Geodesic
Short spirals
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 34-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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Some previous results for planar curves with monotone curvature (spirals), limited in length by one way or another, are extended by removing requirements of convexity of the arc, its one-to-one projectability onto the chord, and curvature continuity. A more general class of short spiral arcs is thus introduced. Statements include Vogt's theorem, concerning boundary angles of a convex spiral arc, the necessary and sufficient conditions for its existence, positional inequalities for such arcs. Bibl. – 8 titles. 
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A. I. Kurnosenko. Short spirals. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 34-43. http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a2/

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