Geodesic
Short spirals
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 34-43 
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/
@article{ZNSL_2009_372_a2,
     author = {A. I. Kurnosenko},
     title = {Short spirals},
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     pages = {34--43},
     year = {2009},
     volume = {372},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a2/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] W. Vogt, “Über monotongekrümmte Kurven”, J. reine angew. Math., 144 (1914), 239–248 | DOI | Zbl

[2] A. Ostrowski, “Über die Verbindbarkeit von Linien- und Krümmungselementen durch monoton gekrümmte Kurvebögen”, Enseign. Math. II Ser., 2 (1956), 277–292 | MR | Zbl

[3] D. S. Meek, D. J. Walton, “Approximating smooth planar curves by arc splines”, J. Comp. Appl. Math., 59 (1995), 221–231 | DOI | MR | Zbl

[4] A. I. Kurnosenko, “Interpolyatsionnye svoistva ploskikh spiralnykh krivykh”, Fund. prikl. mat., 7:2 (2001), 441–463 | MR | Zbl

[5] A. I. Kurnosenko, “Obschie svoistva ploskikh spiralnykh krivykh”, Zap. nauchn. semin. POMI, 353, 2008, 93–115 | MR

[6] S. Katsuura, “Ein neuer Beweis des Vogtschen Satzes”, Tohoku Math. J., 47 (1940), 94–95 | MR | Zbl

[7] K. Hirano, “Simple proofs of Vogt's theorem”, Tohoku Math. J., 47 (1940), 126–128 | MR | Zbl

[8] A. I. Kurnosenko, “Inversnyi invariant pary okruzhnostei”, Zap. nauchn. semin. POMI, 261, 1999, 167–186 | MR | Zbl