Abstract
We consider the class of all convex discs with areas and perimeters bounded by given constants. Which disc of this class has the least possible area deviation from ak-gon? This and related questions are the subject of the present paper.
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References
A. S. Besicovitch, Variants of a classical isoperimetric problem,Quart. J. Math. Oxford ser. 2 3 (1952), 42–49.
H. G. Eggleston, Approximation to plane convex curves, I. Dowker-type theorems,Proc. London Math. Soc. (3)7 (1957), 351–377.
G. Fejes Tóth, Covering the plane by convex discs,Acta Math. Acad. Sci. Hungar. 23 (1972), 263–270.
G. Fejes Tóth, Sum of moments of convex polygons,Acta Math. Acad. Sci. Hungar. 24 (1973), 417–421.
G. Fejes Tóth and A. Florian, Covering of the plane by discs,Geom. Dedicata 16 (1984), 315–333.
L. Fejes Tóth, Filling of a domain by isoperimetric discs,Publ. Math. Debrecen,5 (1957), 119–127.
L. Fejes Tóth, On the isoperimetric property of the regular hyperbolic tetrahedra,Magyar Tud. Akad. Mat. Kut. Int. Közl. 8A (1963), 53–57.
L. Fejes Tóth,Regular Figures, Pergamon Press, Oxford, 1964.
L. Fejes Tóth,Lagerungen in der Ebene, auf der Kugel und im Raum, 2nd ed., Springer-Verlag, Berlin-Heidelberg-New York, 1972.
L. Fejes Tóth and A. Florian, Packing and covering with convex discs,Mathematika 29 (1982), 181–193.
L. Fejes Tóth and A. Heppes, Filling of a domain by equiareal discs,Publ. Math. Debrecen 7 (1960), 198–203.
A. Florian, Integrale auf konvexen Mosaiken,Period. Math. Hungar. 6 (1975), 23–38.
A. Florian, Packing and covering with convex discs,Studia Sci. Math. Hungar., to appear.
P. M. Gruber, Approximation of convex bodies,Convexity and Its Applications, Birkhäuser-Verlag, Basel-Boston-Stuttgart, 1983.
G. Hajós, Über den Durchschnitt eines Kreises und eines Polygons,Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 11 (1968), 137–144.
K. Leichtweiss,Konvexe Mengen, Springer-Verlag, Berlin-Heidelberg-New York, 1980.
G. C. Shephard and R. J. Webster, Metrics for sets of convex bodies,Mathematika 12 (1965), 73–88.
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Dedicated to Professor E. Hlawka on the occasion of his birthday.
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Florian, A. Approximation of convex discs by polygons. Discrete Comput Geom 1, 241–263 (1986). https://doi.org/10.1007/BF02187698
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DOI: https://doi.org/10.1007/BF02187698