Short spirals

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.