISAC Subject(s): General

Examensarbeit aus dem Jahr 2004 im Fachbereich Didaktik - Mathematik, Note: 2,0, Technische Universität Dortmund, Sprache: Deutsch, Abstract: Diese Staatsarbeit ist eine fachwissenschaftliche Erarbeitung des Themas "Ein zahlentheoretischer Exkurs: - Geometrische Zahlen und das Pythagoräische Zahlenfeld -" Das Thema ist sehr weit gefasst und bietet viel Platz für Interpretationsmöglichkeiten. Daher werde ich an dieser Stelle darauf eingehen, wie ich das gegebene Thema auffasse. Der Begriff Geometrische Zahlen wird im Rahmen dieser Arbeit die Verknüpfung zwischen Arithmetik bzw. Algebra und der Geometrie darstellen. Der Schwerpunkt meiner Untersuchungen in Bezug auf die Geometrischen Zahlen liegt auf dem Aspekt der Anzahlen. Unter diesem Gesichtspunkt werden in dieser Arbeit die Themen gerade und ungerade Zahlen, Flächen- und Körperzahlen, Fibonacci- Zahlen, Pythagoräische Zahlentripel, Schnittpunkt- und Flächenanzahlen sowie selbst kreierte Zahlen betrachtet. Um einen Ausblick auf weitere Geometrische Zahlen zu geben, werden in dieser Arbeit auch einzelne geometrische Beweise vorgestellt, die nicht so eng an den Aspekt der Anzahlen gebunden sind. Das Pythagoräische Zahlenfeld wird zum einen als eigener Untersuchungspunkt vorgestellt, zum anderen werden in ihm Muster bezüglich der Flächen - und Körperzahlen gezeigt. Die weiteren Geometrischen Zahlen treten in diesem Zusammenhang nicht auf, da sie keinerlei Verbindung zum Pythagoräischen Zahlenfeld haben. Die Arbeit beginnt mit einem kurzen geschichtlichen Überblick über die Zeit der Pythagoräer. In diesem Bereich wird die Mathematikgeschichte vor und teils kurz nach Christi Geburt in Ägypten, Babylon und Griechenland angesehen, da Pythagoras selbst all diese Länder bereiste. Pythagoras und die Pythagoräer sind in dieser Arbeit von Bedeutung, da sie nahezu alle mathematischen Erkenntnisse aus der Geometrie gewonnen haben. Das Vorgehen dieser Arbeit ist demnach ähnlich dem des Pythagoras und der Pythagoräer. A

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