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Home > Mathematics and Science Textbooks > Mathematics > Geometry > Ebene euklidische Geometrie: Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik
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Ebene euklidische Geometrie: Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik

Ebene euklidische Geometrie: Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik


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About the Book

In diesem Lehrbuch stellen die Autoren einen axiomatischen Zugang zur ebenen Geometrie dar, der im Vergleich zu den Hilbertaxiomen und anderen oft gewählten Zugängen strukturelle und didaktische Vorteile bietet. Dieser auf metrischen Räumen basierende Zugang wird ausführlich motiviert und didaktisch aufbereitet. Ein besonderes Augenmerk liegt auf der besseren Verzahnung der Mathematikausbildung der Lehramtsstudierenden mit dem Schulstoff. In Ergänzung des axiomatischen Zugangs erklären die Autoren auch, wie man sich der ebenen Geometrie mit Mitteln der linearen Algebra nähern kann und stellen so den Bezug zur analytischen Geometrie der Oberstufe her. Als weitere Schnittstellen zwischen Schulmathematik und axiomatischer Geometrie werden die Begriffe Kongruenz und Symmetrie vertieft und so wichtigen Zusammenhänge zwischen den Begriffen Isometrie, Kongruenz und Symmetrie transparent gemacht und in schultypische Kontexte eingebettet.

Table of Contents:
Teil I.- 1 Kongruenz, Spiegelung und SSS.- 2 Klassifikation der euklidischen Isometrien des R2.- 3 Kongruenz.- Teil II.- 4 Geometrische Grundbegriffe in metrischen Räumen.- 5 Ebene neutrale Geometrie in metrischen Räumen.- 6 Vertiefungen zu neutralen Ebenen.- 7 Symmetrie.- Teil III.- 8 Parallelität in der neutralen Ebene.- 9 Euklidische Ebenen.- 10 Vertiefungen zu euklidischen Ebenen.

About the Author :
Dr. Max Hoffmann ist Lehrer für Mathematik und Informatik. Aktuell forscht und lehrt er an der Universität Paderborn in der Mathematikdidaktik. Prof. Dr. Joachim Hilgert ist Professor im Ruhestand an der Universität Paderborn und hat zuvor die Arbeitsgruppe "Lie-Theorie" geleitet. Prof. Dr. Tobias Weich forscht und lehrt an der Universität Paderborn und leitet dort die Arbeitsgruppe "Spektralanalysis".


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Product Details
  • ISBN-13: 9783662673560
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Springer Spektrum
  • Height: 240 mm
  • No of Pages: 332
  • Sub Title: Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik
  • ISBN-10: 3662673568
  • Publisher Date: 04 Jul 2024
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Width: 168 mm


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Ebene euklidische Geometrie: Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik
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Ebene euklidische Geometrie: Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik
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