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Graves: Die Grenze des Zahlenreichs (26.12.1843)

In: Sternstunden der Mathematik

Author

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  • Jost-Hinrich Eschenburg

    (Unversität Augsburg, Institut für Mathematik)

Abstract

Zusammenfassung Komplexe Zahlen lassen sich als Paare reeller Zahlen und damit als Koordinatenpaare von Punkten der Ebene deuten. Paare reeller Zahlen kann man also multiplizieren und dividieren. Der irische Mathematiker W.R. Hamilton fragte sich, ob Gleiches auch mit Tripeln statt Paaren, also mit den Koordinatentripeln der Punkte des Raumes möglich ist. Schließlich erkannte er, dass man dazu eine weitere Dimension brauchte und fand die Quaternionen (1843). Sein Freund John Graves, dem er davon erzählt hatte, ging noch weiter und konstruierte noch im gleichen Jahr die Oktaven, Oktetts reeller Zahlen, die ebenfalls eine Multiplikation und Division zuließen. Damit ist aber die absolute Grenze erreicht, wie wir sehen werden; das hat Adolf Hurwitz 1898 gezeigt.

Suggested Citation

  • Jost-Hinrich Eschenburg, 2017. "Graves: Die Grenze des Zahlenreichs (26.12.1843)," Springer Books, in: Sternstunden der Mathematik, chapter 10, pages 107-114, Springer.
    • Handle: RePEc:spr:sprchp:978-3-658-17295-4_10
    DOI: 10.1007/978-3-658-17295-4_10
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