A false inequality which is true for a "concrete observer"
A false inequality which is true for a "concrete observer"
The authors discuss the problem of estimating the total absolute curvature of a simply closed curve by some function depending on its geometric degree only. Such an estimate is not existent in general because the total absolute curvature can be raised by adding small ``nonconvex'' parts to convex pieces without affecting the geometric degree. In the case of polygons they show that this difficulty can be overcome by an observer, who should measure these quantities, but cannot distinguish between points which are nearer than some fixed \(\varepsilon>0\). The considerations are in the spirit of the authors' paper in [Ann. Mat. Pura Appl., IV. Ser. 155, 213--241 (1989; Zbl 0715.53003)].
- University of Pisa Italy
Curves in Euclidean and related spaces, total absolute curvature, geometric degree
Curves in Euclidean and related spaces, total absolute curvature, geometric degree
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