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In einem anderen Sinne ist euklidische Geometrie eine am Ende des 19. Jahrhunderts entstandene, streng axiomatische Theorie. Die oben genannten Probleme wurden deutlich, als sich Bertrand Russell, David Hilbert und andere Mathematiker um eine strengere Grundlegung der Mathematik bemühten.
Bereits in den altorientalischen Hochkulturen gab es Verfahren zur Berechnung von Kreisflächen. Beispielsweise wird in einer Problemstellung des Papyrus Rhind (um 1650 v. Chr.) die Fläche eines Kreises vom Durchmesser 9 über ein (unregelmäßiges) Achteck angenähert – indem beide einem Quadrat der Seitenlänge 9 einbeschrieben werden, das ...