Abstract
For every plane convex body there is a pair of inscribed and circumscribed homothetic rectangles. The positive ratio of homothety is not greater than 2.
Similar content being viewed by others
References
Asplund, E., ‘Comparison between plane symmetric vonvex bodies and parallelograms’,Math. Scand. 7 (1960), 171–180.
Chakerian, G. D. and Stein, S. K., ‘Some intersection properties of convex bodies’,Proc. Amer. Math. Soc. 18 (1967), 109–112.
Eggleston, H. D.,Convexity, Cambridge University Press, Cambridge, 1969.
Grünbaum, B., ‘Measures of symmetry for convex sets’, inConvexity, Proceedings of Symposia in Pure Mathematics 7, American Mathematical Society, Providence, 1963, pp. 233–270.
Hadwiger, H., ‘Volumschätzung für die einen Eikörper überdeckenden und unterdeckenden Parallelotope’,Elem. Math. 10 (1955), 122–124.
John, F., ‘Extremum problems with inequalities as subsidiary conditions’,Studies and Essays presented to R. Courant, New York, 1948, pp. 187–204.
Kosiński, A., ‘A proof of an Auerbach-Banach-Mazur-Ulam theorem on convex bodies’,Colloq. Math. 17 (1957), 216–218.
Lassak, M., ‘Approximation of plane convex bodies by centrally symmetric convex bodies’,J. London Math. Soc. (2) 40 (1989), 369–377.
Lassak, M., ‘Approximation of convex bodies by parallelotopes’,Bull. Polish Acad. Math. 39 (1991), 219–223.
Pólya, G. and Szegö, G., ‘Isoperimetric inequalities in mathematical physics’,Ann. Math. Stud. 27 (1951).
Radziszewski, K., ‘Sur une problème extrémal relatif aux figures inscrites et circonscrites aux figures convexes’,Ann. Univ. Mariae Curie-Sklodowska, Sect A 6 (1952), 5–18.
Author information
Authors and Affiliations
Additional information
Research supported in part by Komitet Badan Naukowych (Committee of Scientific Research), grant number 2 2005 92 03.
Rights and permissions
About this article
Cite this article
Lassak, M. Approximation of convex bodies by rectangles. Geom Dedicata 47, 111–117 (1993). https://doi.org/10.1007/BF01263495
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01263495