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Über Anzahl und Verteilung der Scheitel ebener Bogen. (On the number and distribution of the vertices of plane arcs). (German) Zbl 0628.51012
The system of axioms of order geometry in the plane given by O. Haupt and H. Künneth, Geometrische Ordnungen (1967; Zbl 0172.239) is simplified. Within this frame the authors give upper and lower bounds for the number of singular points (vertices) of an arc and study how a smooth arc is built up as the union of normal subarcs.
Reviewer: E.Heil
MSC:
51L10 Directly differentiable curves in geometric order structures
51L15 \(n\)-vertex theorems via direct methods
53C75 Geometric orders, order geometry
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