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Die klassischen Probleme der griechischen Mathematik

In: Die antike Mathematik

Author

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  • Dietmar Herrmann

    (FH München)

Abstract

Zusammenfassung Das Kapitel behandelt die drei klassischen Probleme wie die Winkeldreiteilung, Quadratur des Kreises und Würfelverdopplung. Es gibt keinen genauen Hinweis bei Euklid, welche Konstruktionen er als legitim erachtet. Deswegen haben Mathematiker nach Euklid auch Konstruktionen mit Linealmarkierungen (sog. Neusis-Konstruktionen) und Schnitte mit höheren Kurven, wie Kegelschnitten, zugelassen. Ferner wird die Konstruierbarkeit von regulären Vielecken, wie dem Fünf- bzw. Siebeneck dargestellt; allgemein wird untersucht, bei welchen Möndchenfiguren die Quadratur gelingt. Von den Kurven zweiter bzw. höherer Ordnung werden besprochen die Quadratrix, die Konchoide, die Zissoide und die Spirale des Archimedes.

Suggested Citation

  • Dietmar Herrmann, 2024. "Die klassischen Probleme der griechischen Mathematik," Springer Books, in: Die antike Mathematik, edition 3, chapter 0, pages 185-207, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-68478-8_11
    DOI: 10.1007/978-3-662-68478-8_11
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